Search results

Filters

  • Journals
  • Authors
  • Keywords
  • Date
  • Type

Search results

Number of results: 188
items per page: 25 50 75
Sort by:
Download PDF Download RIS Download Bibtex

Abstract

In this work, we present optimal control formulation and numerical algorithm for fractional order discrete time singular system (DTSS) for fixed terminal state and fixed terminal time endpoint condition. The performance index (PI) is in quadratic form, and the system dynamics is in the sense of Riemann-Liouville fractional derivative (RLFD). A coordinate transformation is used to convert the fractional-order DTSS into its equivalent non-singular form, and then the optimal control problem (OCP) is formulated. The Hamiltonian technique is used to derive the necessary conditions. A solution algorithm is presented for solving the OCP. To validate the formulation and the solution algorithm, an example for fixed terminal state and fixed terminal time case is presented.
Go to article

Bibliography

[1] G.W. Leibniz and C.I. Gerhardt: Mathematische Schriften. Hildesheim, G. Olms, 1962.
[2] I. Podlubny: Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications. 1st edition, 198. San Diego, Academic Press, 1998.
[3] J.A. Tenreiro Machado et al.: Some applications of fractional calculus in engineering. Mathematical Problems in Engineering, 2010, (2009), p. e639801, DOI: 10.1155/2010/639801.
[4] T. Yuvapriya, P. Lakshmi, and S. Rajendiran: Vibration control and performance analysis of full car active suspension system using fractional order terminal sliding mode controller. Archives of Control Sciences, 30(2), (2020), 295–324, DOI: 10.24425/ACS.2020.133501.
[5] D.S. Naidu: Optimal Control Systems. 1st edition, CRC Press, 2018.
[6] O.P. Agrawal: A general formulation and solution scheme for fractional optimal Control problems. Nonlinear Dynamics, 38(1), (2004), 323–337, DOI: 10.1007/s11071-004-3764-6.
[7] T. Chiranjeevi and R.K. Biswas: Formulation of optimal control problems of fractional dynamic systems with control constraints. Journal of Advanced Research in Dynamical and Control Systems, 10(3), (2018), 201–212.
[8] R.K. Biswas and S. Sen: Fractional optimal control problems with specified final time. Journal of Computational and Nonlinear Dynamics, 6(021009), (2010), DOI: 10.1115/1.4002508.
[9] R.K. Biswas and S. Sen: Free final time fractional optimal control problems. Journal of the Franklin Institute, 351(2), (2014), 941–951, DOI: 10.1016/j.jfranklin.2013.09.024.
[10] R.K. Biswas and S. Sen: Numerical method for solving fractional optimal control problems. In: Proceedings of the ASME IDETC/CIE Conference, (2010), 1205–120, DOI: 10.1115/DETC2009-87008.
[11] C. Tricaud and Y. Chen: An approximate method for numerically solving fractional order optimal control problems of general form. Computers & Mathematics with Applications, 59(5), (2010), 1644–1655, DOI: 10.1016/j.camwa.2009.08.006.
[12] Y. Ding, Z. Wang, and H. Ye: Optimal control of a fractional-order HIVimmune system with memory. IEEE Transactions on Control Systems Technology, 20(3), (2012), 763–769, DOI: 10.1109/TCST.2011.2153203.
[13] T. Chiranjeevi and R.K. Biswas: Closed-form solution of optimal control problem of a fractional order system. Journal of King Saud University – Science, 31(4), (2019), 1042–1047, DOI: 10.1016/j.jksus.2019.02.010.
[14] R. Dehghan and M. Keyanpour: A semidefinite programming approach for solving fractional optimal control problems. Optimization, 66(7), (2017), 1157–1176, DOI: 10.1080/02331934.2017.1316501.
[15] M. Dehghan, E.-A. Hamedi, and H. Khosravian-Arab: A numerical scheme for the solution of a class of fractional variational and optimal control problems using the modified Jacobi polynomials. Journal of Vibration and Control, 22(6), (2016), 1547–1559, DOI: 10.1177/1077546314543727.
[16] S. Yousefi, A. Lotfi, and M. Dehghan: The use of a Legendre multiwavelet collocation method for solving the fractional optimal control problems. Journal of Vibration and Control, 17(13), (2011), 2059–2065, DOI: 10.1177/1077546311399950.
[17] M. Gomoyunov: Optimal control problems with a fixed terminal time in linear fractional-order systems. Archives of Control Sciences, 30(2), (2019), 295–324, DOI: 10.24425/acs.2020.135849.
[18] T. Chiranjeevi and R.K. Biswas: Discrete-time fractional optimal control. Mathematics, 5(2), (2017), DOI: 10.3390/math5020025.
[19] A. Dzielinski and P.M. Czyronis: Fixed final time and free final state optimal control problem for fractional dynamic systems – linear quadratic discrete-time case. Bulletin of the Polish Academy of Sciences: Technical Sciences, 61(3), (2013), 681–690, DOI: 10.2478/bpasts-2013-0072.
[20] T. Chiranjeevi, R.K. Biswas, and N.R. Babu: Effect of initialization on optimal control problem of fractional order discrete-time system. Journal of Interdisciplinary Mathematics, 23(1), (2020), 293–302, DOI: 10.1080/09720502.2020.1721924.
[21] P.M. Czyronis: Dynamic programming problem for fractional discretetime dynamic systems. Quadratic index of performance case. Circuits, Systems, and Signal Processing, 33(7), 2131–2149, DOI: 10.1007/s00034-014-9746-0.
[22] J.J. Trujillo and V.M. Ungureanu: Optimal control of discrete-time linear fractional order systems with multiplicative noise. International Journal of Control, 91(1), (2018), 57–69, DOI: 10.1080/00207179.2016.1266520.
[23] A. Ruszewski: Stability of discrete-time fractional linear systems with delays. Archives of Control Sciences, 29(3), (2019), 549–567, DOI: 10.24425/acs.2019.130205.
[24] L.Dai: Singular Control Systems. Berlin Heidelberg, Springer-Verlag, 1989, DOI: 10.1007/BFb0002475.
[25] R.K. Biswas and S. Sen: Fractional optimal control problems: a pseudostate- space approach. Journal of Vibration and Control, 17(7), (2011), 1034–1041, DOI: 10.1177/1077546310373618.
[26] R.K. Biswas and S. Sen: Fractional optimal control within Caputo’s derivative. In: Proceedings of the ASME IDETC/CIE Conference, (2012), 353– 360, DOI: 10.1115/DETC2011-48045.
[27] T. Chiranjeevi, R.K. Biswas, and C. Sethi: Optimal control of fractional order singular system. The International Journal of Electrical Engineering & Education, p. 0020720919833031, (2019), DOI: 10.1177/0020720919833031.
[28] T. Chiranjeevi and R.K. Biswas: Numerical approach to the fractional optimal control problem of continuous-time singular system. In: Advances in Electrical Control and Signal Systems, Singapore, (2020), 239–248, DOI: 10.1007/978-981-15-5262-5_16.
[29] T. Chiranjeevi and R.K. Biswas: Linear quadratic optimal control problem of fractional order continuous-time singular system. Procedia Computer Science, 171 (2020), 1261–1268, DOI: 10.1016/j.procs.2020.04.134.
[30] M.R.A. Moubarak, H.F. Ahmed, and O. Khorshi: Numerical solution of the optimal control for fractional order singular systems. Differential Equations and Dynamical Systems, 26(1), (2018), 279–291, DOI: 10.1007/s12591-016-0320-z.
[31] T. Chiranjeevi, R.K. Biswas, and S.K. Pandey: Fixed final time and fixed final state linear quadratic optimal control problem of fractional order singular system. In: Computing Algorithms with Applications in Engineering, Singapore, (2020), 285–294. DOI: 10.1007/978-981-15-2369-4_24.
[32] Muhafzan, A. Nazra, L. Yulianti, Zulakmal, and R. Revina: On LQ optimization problem subject to fractional order irregular singular systems. Archives of Control Sciences, 30(4), (2020), 745–756, DOI: 10.24425/acs.2020.135850.
[33] T. Chiranjeevi and R.K. Biswas: Computational method based on reflection operator for solving a class of fractional optimal control problem. Procedia Computer Science, 171 (2020), 2030–2039, DOI: 10.1016/j.procs.2020.04.218.
[34] T. Chiranjeevi and R.K. Biswas: Numerical simulation of fractional order optimal control problem. Journal of Statistics and Management Systems, 23(6), (2020), 1069–1077, DOI: 10.1080/09720510.2020.1800188.
[35] T. Kaczorek: Singular fractional continuous-time and discrete-time linear systems. Acta Mechanica et Automatica, 7(1), (2013), 26–33, DOI: 10.2478/ama-2013-0005.
[36] T. Kaczorek: Selected Problems of Fractional Systems Theory. Berlin Heidelberg, Springer-Verlag, 2011, DOI: 10.1007/978-3-642-20502-6.
[37] T. Kaczorek: Polynomial and Rational Matrices: Applications in Dynamical Systems Theory. London, Springer-Verlag, 2007, DOI: 10.1007/978-1-84628-605-6.
Go to article

Authors and Affiliations

Tirumalasetty Chiranjeevi
1
Raj Kumar Biswas
2
Ramesh Devarapalli
3
ORCID: ORCID
Naladi Ram Babu
2
Fausto Pedro García Márquez
4

  1. Department of Electrical Engineering, Rajkiya Engineering College Sonbhadra, U. P., India
  2. Department of Electrical Engineering, National Institute of Technology, Silchar, India
  3. Department of Electrical Engineering, BIT Sindri, Dhanbad 828123, Jharkhand, India
  4. Ingenium Research Group, University of Castilla-La Mancha, Spain
Download PDF Download RIS Download Bibtex

Abstract

A problem of optimization for production and storge costs is studied. The problem consists in manufacture of n types of products, with some given restrictions, so that the total production and storage costs are minimal. The mathematical model is built using the framework of driftless control affine systems. Controllability is studied using Lie geometric methods and the optimal solution is obtained with Pontryagin Maximum Principle. It is proved that the economical system is not controllable, in the sense that we can only produce a certain quantity of products. Finally, some numerical examples are given with graphical representation.
Go to article

Bibliography

[1] A. Agrachev and Y.L. Sachkov: Control theory from the geometric viewpoint. Encyclopedia of Mathematical Sciences, Control Theory and Optimization, 87, Springer, 2004.
[2] K.J. Arrow: Applications of control theory of economic growth. Mathematics of Decision Sciences, 2, AMS, 1968.
[3] S. Axsater: Control theory concepts in production and inventory control. International Journal of Systems Science, 16(2), (1985), 161–169, DOI: 10.1080/00207728508926662.
[4] R. Bellmann: Adaptive control processes: a guided tour. Princeton Univ. Press: Princeton, 1972.
[5] S. Benjaafar, J.P. Gayon, and S. Tepe: Optimal control of a productioninventory system with customer impatience. Operations Research Letters, 38(4), (2010), 267–272, DOI: 10.1016/j.orl.2010.03.008.
[6] R. Brocket: Lie algebras and Lie groups in control theory. In: Mayne D.Q., Brockett R.W. (eds) Geometric Methods in System Theory. NATO Advanced Study Institutes Series (Series C – Mathematical and Physical Sciences), vol. 3. Springer, Dordrecht, 1973, 43–82, DOI: 10.1007/978-94-010-2675-8_2.
[7] M. Caputo: Foundations of Dynamic Economic Analysis: Optimal Control Theory and Applications. Cambridge Univ. Press, 2005, DOI: 10.1017/CBO9780511806827.
[8] M. Danahe, A. Chelbi, and N. Rezg: Optimal production plan for a multiproducts manufacturing system with production rate dependent failure rate. International Journal of Production Research, 50(13), (2012), 3517–3528, DOI: 10.1080/00207543.2012.671585.
[9] G. Feichtinger and R. Hartl: Optimal pricing and production in an inventory model. European Journal of Operational Research, 19 (1985), 45–56, DOI: 10.1016/0377-2217(85)90307-8.
[10] C. Gaimon: Simultaneous and dynamic price, production, inventory and capacity decisions. European Journal of Operational Research, 35 (1988), 426–441.
[11] J.P. Gayon, S. Vercraene, and S.D. Flapper: Optimal control of a production-inventory system with product returns and two disposal options. European Journal of Operational Research, 262(2), (2017), 499–508, DOI: 10.1016/j.ejor.2017.03.018.
[12] C. Hermosilla, R. Vinter, and H. Zidani: Hamilton–Jacobi–Bellman equations for optimal control processes with convex state constraints. Systems & Control Letters, 109 (2017), 30–36, DOI: 10.1016/j.sysconle.2017.09.004.
[13] V. Jurdjevic: Geometric Control Theory. Cambridge Studies in Advanced Mathematics, 52, Cambridge Univ. Press, 1997, DOI: 10.1017/CBO9780511530036.
[14] M.I. Kamien and N.L. Schwartz: Dynamic optimization: The Calculus of Variations and Optimal Control in Economics and Management, 31 Elsevier, 1991.
[15] K. Kogan and E. Khmelnitsky: An optimal control model for continuous time production and setup scheduling. International Journal of Production Research, 34(3), (1996), 715–725.
[16] Y. Qiu, J. Qiao, and P. Pardalos: Optimal production, replenishment, delivery, routing and inventory management policies for products with perishable inventory. Omega-International Journal of Management Science, 82 (2019), 193–204, DOI: 10.1016/j.omega.2018.01.006.
[17] S.M. LaValle: Planning Algorithms. Cambridge University Press, 2006.
[18] M. Li and Z. Wang: An integrated replenishment and production control policy under inventory inaccuracy and time-delay. Computers&Operations Research, 88 (2017), 137–149, DOI: 10.1016/j.cor.2017.06.014.
[19] B. Li and A. Arreola-Risa: Optimizing a production-inventory system under a cost target. Computers&Operations Research, 123 (2020), 105015, DOI: 10.1016/j.cor.2020.105015.
[20] M. Ortega and L. Lin: Control theory applications to the productioninventory problem: a review. International Journal of Production Research, 42(11), (2004), 2303–2322, DOI: 10.1080/00207540410001666260.
[21] V. Pando and J. Sicilia: A new approach to maximize the profit/cost ratio in a stock-dependent demand inventory model. Computers & Operations Research, 120 (2020), 104940, DOI: 10.1016/j.cor.2020.104940.
[22] L. Popescu: Applications of driftles control affine sytems to a problem of inventory and production. Studies in Informatics and Control, 28(1), (2019), 25–34, DOI: 10.24846/v28i1y201903.
[23] L. Popescu: Applications of optimal control to production planning. Information Technology and Control, 49(1), (2020), 89–99, DOI: 10.5755/j01.itc.49.1.23891.
[24] L. Popescu, D. Militaru, and O. Mituca: Optimal control applications in the study of production management. International Journal of Computers, Communications & Control, 15(2), (2020), 3859, DOI: 10.15837/ijccc.2020.2.3859.
[25] A. Seierstad and K. Sydsater: Optimal Control Theory with Economic Applications. North-Holland, Amsterdam, NL, 1987.
[26] S.P. Sethi: Applications of the Maximum Principle to Production and Inventory Problems. Proceedings Third International Symposium on Inventories, Budapest, Aug. 27-31, (1984), 753–756.
[27] S.P. Sethi and G.L.Thompson: Optimal Control Theory: Applications to Management Science and Economics. Springer, New York, 2000.
[28] J.D. Schwartz and D.E. Rivera: A process control approach to tactical inventory management in production-inventory systems. International Journal of Production Economics, 125(1), (2010), 111–124, DOI: 10.1016/j.ijpe.2010.01.011.
[29] D.R. Towill, G.N. Evans, and P. Cheema: Analysis and design of an adaptive minimum reasonable inventory control system. Production Planning & Control, 8(6), (1997), 545–557, DOI: 10.1080/095372897234885.
[30] T.A. Weber, Optimal control theory with applications in economics. MIT Press, 2011.
Go to article

Authors and Affiliations

Liviu Popescu
1
Ramona Dimitrov
1

  1. University of Craiova, Faculty of Economics and Business Administration, Department of Statistics and Economic Informatics, Al. I. Cuza st., No. 13, Craiova 200585, Romania
Download PDF Download RIS Download Bibtex

Abstract

Small bucket models with many short fictitious micro-periods ensure high-quality schedules in multi-level systems, i.e., with multiple stages or dependent demand. In such models, setup times longer than a single period are, however, more likely. This paper presents new mixedinteger programming models for the proportional lot-sizing and scheduling problem (PLSP) with setup operations overlapping multiple periods with variable capacity.
A new model is proposed that explicitly determines periods overlapped by each setup operation and the time spent on setup execution during each period. The model assumes that most periods have the same length; however, a few of them are shorter, and the time interval determined by two consecutive shorter periods is always longer than a single setup operation. The computational experiments showthat the newmodel requires a significantly smaller computation effort than known models.
Go to article

Bibliography

[1] I. Barany, T.J. van Roy and L.A. Wolsey: Uncapacitated lot-sizing: The convex hull of solutions. Mathematical Programming Studies, 22 (1984), 32–43, DOI: 10.1007/BFb0121006.
[2] G. Belvaux and L.A. Wolsey: Modelling practical lot-sizing problems as mixed-integer programs. Management Science, 47(7), (2001), 993–1007, DOI: 10.1287/mnsc.47.7.993.9800.
[3] J.D. Blocher, S. Chand and K. Sengupta: The changeover scheduling problem with time and cost considerations: Analytical results and a forward algorithm. Operations Research, 47(7), (1999), 559-569, DOI: 10.1287/opre.47.4.559.
[4] W. Bozejko, M. Uchronski and M. Wodecki: Multi-machine scheduling problem with setup times. Archives of Control Sciences, 22(4), (2012), 441– 449, DOI: 10.2478/v10170-011-0034-y.
[5] W. Bozejko, A. Gnatowski, R. Idzikowski and M. Wodecki: Cyclic flow shop scheduling problem with two-machine cells. Archives of Control Sciences, 27(2), (2017), 151–167, DOI: 10.1515/acsc-2017-0009.
[6] D. Cattrysse, M. Salomon, R. Kuik and L. vanWassenhove: A dual ascent and column generation heuristic for the discrete lotsizing and scheduling problem with setup times. Management Science, 39(4), (1993), 477–486, DOI: 10.1287/mnsc.39.4.477.
[7] K. Copil, M. Worbelauer, H. Meyr and H. Tempelmeier: Simultaneous lotsizing and scheduling problems: a classification and review of models. OR Spectrum, 39(1), (2017), 1–64, DOI: 10.1007/s00291-015-0429-4.
[8] A. Drexl and K. Haase: Proportional lotsizing and scheduling. International Journal of Production Economics, 40(1), (1995), 73–87, DOI: 10.1016/0925-5273(95)00040-U.
[9] B. Fleischmann: The discrete lot-sizing and scheduling problem. European Journal of Operational Research, 44(3), (1990), 337-348, DOI: 10.1016/0377-2217(90)90245-7.
[10] K. Haase: Lotsizing and scheduling for production planning. Number 408 in Lecture Notes in Economics and Mathematical Systems. Springer-Verlag, Berlin, 1994.
[11] W. Kaczmarczyk: Inventory cost settings in small bucket lot-sizing and scheduling models. In Total Logistic Management Conference, Zakopane, Poland, November 25-28 2009.
[12] W. Kaczmarczyk: Modelling multi-period set-up times in the proportional lot-sizing problem. Decision Making in Manufacturing and Services, 3(1-2), (2009), 15–35, DOI: 10.7494/dmms.2009.3.2.15.
[13] W. Kaczmarczyk: Proportional lot-sizing and scheduling problem with identical parallel machines. International Journal of Production Research, 49(9), (2011), 2605–2623, DOI: 10.1080/00207543.2010.532929.
[14] W. Kaczmarczyk: Valid inequalities for proportional lot-sizing and scheduling problem with fictitious microperiods. International Journal of Production Economics, 219(1), (2020), 236–247, DOI: 10.1016/j.ijpe.2019.06.005.
[15] W.Kaczmarczyk: Explicit modelling of multi-period setup times in proportional lot-sizing problem with constant capacity. (2021), Preprint available at Research Square, DOI: 10.21203/rs.3.rs-1086310/v1.
[16] U.S. Karmarkar and L. Schrage: The deterministic dynamic product cycling problem. Operations Research, 33(2), (1985), 326–345, DOI: 10.1287/opre.33.2.326.
Go to article

Authors and Affiliations

Waldemar Kaczmarczyk
1

  1. Department of Strategic Management, AGH University of Science and Technology, Al.Mickiewicza 30, 30-059, Kraków, Poland
Download PDF Download RIS Download Bibtex

Abstract

The problem of control of rod heating process by changing the temperature along the rod whose ends are thermally insulated is considered. It is assumed that, along with the classical boundary conditions, nonseparated multipoint intermediate conditions are also given. Using the method of separation of variables and methods of the theory of control of finite-dimensional systems with multipoint intermediate conditions, a constructive approach is proposed to build the sought function of temperature control action. A necessary and sufficient condition is obtained, which the function of the distribution of the rod temperature must satisfy, so that under any feasible initial, nonseparated intermediate, and final conditions, the problem is completely controllable. As an application of the proposed approach, control action with given nonseparated conditions on the values of the rod temperature distribution function at the two intermediate moments of time is constructed.
Go to article

Bibliography

[1] A.G. Butkovskii: Control Methods for Systems with Distributed Parameters. Nauka, 1975 (in Russian).
[2] A.G Butkovskii, S.A Malyi, and Yu.N. Andreev: Optimal Control of Metal Heating. Moscow, Metallurgy, 1972 (in Russian).
[3] A.I. Egorov: Optimal Control of Thermal and Diffusion Processes. Nauka, 1978 (in Russian).
[4] A.I. Egorov and L.N. Znamenskaya: Introduction to the Theory of Control of Systems with Distributed Parameters. Textbook, Saint Petersburg, LAN, 2017 (in Russian).
[5] E.Ya. Rapoport: Structural Modeling of Objects and Control Systems with Distributed Parameters. Higher School, 2003 (in Russian).
[6] A.N. Tikhonov and A.A. Samarskii: Equations of Mathematical Physics. Nauka, 1977 (in Russian).
[7] V.I. Ukhobotov and I.V. Izmest’ev: A control problem for a rod heating process with unknown temperature at the right end and unknown density of the heat source. Trudy Instituta Matematiki i Mekhaniki, UrO RAN, 25(1), (2019), 297–305 (in Russian), DOI: 10.21538/0134-4889-2019-25-1-297-305.
[8] V.I. Ukhobotov and I.V. Izmest’ev: The problem of controlling the process of heating the rod in the presence of disturbance and uncertainty. IFAC Papers OnLine, 51(32), (2018), 739–742, DOI: 10.1016/j.ifacol.2018.11.458.
[9] V.I. Butyrin and L.A. Fylshtynskyi: Optimal control of the temperature field in the rod when changing the control zone programmatically. Applied Mechanics, 12(84), (1976), 115–118 (in Russian).
[10] M.M. Kopets: Optimal control over the process of heating of a thin core. Reports of the National Academy of Sciences of Ukraine, 7, (2014), 48–52 (in Ukrainian), http://dspace.nbuv.gov.ua/handle/123456789/87951.
[11] N.V.Gybkina, D.Yu. Podusov, and M.V. Sidorov: The optimal control of a homogeneous rod final temperature state. Radioelectronics and Informatics, 2 (2014), 9–15 (in Russian).
[12] E.Y. Vedernikova and A.A. Kornev: To the problem of rod heating. Moscow Univ. Math. Bull., 69, (2014), 237–241, DOI: 10.3103/S0027132214060023.
[13] J.F. Bonnans and P. Jaisson: Optimal control of a parabolic equation with time-dependent state constraints. SIAM Journal on Control and Optimization, 48(7), (2010), 4550–4571.
[14] A. Lapin and E. Laitinen: Iterative solution of mesh constrained optimal control problems with two-level mesh approximations of parabolic state equation. Journal of Applied Mathematics and Physics, 6, (2018), 58–68, DOI: 10.4236/jamp.2018.61007.
[15] K. Kunisch and L. Wang: Time optimal control of the heat equation with pointwise control constraints. ESAIM: Control, Optimisation and Calculus of Variations, 19(2), (2013), 460–485, http://eudml.org/doc/272753.
[16] J.M. Lemos, L. Marreiro, and B. Costa: Supervised multiple model adaptive control of a heating fan. Archives of Control Sciences, 18(1), (2008), 5–16.
[17] S.H. Jilavyan, E.R. Grigoryan, and A.Zh. Khurshudyan: Heating control of a finite rod with a mobile source. Archives of Control Sciences, 31(2), (2021), 417–430, DOI: 10.24425/acs.2021.137425.
[18] V.R. Barseghyan: Control problem of string vibrations with inseparable multipoint conditions at intermediate points in time. Mechanics of Solids, 54(8), (2019), 1216–1226. DOI: 10.3103/S0025654419080120.
[19] V.R. Barseghyan: Optimal control of string vibrations with nonseparate state function conditions at given intermediate instants. Automation and Remote Control, 81(2), (2020), 226–235, DOI: 10.1134/S0005117920020034.
[20] V.R. Barseghyan: Control of Compound Dynamic Systems and of Systems with Multipoint Intermediate Conditions. Nauka, 2016 (in Russian).
[21] V.R. Barseghyan and T.V. Barseghyan: On an approach to the problems of control of dynamic system with nonseparated multipoint intermediate conditions. Automation and Remote Control, 76(4), (2015), 549–559, DOI: 10.1134/S0005117915040013.
Go to article

Authors and Affiliations

Vanya R. Barseghyan
1

  1. Institute of Mechanics of the National Academyof Sciences of Armenia, Yerevan State University, Armenia
Download PDF Download RIS Download Bibtex

Abstract

This paper presents how Q-learning algorithm can be applied as a general-purpose selfimproving controller for use in industrial automation as a substitute for conventional PI controller implemented without proper tuning. Traditional Q-learning approach is redefined to better fit the applications in practical control loops, including new definition of the goal state by the closed loop reference trajectory and discretization of state space and accessible actions (manipulating variables). Properties of Q-learning algorithm are investigated in terms of practical applicability with a special emphasis on initializing of Q-matrix based only on preliminary PI tunings to ensure bumpless switching between existing controller and replacing Q-learning algorithm. A general approach for design of Q-matrix and learning policy is suggested and the concept is systematically validated by simulation in the application to control two examples of processes exhibiting first order dynamics and oscillatory second order dynamics. Results show that online learning using interaction with controlled process is possible and it ensures significant improvement in control performance compared to arbitrarily tuned PI controller.
Go to article

Bibliography

[1] H. Boubertakh, S. Labiod, M. Tadjine and P.Y. Glorennec: Optimization of fuzzy PID controllers using Q-learning algorithm. Archives of Control Sciences, 18(4), (2008), 415–435
[2] I.Carlucho, M. De Paula, S.A. Villar and G.G.Acosta: Incremental Qlearning strategy for adaptive PID control of mobile robots. Expert Systems With Applications, 80, (2017), 183–199, DOI: 10.1016/j.eswa.2017.03.002.
[3] K. Delchev: Simulation-based design of monotonically convergent iterative learning control for nonlinear systems. Archives of Control Sciences, 22(4), (2012), 467–480.
[4] M. Jelali: An overview of control performance assessment technology and industrial applications. Control Eng. Pract., 14(5), (2006), 441–466, DOI: 10.1016/j.conengprac.2005.11.005.
[5] M. Jelali: Control Performance Management in Industrial Automation: Assessment, Diagnosis and Improvement of Control Loop Performance. Springer-Verlag London, (2013)
[6] H.-K. Lam, Q. Shi, B. Xiao, and S.-H. Tsai: Adaptive PID Controller Based on Q-learning Algorithm. CAAI Transactions on Intelligence Technology, 3(4), (2018), 235–244, DOI: 10.1049/trit.2018.1007.
[7] D. Li, L. Qian, Q. Jin, and T. Tan: Reinforcement learning control with adaptive gain for a Saccharomyces cerevisiae fermentation process. Applied Soft Computing, 11, (2011), 4488–4495, DOI: 10.1016/j.asoc.2011.08.022.
[8] M.M. Noel and B.J. Pandian: Control of a nonlinear liquid level system using a new artificial neural network based reinforcement learning approach. Applied Soft Computing, 23, (2014), 444–451, DOI: 10.1016/j.asoc.2014.06.037.
[9] T. Praczyk: Concepts of learning in assembler encoding. Archives of Control Sciences, 18(3), (2008), 323–337.
[10] M.B. Radac and R.E. Precup: Data-driven model-free slip control of antilock braking systems using reinforcement Q-learning. Neurocomputing, 275, (2017), 317–327, DOI: 10.1016/j.neucom.2017.08.036.
[11] A.K. Sadhu and A. Konar: Improving the speed of convergence of multi-agent Q-learning for cooperative task-planning by a robot-team. Robotics and Autonomous Systems, 92, (2017), 66–80, DOI: 10.1016/j.robot.2017.03.003.
[12] N. Sahebjamnia, R. Tavakkoli-Moghaddam, and N. Ghorbani: Designing a fuzzy Q-learning multi-agent quality control system for a continuous chemical production line – A case study. Computers & Industrial Engineering, 93, (2016), 215–226, DOI: 10.1016/j.cie.2016.01.004.
[13] K. Stebel: Practical aspects for the model-free learning control initialization. in Proc. of 2015 20th International Conference on Methods and Models in Automation and Robotics (MMAR), Poland, (2015), DOI: 10.1109/MMAR.2015.7283918.
[14] R.S. Sutton and A.G. Barto: Reinforcement learning: An Introduction, MIT Press, (1998)
[15] S. Syafiie, F. Tadeo, and E. Martinez: Softmax and "-greedy policies applied to process control. IFAC Proceedings, 37, (2004), 729–734, DOI: 10.1016/S1474-6670(16)31556-2.
[16] S. Syafiie, F. Tadeo, and E. Martinez: Model-free learning control of neutralization process using reinforcement learning. Engineering Applications of Artificial Intelligence, 20, (2007), 767–782, DOI: 10.1016/j.engappai.2006.10.009.
[17] S. Syafiie, F. Tadeo, and E. Martinez: Learning to control pH processes at multiple time scales: performance assessment in a laboratory plant. Chemical Product and Process Modeling, 2(1), (2007), DOI: 10.2202/1934- 2659.1024.
[18] S. Syafiie, F. Tadeo, E. Martinez, and T. Alvarez: Model-free control based on reinforcement learning for a wastewater treatment problem. Applied Soft Computing, 11, (2011), 73–82, DOI: 10.1016/j.asoc.2009.10.018.
[19] P. Van Overschee and B. De Moor: RAPID: The End of Heuristic PID Tuning. IFAC Proceedings, 33(4), (2000), 595–600, DOI: 10.1016/S1474- 6670(16)38308-8.
[20] M. Wang, G. Bian, and H. Li: A new fuzzy iterative learning control algorithm for single joint manipulator. Archives of Control Sciences, 26(3), (2016), 297–310. DOI: 10.1515/acsc-2016-0017.
[21] Ch.J.C.H. Watkins and P. Dayan: Technical Note: Q-learning. Machine Learning, 8, (1992), 279–292, DOI: 10.1023/A:1022676722315.
Go to article

Authors and Affiliations

Jakub Musial
1
Krzysztof Stebel
1
Jacek Czeczot
1

  1. Silesian University of Technology, Faculty of Automatic Control, Electronics and Computer Science, Department of Automatic Control and Robotics, 44-100 Gliwice, ul. Akademicka 16, Poland
Download PDF Download RIS Download Bibtex

Abstract

The hybridization of a recently suggested Harris hawk’s optimizer (HHO) with the traditional particle swarm optimization (PSO) has been proposed in this paper. The velocity function update in each iteration of the PSO technique has been adopted to avoid being trapped into local search space with HHO. The performance of the proposed Integrated HHO-PSO (IHHOPSO) is evaluated using 23 benchmark functions and compared with the novel algorithms and hybrid versions of the neighbouring standard algorithms. Statistical analysis with the proposed algorithm is presented, and the effectiveness is shown in the comparison of grey wolf optimization (GWO), Harris hawks optimizer (HHO), barnacles matting optimization (BMO) and hybrid GWO-PSO algorithms. The comparison in convergence characters with the considered set of optimization methods also presented along with the boxplot. The proposed algorithm is further validated via an emerging engineering case study of controller parameter tuning of power system stability enhancement problem. The considered case study tunes the parameters of STATCOM and power system stabilizers (PSS) connected in a sample power network with the proposed IHHOPSO algorithm. A multi-objective function has been considered and different operating conditions has been investigated in this papers which recommends proposed algorithm in an effective damping of power network oscillations.
Go to article

Bibliography

[1] M. Crepinsek, S.-H. Liu, and L. Mernik: A note on teaching–learningbased optimization algorithm. Information Sciences, 212 (2012), 79–93, DOI: 10.1016/j.ins.2012.05.009.
[2] Anita and A. Yadav: AEFA: Artificial electric field algorithm for global optimization. Swarm and Evolutionary Computation, 48 (2019), 93–108, DOI: 10.1016/j.swevo.2019.03.013.
[3] R. Devarapalli and B. Bhattacharyya: A hybrid modified grey wolf optimization-sine cosine algorithm-based power system stabilizer parameter tuning in a multimachine power system. Optimal Control Applications and Methods, 41(4), (2020), 1143-1159, DOI: 10.1002/oca.2591.
[4] M. Jain, V. Singh, and A. Rani: A novel nature-inspired algorithm for optimization: Squirrel search algorithm, Swarmand Evolutionary Computation, 44 (2019), 148–175, DOI: 10.1016/j.swevo.2018.02.013.
[5] A.E. Eiben and J.E. Smith: What is an Evolutionary Algorithm? In Introduction to Evolutionary Computing, Berlin, Heidelberg: Springer Berlin Heidelberg, 2015, 25–48, DOI: 10.1007/978-3-662-44874-8_3.
[6] A. Kaveh and M. Khayatazad: A new meta-heuristic method: Ray Optimization. Computers & Structures, 112–113, (2012), 283–294, DOI: 10.1016/j.compstruc.2012.09.003.
[7] P.J.M. van Laarhoven and E.H.L. Aarts: Simulated annealing. In Simulated Annealing: Theory and Applications, P.J.M. van Laarhoven and E.H.L. Aarts, Eds. Dordrecht: Springer Netherlands, 1987, 7–15, DOI: 10.1007/978-94-015-7744-1_2.
[8] Agenetic algorithm tutorial. SpringerLink. https://link.springer.com/article/10.1007/BF00175354 (accessed Mar. 20, 2020).
[9] J. Kennedy and R. Eberhart: Particle Swarm Optimization. Proc. of ICNN’95 International Conference on Neural Networks, 4 (1995), 1942– 1948.
[10] M. Neshat, G. Sepidnam, M. Sargolzaei, and A.N. Toosi: Artificial fish swarm algorithm: a survey of the state-of-the-art, hybridization, combinatorial and indicative applications. Artificial Intelligence Review, 42(4), (2014), 965–997, DOI: 10.1007/s10462-012-9342-2.
[11] M. Dorigo, M. Birattari, and T. Stutzle: Ant colony optimization. IEEE Computational Intelligence Magazine, 1(4), (2006), 28–39, DOI: 10.1109/ MCI.2006.329691.
[12] M. Roth and S. Wicker: Termite: ad-hoc networking with stigmergy. In GLOBECOM’03. IEEE Global Telecommunications Conference (IEEE Cat. No.03CH37489), 5 (2003), 2937–2941, DOI: 10.1109/GLOCOM.2003.1258772.
[13] D. Karaboga and B. Akay: A comparative study of Artificial Bee Colony algorithm. Applied Mathematics and Computation, 214(1), (2009), 108– 132, DOI: 10.1016/j.amc.2009.03.090.
[14] A. Mucherino and O. Seref: Monkey search: a novel metaheuristic search for global optimization. AIP Conference Proceedings, 953(1), (2007), 162– 173, DOI: 10.1063/1.2817338.
[15] E.Atashpaz-Gargari and C. Lucas: Imperialist competitive algorithm: An algorithm for optimization inspired by imperialistic competition. In 2007 IEEE Congress on Evolutionary Computation, (2007), 4661–4667, DOI: 10.1109/CEC.2007.4425083.
[16] D. Simon: Biogeography-based optimization. IEEE Transactions on Evolutionary Computation, 12(6), (2008), 702–713, DOI: 10.1109/TEVC.2008.919004.
[17] X.-S. Yang: Firefly algorithm. Stochastic, test, functions and design optimisation. arXiv:1003.1409 [math], Mar. 2010, Accessed: Mar. 20, 2020. [Online]. Available: http://arxiv.org/abs/1003.1409.
[18] K.M.Gates and P.C.M. Molenaar: Group search algorithm recovers effective connectivity maps for individuals in homogeneous and heterogeneous samples. NeuroImage, 63(1), (2012), 310–319, DOI: 10.1016/j.neuroimage.2012.06.026.
[19] E. Rashedi, H. Nezamabadi-Pour, and S. Saryazdi: GSA: A gravitational search algorithm. Information Sciences, 179(13), (2009), 2232–2248, DOI: 10.1016/j.ins.2009.03.004.
[20] Y. Tan andY. Zhu: Fireworks Algorithm for Optimization. In: TanY., ShiY., Tan K.C. (eds) Advances in Swarm Intelligence. ICSI 2010. Lecture Notes in Computer Science, 6145, Springer, Berlin, Heidelberg. DOI: 10.1007/978-3-642-13495-1_44.
[21] X.-S. Yang: Bat algorithm for multi-objective optimisation. arXiv: 1203. 6571 [math], Mar. 2012, Accessed: Mar. 20, 2020. [Online]. Available: http://arxiv.org/abs/1203.6571.
[22] LingWang, Xiao-long Zheng, and Sheng-yaoWang:Anovel binary fruit fly optimization algorithm for solving the multidimensional knapsack problem. Knowledge-Based Systems, 48 17–23, (2013), DOI: 10.1016/j.knosys.2013.04.003.
[23] X.-S. Yang: Flower Pollination Algorithm for Global Optimization. In Unconventional Computation and Natural Computation, Berlin, Heidelberg, 2012, 240–249, DOI: 10.1007/978-3-642-32894-7_27.
[24] G.-G. Wang, L. Guo, A.H. Gandomi, G.-S. Hao, and H. Wang: Chaotic Krill Herd algorithm. Information Sciences, 274 (2014), 17–34, DOI: 10.1016/j.ins.2014.02.123.
[25] A. Kaveh and N. Farhoudi: A new optimization method: Dolphin echolocation. Advances in Engineering Software, 59 (2013), 53–70, DOI: 10.1016/ j.advengsoft.2013.03.004.
[26] S. Mirjalili, S.M. Mirjalili, and A. Lewis: GreyWolf optimizer. Advances in Engineering Software, 69 (2014), 46–61, DOI: 10.1016/j.advengsoft.2013.12.007.
[27] A. Hatamlou: Black hole: A new heuristic optimization approach for data clustering. Information Sciences, 222 (2013), 175–184, DOI: 10.1016/ j.ins.2012.08.023.
[28] A. Sadollah, A. Bahreininejad, H. Eskandar and M. Hamdi: Mine blast algorithm: A new population based algorithm for solving constrained engineering optimization problem. Applied Soft Computing, 13(5), (2013), 2592–2612, DOI: 10.1016/j.asoc.2012.11.026.
[29] S. Mirjalili: Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Computing and Applications, 27(4), (2016), 1053–1073, DOI: 10.1007/s00521-015-1920-1.
[30] S. Mirjalili: Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm. Knowledge-Based Systems, 89 (2015), 228–249, DOI: 10.1016/j.knosys.2015.07.006.
[31] F.A. Hashim, E.H. Houssein, M.S. Mabrouk, W. Al-Atabany, and S. Mirjalili: Henry gas solubility optimization: A novel physics-based algorithm. Future Generation Computer Systems, 101 (2019), 646–667, DOI: 10.1016/j.future.2019.07.015.
[32] S. Mirjalili: The ant lion optimizer. Advances in Engineering Software, 83 (2015), 80–98, DOI: 10.1016/j.advengsoft.2015.01.010.
[33] H. Shareef, A.A. Ibrahim, and A.H. Mutlag: Lightning search algorithm. Applied Soft Computing, 36 (2015), 315–333, DOI: 10.1016/j.asoc.2015.07.028.
[34] S.A. Uymaz, G. Tezel, and E. Yel: Artificial algae algorithm (AAA) for nonlinear global optimization. Applied Soft Computing, 31 (2015), 153–171, DOI: 10.1016/j.asoc.2015.03.003.
[35] M.D. Li, H. Zhao, X.W. Weng, and T. Han: A novel nature-inspired algorithm for optimization: Virus colony search. Advances in Engineering Software, 92 (2016), 65–88, DOI: 10.1016/j.advengsoft.2015.11.004.
[36] O. Abedinia, N. Amjady, and A. Ghasemi: A new metaheuristic algorithm based on shark smell optimization. Complexity, 21(5), (2016), 97–116, DOI: 10.1002/cplx.21634.
[37] S. Mirjalili, S.M. Mirjalili, and A. Hatamlou: Multi-Verse optimizer: a nature-inspired algorithm for global optimization. Neural Computing and Applications, 27(2), (2016), 495–513, DOI: 10.1007/s00521-015-1870-7.
[38] S. Mirjalili and A. Lewis: The whale optimization algorithm. Advances in Engineering Software, 95 (2016), 51–67, DOI: 10.1016/j.advengsoft. 2016.01.008.
[39] A. Askarzadeh: A novel metaheuristic method for solving constrained engineering optimization problems: Crow search algorithm. Computers and Structures, 169 (2016), 1–12, DOI: 10.1016/j.compstruc.2016.03.001.
[40] T. Wu, M. Yao, and J. Yang: Dolphin swarm algorithm. Frontiers of Information Technology & Electronic Engineering, 17(8), (2016), 717–729, DOI: 10.1631/FITEE.1500287.
[41] S. Mirjalili: SCA: A sine cosine algorithm for solving optimization problems. Knowledge-Based Systems, 96 (2016), 120–133, DOI: 10.1016/j.knosys.2015.12.022.
[42] A. Kaveh and A. Dadras: A novel meta-heuristic optimization algorithm: Thermal exchange optimization. Advances in Engineering Software, 110, (2017), 69–84, DOI: 10.1016/j.advengsoft.2017.03.014.
[43] M.M. Mafarja, I. Aljarah, A. Asghar Heidari, A.I. Hammouri, H. Faris, Ala’M. Al-Zoubi, and S. Mirjalili: Evolutionary population dynamics and grasshopper optimization approaches for feature selection problems. Knowledge-Based Systems, 145 (2018), 25–45, DOI: 10.1016/j.knosys.2017.12.037.
[44] A. Tabari and A. Ahmad: A new optimization method: Electro-search algorithm. Computers and Chemical Engineering, 103 (2017), 1–11, DOI: 10.1016/j.compchemeng.2017.01.046.
[45] G. Dhiman and V. Kumar: Spotted hyena optimizer: A novel bio-inspired based metaheuristic technique for engineering applications. Advances in Engineering Software, 114 (2017), 48–70, DOI: 10.1016/j.advengsoft. 2017.05.014.
[46] S.-A. Ahmadi: Human behavior-based optimization: a novel metaheuristic approach to solve complex optimization problems. Neural Comput and Applications, 28(S1), (2017), 233–244, DOI: 10.1007/s00521-016-2334-4.
[47] A.F. Nematollahi, A. Rahiminejad, and B. Vahidi: A novel physical based meta-heuristic optimization method known as lightning attachment procedure optimization. Applied Soft Computing, 59 (2017), 596–621, DOI: 10.1016/j.asoc.2017.06.033.
[48] R.A. Ibrahim, A.A. Ewees, D. Oliva, M. Abd Elaziz, and S. Lu: Improved salp swarm algorithm based on particle swarm optimization for feature selection. Journal of Ambient Intelligence and Humanized Computing, 10(8), (2019), 3155–3169, DOI: 10.1007/s12652-018-1031-9.
[49] E. Jahani and M. Chizari: Tackling global optimization problems with a novel algorithm – Mouth brooding fish algorithm. Applied Soft Computing, 62 (2018), 987–1002, DOI: 10.1016/j.asoc.2017.09.035.
[50] X. Qi, Y. Zhu, and H. Zhang: A new meta-heuristic butterfly-inspired algorithm. Journal of Computational Science, 23 (2017), 226–239, DOI: 10.1016/j.jocs.2017.06.003.
[51] S. Mirjalili: Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm. Knowledge-Based Systems, 89 (2015), 228–249, DOI: 10.1016/j.knosys.2015.07.006.
[52] M. Dorigo, V. Maniezzo, and A. Colorni: Ant system: optimization by a colony of cooperating agents. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 26(1), (1996), 29–41, DOI: 10.1109/3477.484436.
[53] S. Mirjalili and S.Z.M. Hashim: A new hybrid PSOGSA algorithm for function optimization. In 2010 International Conference on Computer and Information Application, (2010), 374–377, DOI: 10.1109/ICCIA.2010.6141614.
[54] F.A. Senel, F. Gokce, A.S. Yuksel, and T. Yigit: A novel hybrid PSO– GWO algorithm for optimization problems. Engineering with Computers, 35(4), 1359–1373, DOI: 10.1007/s00366-018-0668-5.
[55] D.T. Bui, H. Moayedi, B. Kalantar, and A. Osouli: Harris hawks optimization: A novel swarm intelligence technique for spatial assessment of landslide susceptibility. Sensors, 19(14), (2019), 3590, DOI: 10.3390/s19163590.
[56] H. Chen, S. Jiao, M.Wang, A.A. Heidari, and X. Zhao: Parameters identification of photovoltaic cells and modules using diversification-enriched Harris hawks optimization with chaotic drifts. Journal of Cleaner Production, 244 (2020), p. 118778, DOI: 10.1016/j.jclepro.2019.118778.
[57] A.A. Heidari, S. Mirjalili, H. Faris, I. Aljarah, M. Mafarja, and H. Chen: Harris hawks optimization: Algorithm and applications. Future Generation Computer Systems, 97 (2019), 849–872, DOI: 10.1016/ j.future.2019.02.028.
[58] M. Jamil and X.-S. Yang: A literature survey of benchmark functions for global optimization problems. International Journal of Mathematical Modelling and Numerical Optimisation, 4(2), (2013), 150, DOI: 10.1504/IJMMNO.2013.055204.
[59] A. Kaveh and S. Talatahari: A novel heuristic optimization method: charged system search. Acta Mechanica, 213(3–4), (2010), 267–289, DOI: 10.1007/s00707-009-0270-4.
[60] J. Luo and B. Shi: Ahybrid whale optimization algorithm based on modified differential evolution for global optimization problems. Applied Intelligence, 49(5), (2000), 1982–2000, DOI: 10.1007/s10489-018-1362-4.
[61] A.A. Heidari, S. Mirjalili, H. Faris, I. Aljarah, M. Mafarja, and H. Chen: Harris hawks optimization: Algorithm and applications. Future Generation Computer Systems, 97 (2019), 849–872, DOI: 10.1016/ j.future.2019.02.028.
[62] P. Pruski and S. Paszek: Location of generating units most affecting the angular stability of the power system based on the analysis of instantaneous power waveforms. Archives of Control Sciences, 30(2), (2020), 273–293, DOI: 10.24425/acs.2020.133500.
[63] M.M. Hossain and A.Z. Khurshudyan: Heuristic control of nonlinear power systems: Application to the infinite bus problem. Archives of Control Sciences, 29(2), (2019), 279–288, DOI: 10.24425/acs.2019.129382.
[64] R. Devarapalli and B. Bhattacharyya:Aframework for H2=H? synthesis in damping power network oscillations with STATCOM. Iranian Journal of Science and Technology, Transactions of Electrical Engineering, 44 (2020), 927-948, DOI: 10.1007/s40998-019-00278-4.
[65] G. Gurrala and I. Sen: Power system stabilizers design for interconnected power systems. IEEE Transactions on Power Systems, 25(2), (2010), 1042– 1051, DOI: 10.1109/TPWRS.2009.2036778.
[66] R.K. Varma: Introduction to FACTS controllers. In 2009 IEEE/PES Power Systems Conference and Exposition, (2009), 1–6, DOI: 10.1109/PSCE.2009.4840114.
[67] P. Kundur: Power System Stability and Control. Tata McGraw-Hill Education, 1994.
[68] M. Belazzoug, M. Boudour, and K. Sebaa: FACTS location and size for reactive power system compensation through the multi-objective optimization. Archives of Control Sciences, 20(4), (2010), 473–489, DOI: 10.2478/v10170-010-0027-2
Go to article

Authors and Affiliations

Ramesh Devarapalli
1
ORCID: ORCID
Vikash Kumar
1

  1. Department of Electrical Engineering, B.I.T. Sindri, Dhanbad, Jharkhand, India
Download PDF Download RIS Download Bibtex

Abstract

The basic objective of the research is to construct a difference model of the melt motion. The existence of a solution to the problem is proven in the paper. It is also proven the convergence of the difference problem solution to the original problem solution of the melt motion. The Rothe method is implemented to study the Navier–Stokes equations, which provides the study of the boundary value problems correctness for a viscous incompressible flow both numerically and analytically.
Go to article

Bibliography

[1] R. Lakshminarayana, K. Dadzie, R. Ocone, M. Borg, and J. Reese: Recasting Navier–Stokes equations. Journal of Physics Communications, 3(10), (2019), 13–18, DOI: 10.1088/2399-6528/ab4b86.
[2] S.Sh. Kazhikenova, S.N. Shaltaqov, D. Belomestny, and G.S. Shai- hova: Finite difference method implementation for Numerical integration hydrodynamic equations melts. Eurasian Physical Technical Journal, 17(33), (2020), 50–56.
[3] C. Bardos: A basic example of non linear equations: The Navier– Stokes equations. Mathematics: Concepts and Foundations, III (2002), http://www.eolss.net/sample-chapters/c02/e6-01-06-02.pdf.
[4] J.XuandW.Yu:ReducedNavier–Stokes equations with streamwise viscous diffusion and heat conduction terms. AIAA Pap., 1441 (1990), 1–6, DOI: 10.2514/6.1990-1441.
[5] Y. Seokwan and K. Dochan: Three-dimensional incompressible Navier– Stokes solver using lower-upper symmetric Gauss–Seidel algorithm. AIAA Journal, 29(6), (1991), 874–875, DOI: 10.2514/3.10671.
[6] P.M. Gresho: Incompressible fluid dynamics: some fundamental formulation issues. Annual Review of Fluid Mechanics, 23, (1991), 413–453, DOI: 10.1146/annurev.fl.23.010191.002213.
[7] S.E. Rogers, K. Dochan, and K. Cetin: Steady and unsteady solutions of the incompressible Navier–Stokes equations. AIAA Journal, 29(4), (1991), 603–610, DOI: 10.2514/3.10627.
[8] S. Masayoshi, T. Hiroshi, S. Nobuyuki, and N. Hidetoshi: Numerical simulation of three-dimensional viscous flows using the vector potential method. JSME International Journal, 34(2), (1991), 109–114, DOI: 10.1299/jsmeb1988.34.2_109.
[9] E. Sciubba: A variational derivation of the Navier–Stokes equations based on the exergy destruction of the flow. Journal of Mathematical and Physical Sciences, 25(1), (1991), 61–68.
[10] A. Bouziani and R. Mechri: The Rothe’s method to a parabolic integrodifferential equation with a nonclassical boundary conditions. International Journal of Stochastic Analysis, Article ID 519684, (2010), DOI: 10.1155/2010/519684.
[11] N. Merazga and A. Bouziani: Rothe time-discretization method for a nonlocal problem arising in thermoelasticity. Journal of Applied Mathematics and Stochastic Analysis, 2005(1), (2005), 13–28, DOI: 10.1080/00036818908839869.
[12] T.A. Barannyk, A.F. Barannyk, and I.I. Yuryk: Exact solutions of the nonliear equation. Ukrains’kyi Matematychnyi Zhurnal, 69(9), (2017), 1180–1186, http://umj.imath.[K]iev.ua/index.php/umj/article/view/1768.
[13] N.B. Iskakova, A.T. Assanova, and E.A. Bakirova: Numerical method for the solution of linear boundary-value problem for integrodifferential equations based on spline approximations. Ukrains’kyi Matematychnyi Zhurnal, 71(9), (2019), 1176–91, http://umj.imath.[K]iev.ua/index.php/ umj/article/view/1508.
[14] S.L. Skorokhodov and N.P. Kuzmina: Analytical-numerical method for solving an Orr-Sommerfeld type problem for analysis of instability of ocean currents. Zh. Vychisl. Mat. Mat. Fiz., 58(6), (2018), 1022–1039, DOI: 10.7868/S0044466918060133.
Go to article

Authors and Affiliations

Saule Sh. Kazhikenova
1
ORCID: ORCID
Sagyndyk N. Shaltakov
1
ORCID: ORCID
Bekbolat R. Nussupbekov
2
ORCID: ORCID

  1. Karaganda Technical University, Kazakhstan
  2. Karaganda University E.A. Buketov, Kazakhstan
Download PDF Download RIS Download Bibtex

Abstract

This paper studies an evacuation problem described by a leader-follower model with bounded confidence under predictive mechanisms. We design a control strategy in such a way that agents are guided by a leader, which follows the evacuation path. The proposed evacuation algorithm is based on Model Predictive Control (MPC) that uses the current and the past information of the system to predict future agents’ behaviors. It can be observed that, with MPC method, the leader-following consensus is obtained faster in comparison to the conventional optimal control technique. The effectiveness of the developed MPC evacuation algorithm with respect to different parameters and different time domains is illustrated by numerical examples.
Go to article

Bibliography

[1] H. Abdelgawad and B. Abdulhai: Emergency evacuation planning as a network design problem: A critical review. Transportation Letters: The International Journal of Transportation Research, 1 (2009), 41–58, DOI: 10.3328/TL.2009.01.01.41-58.
[2] R. Alizadeh: A dynamic cellular automaton model for evacuation process with obstacles, Safety Science, 49(2), (2011), 315–323, DOI: 10.1016/j.ssci.2010.09.006.
[3] R. Almeida, E. Girejko, L. Machado, A.B. Malinowska, and N. Mar- tins: Application of predictive control to the Hegselmann-Krause model, Mathematical Methods in the Applied Sciences, 41(18), (2018), 9191–9202, DOI: 10.10022Fmma.5132.
[4] B. Aulbach and S. Hilger: A unified approach to continuous and discrete dynamics, ser. Colloq. Math. Soc. Janos Bolyai, vol. 53, North-Holland, Amsterdam, 1990.
[5] H. Bi and E. Gelenbe: A survey of algorithms and systems for evacuating people in confined spaces, Electronics, 2019 8(6), (2019), 711, DOI: 10.3390/electronics8060711.
[6] V.D. Blondel, J.M. Hendrickx, and J.N. Tsitsiklis: On Krause’s multiagent consensus model with state-dependent connectivity, IEEE Transactions on Automatics Control, vol. 54(11), (2009), 2586–2597, DOI: 10.1109/TAC.2009.2031211.
[7] V.D. Blondel, J.M. Hendrickx, and J.N. Tsitsiklis: Continuous-time average-preserving opinion dynamics with opinion-dependent communications, SIAM Journal on Control and Optimization, vol. 48(8), (2010), 5214–5240, DOI: 10.1137/090766188.
[8] M. Bohner and A. Peterson: Dynamic equations on time scales, Boston, MA: Birkhäuser Boston, 2001.
[9] R.M. Colombo and M. D. Rosini: Pedestrian flows and non-classical shocks, Mathematical Methods in the Applied Sciences, 28(13), (2005), 1553–1567, DOI: 10.1002/mma.624.
[10] E. Girejko, L. Machado, A.B. Malinowska, and N. Martins: Krause’s model of opinion dynamics on isolated time scales, Mathematical Methods in the Applied Sciences, 39 (2016), 5302–5314, DOI: 10.1002/mma.3916.
[11] R. Hegselmann and U. Krause: Opinion dynamics and bounded confidence models, analysis, and simulation, Journal of Artificial Societies and Social Simulation, 5(3), (2002), http://jasss.soc.surrey.ac.uk/5/3/2.html.
[12] D. Helbing and P. Molnar: Social force model for pedestrian dynamics, Physical Review E, 51(5), (1995), 4282–4286, DOI: 10.1103/Phys-RevE.51.4282.
[13] R. Hilscher and V. Zeidan:Weak maximum principle and accessory problem for control problems on time scales, Nonlinear Analysis, 70(9), (2009), 3209–3226, DOI: 10.1016/j.na.2008.04.025.
[14] L. Huang, S.C.Wong, M. Zhang, C.-W. Shu, andW.H.K. Lam: Revisiting Hughes’ dynamics continuum model for pedestrian flow and the development of an efficient solution algorithm, Transportation Research Part B: Methodological, 43(1), (2009), 127–141, DOI: 10.1016/j.trb.2008.06.003.
[15] R.L. Hughes: A continuum theory for the flow of pedestrians, Transportation Research Part B: Methodological, 36(6), (2002), 507–535, DOI: 10.1016/S0191-2615(01)00015-7.
[16] R. Lohner: On the modeling of pedestrian motion, Applied Mathematical Modeling, 34(2), (2010), 366–382, DOI: 10.1016/j.apm.2009.04.017.
[17] S.J. Qin and T.A. Badgwell: An Overview of Nonlinear Model Predictive Control Applications, Allgöwer F., Zheng A. ed., ser. Nonlinear Model Predictive Control. Progress in Systems and Control Theory. Birkhäuser, Basel, 2000, vol. 26, pp. 369–392.
[18] S. Wojnar, T. Poloni, P. Šimoncic, B. Rohal’-Ilkiv, M. Honek (and) J. Csambál: Real-time implementation of multiple model based predictive control strategy to air/fuel ratio of a gasoline engine. Archives of Control Sciences, 23(1), (2013), 93–106.
[19] S. Daniar, M. Shiroei and R. Aazami: Multivariable predictive control considering time delay for load-frequency control in multi-area power systems. Archives of Control Sciences, 26(4), (2016), 527–549, DOI: 10.1515/acsc-2016-0029.
[20] Y. Yang, D.V. Dimarogonas, and X. Hu: Optimal leader-follower control for crowd evacuation, Proc. 52nd IEEE Conf. Decision Control (CDC), (2013), 2769–2774, DOI: 10.1109/CDC.2013.6760302.
[21] Z. Zainuddin and M. Shuaib: Modification of the decision-making capability in the social force model for the evacuation process, Transport Theory and Statistical Physics, 39(1), (2011), 47–70, DOI: 10.1080/00411450.2010.529979.
[22] H.-T. Zhang, M.Z. Chen, G.-B. Stan, and T. Zhou: Ultrafast consensus via predictive mechanisms, Europhysics Letters, 83, (2008), no. 40003.
[23] H.-T. Zhang, M.Z. Chen, G.-B. Stan, T. Zhou, and J.M.Maciejowski: Collective behaviour coordination with predictive mechanisms, IEEE Circuits Systems Magazine, 8, (2008) 67–85, DOI: 10.1109/MCAS.2008.928446.
[24] L. Zhang, J. Wang, and Q. Shi: Multi-agent based modeling and simulating for evacuation process in stadium, Journal of Systems Science and Complexity, 27(3), (2014), 430–444, DOI: 10.1007/s11424-014-3029-5.
[25] Y. Zheng, B. Jia, X.-G. Li, and N. Zhu: Evacuation dynamics with fire spreading based on cellular automaton, Physica A: Statistical Mechanics and Its Applications, 390(18-19), (2011), 3147–3156, DOI: 10.1016/j.physa.2011.04.011.
Go to article

Authors and Affiliations

Ricardo Almeida
1
Ewa Girejko
2
Luís Machado
3 4
Agnieszka B. Malinowska
2
Natália Martins
1

  1. Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810–193 Aveiro, Portugal
  2. Faculty of Computer Science, Bialystok University of Technology, 15-351 Białystok, Poland
  3. Institute of Systems and Robotics, DEEC – UC, 3030-290 Coimbra, Portugal
  4. Department of Mathematics, University of Trás-os-Montes e Alto Douro (UTAD), 5000-801 Vila Real, Portugal
Download PDF Download RIS Download Bibtex

Abstract

In modern society, people concern more about the evaluation of medical service quality. Evaluation of medical service quality is helpful for medical service providers to supervise and improve their service quality. Also, it will help the public to understand the situation of different medical providers. As a multi-criteria decision-making (MCDM) problem, evaluation of medical service quality can be effectively solved by aggregation operators in interval-valued q-rung dual hesitant fuzzy (IVq-RDHF) environment. Thus, this paper proposes interval-valued q-rung dual hesitant Maclaurin symmetric mean (IVq-RDHFMSM) operator and interval-valued q-rung dual hesitant weighted Maclaurin symmetric mean (IVq-RDHFWMSM) operator. Based on the proposed IVq-RDHFWMSM operator, this paper builds a novel approach to solve the evaluation problem of medical service quality including a criteria framework for the evaluation of medical service quality and a novel MCDM method. What’s more, aiming at eliminating the discordance between decision information and weight vector of criteria determined by decisionmakers (DMs), this paper proposes the concept of cross-entropy and knowledge measure in IVq-RDHF environment to extract weight vector from DMs’ decision information. Finally, this paper presents a numerical example of the evaluation of medical service for hospitals to illustrate the availability of the novel method and compares our method with other MCDM methods to demonstrate the superiority of our method. According to the comparison result, our method has more advantages than other methods.
Go to article

Bibliography

[1] C. Teng, C. Ing, H. Chang, and K. Chung: Development of service quality scale for surgical hospitalization. Journal of the Formosan Medical Association, 106(6), (2007), 475–484, DOI: 10.1016/S0929-6646(09)60297-7.
[2] I. Otay, B. Öztaysi, S. Çevik, and C. Kahraman: Multi-expert performance evaluation of healthcare institutions using an integrated intuitionistic fuzzy AHP&DEA methodology. Knowledge-Based Systems, 33 (2017), 90– 106, DOI: 10.1016/j.knosys.2017.06.028.
[3] J. Shieh, H. Wu, and K. Huang: A DEMATEL method in identifying key success factors of hospital service quality. Knowledge Based Systems, 23(3), (2010), 277–282, DOI: 10.1016/j.knosys.2010.01.013.
[4] M.L. Mccarthy, R. Ding, and S.L. Zeger: A randomized controlled trial of the effect of service delivery information on patient satisfaction in an emergency department fast track. Academic Emergency Medicine, 18(7), (2011), 674–685, DOI: 10.1111/j.1553-2712.2011.01119.x.
[5] L. Fei, J. Lu, and Y. Feng: An extended best-worst multi-criteria decisionmaking method by belief functions and its applications in hospital service evaluation. Computers&Industrial Engineering, 142, (2020), 106355, DOI: 10.1016/j.cie.2020.106355.
[6] E.K. Zavadskas, Z. Turskis, and S. Kildien˙e: State of art surveys of overviews on MCDM/MADM methods. Technological and Economic Development of Economy, 20(1), (2014), 165–179, DOI: 10.3846/20294913.2014.892037.
[7] Y. Xing, R. Zhang, M. Xia,and J. Wang: Generalized point aggregation operators for dual hesitant fuzzy information. Journal of Intelligent and Fuzzy Systems, 33(1), (2017), 515–527, DOI: 10.3233/JIFS-161922.
[8] F. Zhang, S.Wang, J. Sun, J. Ye, and G.K. Liew:Novel parameterized score functions on interval-valued intuitionistic fuzzy sets with three fuzziness measure indexes and their application. IEEE Access, 7, (2018), 8172–8180, DOI: 10.1109/ACCESS.2018.2885794.
[9] H. Zhang, R. Zhang, and H. Huang: Some picture fuzzy dombi heronian mean operators with their application to multi-attribute decision-making. Symmetry, 10(11), (2018), 593, DOI: 10.3390/sym10110593.
[10] K.T. Atanassov: Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), (1986), 87–96, DOI: 10.1016/S0165-0114(86)80034-3.
[11] R.R.Yager: Pythagorean membership grades in multicriteria decision making. IEEE Transactions on Fuzzy Systems, 22(4), (2014), 958–965, DOI: 10.1109/TFUZZ.2013.2278989.
[12] J. Wang, R. Zhang, X. Zhu, Z. Zhou, X. Shang, and W. Li: Some q-rung orthopair fuzzy Muirhead means with their application to multi-attribute group decision making. Journal of Intelligent and Fuzzy Systems, 36(2), (2019), 1599–1614, DOI: 10.3233/JIFS-18607.
[13] R.R. Yager: Generalized orthopair fuzzy sets. IEEE Transactions on Fuzzy Systems, 25(5), (2017), 1222–1230, DOI: 10.1109/TFUZZ.2016.2604005.
[14] P. Liu and P.Wang: Some q-rung orthopair fuzzy aggregation operators and their applications to multiple-attribute decision making. International Journal of Intelligent Systems, 33(4), (2017), 259–280, DOI: 10.1002/int.21927.
[15] C. Bonferroni: Sulle medie multiple di potenze. Bollettino dell’Unione Matematica Italiana, 5(3-4), (1950), 267–270. [16] S. Sykora: Mathematical means and averages: Generalized Heronian means. Stan’s Library, Ed. S. Sykora, 3, (2009), DOI: 10.3247/SL3Math 09.002.
[17] C. Maclaurin: A second letter to Martin Folkes, Esq.: concerning the roots of equations, with the demonstration of other rules in algebra. Phil, Transaction (1683–1775), 394, (1729), 59–96.
[18] R.F. Muirhead: Some methods applicable to identities and inequalities of symmetric algebraic functions of n letters. Proceedings of the Edinburgh Mathematical Societ., 21, (1902), 144–162, DOI: 10.1017/ S001309150003460X.
[19] P. Liu and J. Liu: Some q-rung orthopair fuzzy Bonferroni mean operators and their application to multi-attribute group decision making. International Journal of Intelligent Systems, 33(2), (2018), 315–347, DOI: 10.1002/int.21933.
[20] G. Wei, H. Gao, and Y. Wei: Some q-rung orthopair fuzzy Heronian mean operators in multiple attribute decision making. International Journal of Intelligent Systems, 33(7), (2017), 1426–1458, DOI: 10.1002/int.21985.
[21] P. Liu and D. Li: Some Muirhead mean operators for intuitionistic fuzzy numbers and their applications to group decision making. PloS ONE, 12(1), (2017), 423–431, DOI: 10.1371/journal.pone.0168767.
[22] G. Wu, H. Garg, H. Gao, and C. Wei: Interval-valued Pythagorean fuzzy maclaurin symmetric mean operators in multiple attribute decision making. IEEE Access, 99(1), (2018), 67866–67884, DOI: 10.1109/ACCESS.2018.2877725.
[23] K. Bai, X. Zhu, J. Wang, and R. Zhang: Some partitioned Maclaurin symmetric mean based on q-rung orthopair fuzzy information for dealing with multi-attribute group decision making. Symmetry, 10(9), (2018), 383, DOI: 10.3390/sym10090383.
[24] G. Wei and M. Lu: Pythagorean fuzzy Maclaurin symmetric mean operators in multiple attribute decision making. International Journal of Intelligent Systems, 33(6), (2017), 1043–1070, DOI: 10.1002/int.21911.
[25] J. Qin: Generalized Pythagorean fuzzy Maclaurin symmetric means and its application to multiple attribute SIR group decision model. Journal of Intelligent and Fuzzy Systems, 20(1), (2017), 943–957, DOI: 10.1007/s40815- 017-0439-2.
[26] P. Liu, and X. Qin: Maclaurin symmetric mean operators of linguistic intuitionistic fuzzy numbers and their application to multiple-attribute decisionmaking. Journal of Experimental & Theoretical Artificial Intelligence, 29(6), (2017), 1–30, DOI: 10.1080/0952813X.2017.1310309.
[27] H. Wang, P. Liu, and Z. Liu: Trapezoidal interval type-2 fuzzy Maclaurin symmetric mean operators and their applications to multiple attribute group decision making. International Journal for Uncertainty Quantification, 8(44), (2018), 343–360, DOI: 10.1615/Int.J.UncertaintyQuantification.2018020768.
[28] H. Garg: Hesitant Pythagorean fuzzy Maclaurin symmetric mean operators and its applications to multiattribute decision-making process. International Journal of Intelligent Systems, 34(4), (2019), 601–626, DOI: 10.1002/int.22067.
[29] K.T. Atanassov and G. Gargov: Interval valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 31, (1989), 343–349, DOI: 10.1016/0165-0114(89)90205-4.
[30] H. Garg: A novel accuracy function under interval-valued Pythagorean fuzzy environment for solving multicriteria decision making problem. Journal of Intelligent and Fuzzy Systems, 31(1), (2016), 529–540, DOI: 10.3233/IFS-162165.
[31] B.P. Joshi, A. Singh, P.K. Bhatt, and K.S. Vaisla: Interval valued q-rung orthopair fuzzy sets and their properties. Journal of Intelligent and Fuzzy Systems, 35(5), (2018), 5225–5230, DOI: 10.3233/JIFS-169806.
[32] H. Kalani, M. Akbarzadeh, A. Akbarzadeh, and I. Kardan: Intervalvalued fuzzy derivatives and solution to interval-valued fuzzy differential equations. Journal of Intelligent and Fuzzy Systems, 30(6), (2016), 3373– 3384, DOI: 10.3233/IFS-162085.
[33] T. Chen: An interval-valued Pythagorean fuzzy outranking method with a closeness-based assignment model for multiple criteria decision making. International Journal of Intelligent Systems, 33(2), (2017), 126–168, DOI: 10.1002/int.21943.
[34] Z. Li, G. Wei, and H. Gao: Methods for multiple attribute decision making with interval-valued Pythagorean fuzzy information. Mathematics, 6, (2018), 228, DOI: 10.3390/math6110228.
[35] N. Jan, T. Mahmood, L. Zedam, K.Ullah, J.C. Alcantud, and B.Davvaz: Analysis of social networks, communication networks and shortest path problems in the environment of interval valued q-rung orthopair fuzzy information. Journal of Intelligent and Fuzzy Systems, 21, (2019), 1687– 1708, DOI: 10.1007/s40815-019-00643-9.
[36] H. Gao, Y. Ju, W. Zhang, and D. Ju: Multi-attribute decision-making method based on interval-valued q-rung orthopair fuzzy archimedean Muirhead mean operators. IEEE Access, 99(1), (2019), 74300–74315, DOI: 10.1109/ACCESS.2019.2918779.
[37] V. Torra: Hesitant fuzzy sets. International Journal of Intelligent Systems, 25(6), (2010), 529–539, DOI: 10.1002/int.20418.
[38] B. Zhu, Z. Xu, and M. Xia: Dual hesitant fuzzy sets. Journal of Applied Mathematics, 2012, (2012), 1–13, DOI: 10.1155/2012/879629.
[39] D. Yu, W. Zhang, and G.Q. Huang: Dual hesitant fuzzy aggregation operators. textitTechnological and Economic Development of Economy, 22(2), (2015), 1–16, DOI: 10.3846/20294913.2015.1012657.
[40] Y. Xing, R. Zhang, M. Xia, and J. Wang: Generalized point aggregation operators for dual hesitant fuzzy information. Journal of Intelligent and Fuzzy Systems, 33(1), (2017), 515–527, DOI: 10.3233/JIFS-161922.
[41] Z. Su, Z. Xu, H. Zhao, and S. Liu: Distribution-based approaches to deriving weights from dual hesitant fuzzy information. Symmetry, 11(1), (2019), 85, DOI: 10.3390/sym11010085.
[42] G. Maity, D. Mardanya, S.K. Roy, and G.W. Weber: A new approach for solving dual-hesitant fuzzy transportation problem with restrictions, S¯adhan¯a, 44(75), (2019), DOI: 10.1007/s12046-018-1045-1.
[43] G. Qu, Q. An, W. Qu, F. Deng, and T. Li: Multiple attribute decision making based on bidirectional projection measures of dual hesitant fuzzy set. Journal of Intelligent and Fuzzy Systems, 7(5), (2019), 7087–7102, DOI: 10.3233/JIFS-181970.
[44] Y. Xu, X. Shang, J.Wang, H. Zhao, R. Zhang, and K. Bai: Some intervalvalued q-rung dual hesitant fuzzy Muirhead mean operators with their application to multi-attribute decision-making. IEEE Access, 99(1), (2019), 54724–54745, DOI: 10.1109/ACCESS.2019.2912814.
[45] T. Zhu, L. Luo, H. Liao, X. Zhang, and W. Shen: A hybrid multicriteria decision making model for elective admission control in a Chinese public hospital. Knowledge-Based Systems, 173, (2019), 37–51, DOI: 10.1016/j.knosys.2019.02.020.
[46] X. Gou, Z. Xu, H. Liao, and F. Herrera: Multiple criteria decision making based on distance and similarity measures under double hierarchy hesitant fuzzy linguistic environment. Computers & Industrial Engineering, 126, (2018), 516–530, DOI: 10.1016/j.cie.2018.10.020.
[47] Y. Xu, X. Shang, J. Wang, W. Wu, and H. Huang: Some q-rung dual hesitant fuzzy Heronian mean operators with their application to multiple attribute group decision-making. Symmetry, 10(10), (2018), 472, DOI: 10.3390/sym10100472.
[48] Y. Ju, X. Liu, and S. Yang: Interval-valued dual hesitant fuzzy aggregation operators and their applications to multiple attribute decision making. Journal of Intelligent and Fuzzy Systems, 27(3), (2014), 1203–1218, DOI: 10.3233/IFS-131085.
[49] W. Yang and Y. Pang: Hesitant interval-valued Pythagorean fuzzy VIKOR method. International Journal of Intelligent Systems, 34(5), (2018), 754– 789, DOI: 10.1002/int.22075.
[50] H. Hiidenhovi, P. Laippala, and K. Nojonen: Development of a patientorientated instrument to measure service quality in outpatient departments. Journal of Advanced Nursing, 34(5), (2001), 696–705, DOI: 10.1046/j.1365-2648.2001.01799.x.
[51] L. Li and W. Benton: Hospital capacity management decisions: Emphasis on cost control and quality enhancement. European Journal of Operational Research, 146(3), (2003), 596–614, DOI: 10.1016/S0377-2217(02)00225-4.
[52] C. Tian, Y. Tian, and L. Zhang: An evaluation scale of medical services quality based on “patients’ experience”. Journal of Huazhong University of Science and Technology [Medical Sciences], 34, (2014), 289–297, DOI: 10.1007/s11596-014-1273-5.
[53] S. Das, B. Dutta, and De. Guha: Weight computation of criteria in a decision-making problem by knowledge measure with intuitionistic fuzzy set and interval-valued intuitionistic fuzzy set. Soft Computing, 20(9), (2016), 3421–3442, DOI: 10.1007/s00500-015-1813-3.
[54] W. Zhang, X. Li, and Y. Ju: Some aggregation operators based on Einstein operations under interval-valued dual hesitant fuzzy setting and their application. Mathematical Problems in Engineering, 1, (2014), DOI: 10.1155/2014/958927.
[55] K. Rahman, S. Abdullah, M. Shakeel, M.S. Khan, and M. Ullah: Interval-valued Pythagorean fuzzy geometric aggregation operators and their application to group decision making problem. Cogent Mathematics, 4, (2017), DOI: 10.1080/23311835.2017.1338638.
[56] Y. Zang, X. Zhao, and S. Li: Interval-valued dual hesitant fuzzy Heronian mean aggregation operators and their application to multi-attribute decision making, International Journal of Computational Intelligence and Applications, 17(4), (2018), DOI: 10.1142/S1469026818500050.
[57] J. Wang, X. Shang, X. Feng, and M. Sun: A novel multiple attribute decision making method based on q-rung dual hesitant uncertain linguistic sets and Muirhead mean. Archives of Control Sciences, 30(2), (2020), 233– 272, DOI: 10.24425/acs.2020.133499.
[58] L. Li, R. Zhang, J. Wang, and X. Shang: Some q-orthopair linguistic Heronian mean operators with their application to multi-attribute group decision making. Archives of Control Sciences, 28(4), (2018), 551–583, DOI: 10.24425/acs.2018.125483.
[59] A. Biswas and A. Sarkar: Development of dual hesitant fuzzy prioritized operators based on Einstein operations with their application to multicriteria group decision making. Archives of Control Sciences, 28(4), (2018), 527–549, DOI: 10.24425/acs.2018.125482.
Go to article

Authors and Affiliations

Butian Zhao
1
Runtong Zhang
1
Yuping Xing
2

  1. School of Management and Economic, Beijing Jiaotong University, Beijing, 100044, China
  2. Glorious Sun School of Business and Management, DongHua University, Shanghai, 200051, China
Download PDF Download RIS Download Bibtex

Abstract

In this paper, we introduce necessary and sufficient efficiency conditions associated with a class of multiobjective fractional variational control problems governed by geodesic quasiinvex multiple integral functionals and mixed constraints containing m-flow type PDEs. Using the new notion of ( normal) geodesic efficient solution, under ( p; b)-geodesic quasiinvexity assumptions, we establish sufficient efficiency conditions for a feasible solution.
Go to article

Bibliography

[1] R.P. Agarwal, I. Ahmad, A. Iqbal, and S. Ali: Generalized invex sets and preinvex functions on Riemannian manifolds, Taiwanese J. Math., 16(5), (2012), 1719–1732, DOI: 10.11650/twjm/1500406792.
[2] T. Antczak: G-pre-invex functions in mathematical programming, J. Comput. Appl. Math., 217(1), (2008), 212–226, DOI: 10.1016/j.cam.2007.06.026.
[3] M. Arana-Jimenez, B. Hernandez-Jimenez, G. Ruiz-Garzon, and A. Rufian-Lizana: FJ-invex control problem, Appl. Math. Lett., 22(12), (2009), 1887–1891, DOI: 10.1016/j.aml.2009.07.016.
[4] A. Barani and M.R. Pouryayevali: Invex sets and preinvex functions on Riemannian manifolds, J. Math. Anal. Appl., 328(2), (2007), 767–779, DOI: 10.1016/j.jmaa.2006.05.081.
[5] M.A. Hanson: On sufficiency of Kuhn-Tucker conditions, J. Math. Anal. Appl., 80(2), (1981), 545–550, DOI: 10.1016/0022-247X(81)90123-2.
[6] R. Jagannathan: Duality for nonlinear fractional programs, Z. Oper. Res., 17(1-3), (1973), DOI: 10.1007/BF01951364.
[7] V. Jeyakumar: Strong and weak invexity in mathematical programming, Research report (University of Melbourne, Department of Mathematics), 1984, no. 29.
[8] D.H. Martin: The essence of invexity, J. Optim. Theory Appl., 47(1), (1985), 65–76, DOI: 10.1007/BF00941316.
[9] St. Mititelu: Optimality and duality for invex multi-time control problems with mixed constraints, J. Adv. Math. Stud., 2(1), (2009), 25–34.
[10] St. Mititelu, M.Constantinescu, and C. Udriste: Efficiency for multitime variational problems with geodesic quasiinvex functionals on Riemannian manifolds, BSG Proceedings 22. The Intern. Conf. “Differential Geometry – Dynamical Systems”, September 1-4, 2014, Mangalia-Romania, pp. 38–50. Balkan Society of Geometers, Geometry Balkan Press 2015.
[11] St. Mititelu and S. Treanta: Efficiency conditions in vector control problems governed by multiple integrals, J. Appl. Math. Comput., 57(1-2), (2018), 647–665, DOI: 10.1007/s12190-017-1126-z.
[12] M.A. Noor and K.I. Noor: Some characterizations of strongly preinvex functions, J. Math. Anal. Appl., 316(2), (2006), 697–706, DOI: 10.1016/ j.jmaa.2005.05.014.
[13] V.A. de Oliveira and G.N. Silva: On sufficient optimality conditions for multiobjective control problems, J. Global Optim., 64(4), (2016), 721–744, DOI: 10.1007/s10898-015-0351-y.
[14] R. Pini: Convexity along curves and indunvexity, Optimization, 29(4), (1994), 301–309, DOI: 10.1080/02331939408843959.
[15] T. Rapcsak: Smooth Nonlinear Optimization in Rn, Nonconvex Optimization and Its Applications, Kluwer Academic, 1997.
[16] W. Tang and X. Yang: The sufficiency and necessity conditions of strongly preinvex functions, OR Transactions, 10, 3, (2006), 50–58. [17] S. Treanta: PDEs of Hamilton-Pfaff type via multi-time optimization problems, U.P.B. Sci. Bull., Series A: Appl. Math. Phys., 76(1), (2014), 163–168.
[18] S. Treanta: Optimal control problems on higher order jet bundles. The Intern. Conf. “Differential Geometry – Dynamical Systems”, October 10- 13, 2013, Bucharest-Romania, pp. 181–192. Balkan Society of Geometers, Geometry Balkan Press 2014.
[19] S. Treanta: Multiobjective fractional variational problem on higherorder jet bundles, Commun. Math. Stat., 4(3), (2016), 323–340, DOI: 10.1007/s40304-016-0087-0.
[20] S. Treanta: Higher-order Hamilton dynamics and Hamilton-Jacobi divergence PDE, Comput. Math. Appl., 75(2), (2018), 547–560, DOI: 10.1016/j.camwa.2017.09.033.
[21] S. Treanta and M. Arana-Jimenez: KT-pseudoinvex multidimensional control problem, Optim. Control Appl. Meth., 39(4), (2018), 1291–1300, DOI: 10.1002/oca.2410.
[22] S. Treanta and M. Arana-Jimenez: On generalized KT-pseudoinvex control problems involving multiple integral functionals, Eur. J. Control, 43, (2018), 39–45, DOI: 10.1016/j.ejcon.2018.05.004.
[23] S. Treanta: Efficiency in generalized V-KT-pseudoinvex control problems, Int. J. Control, 93(3), (2020), 611–618, DOI: 10.1080/00207179.2018.1483082.
[24] C. Udriste: Convex Functions and Optimization Methods on Riemannian Manifolds, Mathematics and Its Applications, KluwerAcademic, 297, 1994.
[25] T. Weir and B. Mond: Pre-invex functions in multiple objective optimization, J. Math. Anal. Appl., 136(1), (1988), 29–38, DOI: 10.1016/0022-247X(88)90113-8.
Go to article

Authors and Affiliations

Savin Treanţă
1
Ştefan Mititelu
2

  1. University “Politehnica”of Bucharest, Faculty of Applied Sciences, Department of Applied Mathematics, 313 Splaiul Independentei, 060042 – Bucharest, Romania
  2. Technical University of Civil Engineering, Department of Mathematics and Informatics, 124 Lacul Tei, 020396 – Bucharest, Romania
Download PDF Download RIS Download Bibtex

Abstract

This paper presents a new grid integration control scheme that employs spider monkey optimization technique for maximum power point tracking and Lattice Levenberg Marquardt Recursive estimation with a hysteresis current controller for controlling voltage source inverter. This control scheme is applied to a PV system integrated to a three phase grid to achieve effective grid synchronization. To verify the efficacy of the proposed control scheme, simulations were performed. From the simulation results it is observed that the proposed controller provides excellent control performance such as reducing THD of the grid current to 1.75%.
Go to article

Bibliography

[1] I. Dincer: Renewable energy and sustainable development: a crucial review. Renewable and Sustainable Energy Reviews, 4(2), (2000), 157–175, DOI: 10.1016/S1364-0321(99)00011-8.
[2] S. Gulkowski, J.V.M. Diez, J.A. Tejero, and G. Nofuentes: Computational modeling and experimental analysis of heterojunction with intrinsic thin-layer photovoltaic module under different environmental conditions. Energy, 172, (2019), 380–390, DOI: 10.1016/j.energy.2019.01.107.
[3] M. Bahrami, et al.: Hybrid maximum power point tracking algorithm with improved dynamic performance. Renewable Energy, 130, (2019), 982–991, DOI: 10.1016/j.renene.2018.07.020.
[4] K.V. Singh, Krishna, H. Bansal, and D. Singh: A comprehensive review on hybrid electric vehicles: architectures and components. Journal of Modern Transportation, 27, (2019), 1–31, DOI: 10.1007/s40534-019-0184-3.
[5] S. Pradhan, et al.: Performance Improvement of Grid-Integrated Solar PV System Using DNLMS Control Algorithm. IEEE Transactions on Industry Applications, 55(1), (2019), 78–91, DOI: 10.1109/TIA.2018.2863652.
[6] S. Negari and D. Xu: Utilizing a Lagrangian approach to compute maximum fault current in hybrid AC–DC distribution grids withMMCinterface. High Voltage, 4(1), (2019), 18–27, DOI: 10.1049/hve.2018.5087.
[7] V.T. Tran et al.: Mitigation of Solar PV Intermittency Using Ramp-Rate Control of Energy Buffer Unit. IEEE Transactions on Energy Conversion, 34(1), (2019), 435–445, DOI: 10.1109/TEC.2018.2875701.
[8] A. Kihal, et al.: An improved MPPT scheme employing adaptive integral derivative sliding mode control for photovoltaic systems under fast irradiation changes. ISA Transactions, 87, (2019), 297–306, DOI: 10.1016/j.isatra.2018.11.020.
[9] A.M. Jadhav, N.R. Patne, and J.M. Guerrero: A novel approach to neighborhood fair energy trading in a distribution network of multiple microgrid clusters. IEEE Transactions on Industrial Electronics, 66(2), (2019), 1520– 1531, DOI: 10.1109/TIE.2018.2815945.
[10] A. Fragaki, T. Markvart, and G. Laskos: All UK electricity supplied by wind and photovoltaics – The 30–30 rule. Energy, 169, (2019), 228–237, DOI: 10.1016/j.energy.2018.11.151.
[11] S.Z. Ahmed, et al.: Power quality enhancement by using D-FACTS systems applied to distributed generation. International Journal of Power Electronics and Drive Systems, 10(1), (2019), 330, DOI: 10.11591/ijpeds.v10.i1.pp330-341.
[12] H.H. Alhelou, et al.: A Survey on Power System Blackout and Cascading Events: Research Motivations and Challenges. Energies. 12(4), (2019), 1– 28, DOI: 10.3390/en12040682.
[13] M. Badoni, A. Singh, and B. Singh: Implementation of Immune Feedback Control Algorithm for Distribution Static Compensator. IEEE Transactions on Industry Applications, 55(1), (2019), 918–927, DOI: 10.1109/TIA.2018.2867328.
[14] S.R. Das, et al.: Performance evaluation of multilevel inverter based hybrid active filter using soft computing techniques. Evolutionary Intelligence (2019), 1–11, DOI: 10.1007/s12065-019-00217-6.
[15] F. Chishti, S. Murshid, and B. Singh: LMMN Based Adaptive Control for Power Quality Improvement of Grid Intertie Wind-PV System. IEEE Transactions on Industrial Informatics, 15(9), (2019), 4900–4912, DOI: 10.1109/TII.2019.2897165.
[16] S. Pradhan, et al.: Performance Improvement of Grid-Integrated Solar PV System Using DNLMS Control Algorithm. IEEE Transactions on Industry Applications, 55(1), (2019), 78–91, DOI: 10.1109/IICPE.2016.8079455.
[17] V. Jain, I. Hussain, and B. Singh: A HTF-Based Higher-Order Adaptive Control of Single-Stage Grid-Interfaced PV System. IEEE Transactions on Industry Applications, 55(2), (2019), 1873–1881, DOI: 10.1109/TIA.2018.2878186.
[18] N. Kumar, B. Singh, B. Ketan Panigrahi and L. Xu: Leaky Least Logarithmic Absolute Difference Based Control Algorithm and Learning Based InC MPPT Technique for Grid Integrated PV System. IEEE Transactions on Industrial Electronics. 66(11), (2019), 9003–9012, DOI: 10.1109/TIE.2018.2890497.
[19] P. Shah, I. Hussain, and B. Singh: Single-Stage SECS Interfaced with Grid Using ISOGI-FLL- Based Control Algorithm. IEEE Transactions on Industry Applications, 55(1), (2019), 701–711, DOI: 10.1109/TIA.2018.2869880.
[20] V. Jain and B. Singh: A Multiple Improved Notch Filter-Based Control for a Single-StagePVSystem Tied to aWeak Grid. IEEE Transactions on Sustainable Energy, 10(1), (2019), 238–247, DOI: 10.1109/TSTE.2018.2831704.
[21] N. Mohan and T. M. Undeland: Power electronics: converters, applications, and design. John Wiley & Sons, 2007.
[22] M. Badoni, et al.: Grid interfaced solar photovoltaic system using ZA-LMS based control algorithm. Electric Power Systems Research, 160, (2018), 261–272, DOI: 10.1016/j.epsr.2018.03.001.
[23] M. Rezkallah, et al.: Lyapunov function and sliding mode control approach for the solar-PV grid interface system. IEEE Transactions on Industrial Electronics, 64(1), (2016), 785–795, DOI: 10.1109/tie.2016.2607162.
[24] N. Kumar, B. Singh, and B.K. Panigrahi: Integration of Solar PV with Low- Voltage Weak Grid System: using Maximize-M Kalman Filter and Self-Tuned P&O Algorithm. IEEE Transactions on Industrial Electronics, 66(11), (2019), 9013–9022, DOI: 10.1109/tie.2018.2889617.
[25] H. Sharma, G. Hazrati, and J.Ch.Bansal: Spider monkey optimization algorithm. Evolutionary and swarm intelligence algorithms. Springer, Cham, 2019, 43–59.
[26] K. Neelu, P. Devan, Ch.L. Chowdhary, S. Bhattacharya, G. Singh, S. Singh, and B. Yoon: Smo-dnn: Spider monkey optimization and deep neural network hybrid classifier model for intrusion detection. Electronics, 9(4), (2020), 692, DOI: 10.3390/electronics9040692.
[27] M.A.H. Akhand, S.I. Ayon, A.A. Shahriyar, and N. Siddique: Discrete spider monkey optimization for travelling salesman problem. Applied Soft Computing, 86 (2020), DOI: 10.1016/j.asoc.2019.105887.
[28] Avinash Sharma, Akshay Sharma, B.K. Panigrahi, D. Kiran, and R. Kumar: Ageist spider monkey optimization algorithm. Swarm and Evolutionary Computation, 28 (2016), 58–77, DOI: 10.1016/j.swevo.2016.01.002.
[29] Sriram Mounika and K. Ravindra: Backtracking Search Optimization Algorithm Based MPPT Technique for Solar PV System. In Advances in Decision Sciences, Image Processing, Security and Computer Vision. Springer, Cham, 2020, 498–506.
[30] Pilakkat, Deepthi and S. Kanthalakshmi: Single phase PV system operating under Partially Shaded Conditions with ABC-PO as MPPT algorithm for grid connected applications. Energy Reports, 6 (2020), 1910–1921, DOI: 10.1016/j.egyr.2020.07.019.
[31] R. Gessing: Controllers of the boost DC-DC converter accounting its minimum- and non-minimum-phase nature. Archives of Control Sciences, 19(3), (2009), 245–259.
[32] A. Talha and H. Boumaaraf: Evaluation of maximum power point tracking methods for photovoltaic systems. Archives of Control Sciences, 21(2), (2011), 151–165.
[33] S.N. Singh and S. Mishra: FPGA implementation of DPWM utility/DG interfaced solar (PV) power converter for green home power supply. Archives of Control Sciences, 21(4), (2011), 461–469.
Go to article

Authors and Affiliations

Dipak Kumar Dash
1
Pradip Kumar Sadhu
1
Bidyadhar Subudhi
2

  1. Department of Electrical Engineering, Indian Institute of Technology (ISM), Dhanbad, India
  2. School of Electrical Sciences, Indian Institute of Technology Goa, GEC Campus, Farmagudi, Ponda-401403, Goa, India
Download PDF Download RIS Download Bibtex

Abstract

The purpose of this paper is to introduce a new chaotic oscillator. Although different chaotic systems have been formulated by earlier researchers, only a few chaotic systems exhibit chaotic behaviour. In this work, a new chaotic system with chaotic attractor is introduced. It is worth noting that this striking phenomenon rarely occurs in respect of chaotic systems. The system proposed in this paper has been realized with numerical simulation. The results emanating from the numerical simulation indicate the feasibility of the proposed chaotic system. More over, chaos control, stability, diffusion and synchronization of such a system have been dealt with.
Go to article

Bibliography

[1] M.P. Kennedy: Chaos in the Colpitts oscillator. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 41 (1994), 771–774, DOI: 10.1109/81.331536.
[2] S. Vaidyanathan, K. Rajagopal, C.K. Volos, I.M. Kyprianidis, and I.N. Stouboulos: Analysis, adaptive control and synchronization of a seventerm novel 3-D chaotic system with three quadratic nonlinearities and its digital implementation in labview. Journal of Engineering Science and Technology Review, 8 (2015), 130–141.
[3] P. Kvarda: Identifying the deterministic chaos by using the Lyapunov exponents. Radioengineering-Prague, 10 (2001), 38–38.
[4] Y.C. Lai and C. Grebogi: Modeling of coupled chaotic oscillators. Physical Review Letters, 82 (1999), 4803, DOI: 10.1103/PhysRevLett.82.4803.
[5] H. Deng and D. Wang: Circuit simulation and physical implementation for a memristor-based Colpitts oscillator. AIP Advances, 7 (2017), 035118, DOI: 10.1063/1.4979175.
[6] A. Cenys, A. Tamasevicius, A.Baziliauskas, R. Krivickas, and E. Lind- berg: Hyperchaos in coupled Colpitts oscillators. Chaos, Solitons & Fractals, 17 (2003), DOI: 10.1016/S0960-0779(02)00373-9.
[7] C.M. Kim, S. Rim, W.H. Kye, J.W. Ryu, and Y.J. Park: Anti-synchronization of chaotic oscillators. Physics Letters A, 320 (2003), 39–46, DOI: 10.1016/j.physleta.2003.10.051.
[8] A.S. Elwakil and M.P. Kennedy: A family of Colpitts-like chaotic oscillators. Journal of the Franklin Institute, 336 (1999), 687–700, DOI: 10.1016/S0016-0032(98)00046-5.
[9] S. Vaidyanathan, A. Sambas, and S. Zhang: A new 4-D dynamical system exhibiting chaos with a line of rest points, its synchronization and circuit model. Archives of Control Sciences, 29 (2019), DOI: 10.24425/acs.2019.130202.
[10] C.K. Volos, V.T. Pham, S. Vaidyanathan, I.M. Kyprianidis, and I.N. Stouboulos: Synchronization phenomena in coupled Colpitts circuits. Journal of Engineering Science & Technology Review, 8 (2015).
[11] H. Fujisaka and T. Yamada: Stability theory of synchronized motion in coupled-oscillator systems. Progress of theoretical physics, 69 (1983), 32– 47, DOI: 10.1143/PTP.69.32.
[12] N.J. Corron, S.D. Pethel, and B.A. Hopper: Controlling chaos with simple limiters. Physical Review Letters, 84 (2000), 3835, DOI: 10.1103/Phys-RevLett.84.3835.
[13] J.Y. Effa, B.Z. Essimbi, and J.M. Ngundam: Synchronization of improved chaotic Colpitts oscillators using nonlinear feedback control. Nonlinear Dynamics, 58 (2009), 39–47, DOI: 10.1007/s11071-008-9459-7.
[14] S. Mishra, A.K. Singh, and R.D.S. Yadava: Effects of nonlinear capacitance in feedback LC-tank on chaotic Colpitts oscillator. Physica Scripta, 95 (2020), 055203. DOI: 10.1088/1402-4896/ab6f95.
[15] S. Vaidyanathan and S. Rasappan: Global chaos synchronization of nscroll Chua circuit and Lur’e system using backstepping control design with recursive feedback. Arabian Journal for Science and Engineering, 39 (2014), 3351–3364, DOI: 10.1007/s13369-013-0929-y.
[16] R. Suresh and V. Sundarapandian: Hybrid synchronization of nscroll Chua and Lur’e chaotic systems via backstepping control with novel feedback. Archives of Control Sciences, 22 (2012), 343–365, DOI: 10.2478/v10170-011-0028-9.
[17] S. Rasappan: Synchronization of neuronal bursting using backstepping control with recursive feedback. Archives of Control Sciences, 29 (2019), 617–642, DOI: 10.24425/acs.2019.131229.
[18] H.B. Fotsin and J.Daafouz:Adaptive synchronization of uncertain chaotic Colpitts oscillators based on parameter identification. Physics Letters A, 339 (2005), 304–315, DOI: 10.1016/j.physleta.2005.03.049.
[19] S. Sarkar, S. Sarkar, and B.C. Sarkar: On the dynamics of a periodic Colpitts oscillator forced by periodic and chaotic signals. Communications in Nonlinear Science and Numerical Simulation, 19 (2014), 2883–2896, DOI: 10.1016/j.cnsns.2014.01.004.
[20] S.T. Kammogne and H.B. Fotsin: Synchronization of modified Colpitts oscillators with structural perturbations. Physica scripta, 83 (2011), 065011, DOI: 10.1088/0031-8949/83/06/065011.
[21] S.T. Kammogne and H.B. Fotsin: Adaptive control for modified projective synchronization-based approach for estimating all parameters of a class of uncertain systems: case of modified Colpitts oscillators. Journal of Chaos, (2014), DOI: 10.1155/2014/659647.
[22] L.M. Pecora and T.L. Carroll: Synchronization in chaotic systems. Physical review letters, 64 (1990), 821, DOI: 10.1103/PhysRevLett.64.821.
[23] I. Ahmad and B. Srisuchinwong: A simple two-transistor 4D chaotic oscillator and its synchronization via active control. IEEE 26th International Symposium on Industrial Electronics, (2017) 1249–1254, DOI: 10.1109/ISIE.2017.8001424.
[24] S. Bumelien˙e, A. Tamasevicius, G. Mykolaitis, A. Baziliauskas, and E. Lindber: Numerical investigation and experimental demonstration of chaos from two-stage Colpitts oscillator in the ultrahigh frequency range. Nonlinear Dynamics, 44 (2006), 167–172, DOI: 10.1007/s11071-006-1962-0.
[25] F.Q. Wu, J. Ma, and G.D. Ren: Synchronization stability between initialdependent oscillators with periodical and chaotic oscillation. Journal of Zhejiang University-Science A, 19 (2018), 889–903, DOI: 10.1631/jzus.a1800334.
[26] G.H. Li, S.P. Zhou, and K. Yang: Controlling chaos in Colpitts oscillator. Chaos, Solitons & Fractals, 33 (2007), 582–587, DOI: 10.1016/j.chaos.2006.01.072.
[27] S. Vaidyanathan, S.A.J.A.D. Jafari, V.T. Pham, A.T. Azar, and F.E. Al- saadi: A 4-D chaotic hyperjerk system with a hidden attractor, adaptive backstepping control and circuit design. Archives of Control Sciences, 28 (2018), 239–254, DOI: 10.24425/123458.
[28] J.H. Park: Adaptive control for modified projective synchronization of a four-dimensional chaotic system with uncertain parameters. Journal of Computational and Applied Mathematics, 213 (2008), 288–293. DOI: 10.1016/j.cam.2006.12.003.
[29] M. Rehan: Synchronization and anti-synchronization of chaotic oscillators under input saturation. Applied Mathematical Modelling, 37 (2013), 6829– 6837. DOI: 10.1016/j.apm.2013.02.023.
[30] M.C. Liao, G. Chen, J.Y. Sze, and C.C. Sung: Adaptive control for promoting synchronization design of chaotic Colpitts oscillators. Journal of the Chinese Institute of Engineers, 31 (2008), 703–707. DOI: 10.1080/02533839.2008.9671423.
[31] S. Rasappan and S. Vaidyanathan: Hybrid synchronization of n-scroll chaotic Chua circuits using adaptive backstepping control design with recursive feedback. Malaysian Journal of Mathematical Sciences, 7 (2013), 219–246. DOI: 10.1080/23311916.2015.1009273.
[32] J. Kengne, J.C. Chedjou, G. Kenne, and K. Kyamakya: Dynamical properties and chaos synchronization of improved Colpitts oscillators. Communications in Nonlinear Science and Numerical Simulation, 17 (2012), 2914–2923. DOI: 10.1016/j.cnsns.2011.10.038.
[33] W. Hahn: Stability of motion. Springer, 138, 1967.
[34] J.P. Singh and B.K. Roy: The nature of Lyapunov exponents is (+,+,-,-). Is it a hyperchaotic system? Chaos, Solitons & Fractals, 92 (2016), 73–85. DOI: 10.1016/j.chaos.2016.09.010.
[35] A. Wolf, J.B. Swift, H.L. Swinney, and J.A. Vastano: Determining Lyapunov exponents from a time series. Physica D: Nonlinear Phenomena, 16 (1985), 285–317. DOI: 10.1016/0167-2789(85)90011-9.
Go to article

Authors and Affiliations

Suresh Rasappan
1
K.A. Niranjan Kumar
1

  1. Department of Mathematics, Vel Tech Rangarajan Dr.Sagunthala R&D Institute of Science and Technology, Avadi, Chennai-62, India
Download PDF Download RIS Download Bibtex

Abstract

Dynamics and control of discrete chaotic systems of fractional-order have received considerable attention over the last few years. So far, nonlinear control laws have been mainly used for stabilizing at zero the chaotic dynamics of fractional maps. This article provides a further contribution to such research field by presenting simple linear control laws for stabilizing three fractional chaotic maps in regard to their dynamics. Specifically, a one-dimensional linear control law and a scalar control law are proposed for stabilizing at the origin the chaotic dynamics of the Zeraoulia-Sprott rational map and the Ikeda map, respectively. Additionally, a two-dimensional linear control law is developed to stabilize the chaotic fractional flow map. All the results have been achieved by exploiting new theorems based on the Lyapunov method as well as on the properties of the Caputo h-difference operator. The relevant simulation findings are implemented to confirm the validity of the established linear control scheme.
Go to article

Bibliography

[1] C. Goodrich and A.C. Peterson: Discrete Fractional Calculus. Springer: Berlin, Germany, 2015, ISBN 978-3-319-79809-7.
[2] P. Ostalczyk: Discrete Fractional Calculus: Applications in Control and Image Processing. World Scientific, 2016.
[3] K. Oprzedkiewicz and K. Dziedzic: Fractional discrete-continuous model of heat transfer process. Archives of Control Sciences, 31(2), (2021), 287– 306, DOI: 10.24425/acs.2021.137419.
[4] T. Kaczorek and A. Ruszewski: Global stability of discrete-time nonlinear systems with descriptor standard and fractional positive linear parts and scalar feedbacks. Archives of Control Sciences, 30(4), (2020), 667–681, DOI: 10.24425/acs.2020.135846.
[5] J.B. Diaz and T.J. Olser: Differences of fractional order. Mathematics of Computation, 28 (1974), 185–202, DOI: 10.1090/S0025-5718-1974-0346352-5.
[6] F.M. Atici and P.W. Eloe: A transform method in discrete fractional calculus. International Journal of Difference Equations, 2 (2007), 165–176.
[7] F.M. Atici and P.W. Eloe: Discrete fractional calculus with the nabla operator. Electronic Journal of Qualitative Theory of Differential Equations, Spec. Ed. I, 3 , (2009), 1–12.
[8] G. Anastassiou: Principles of delta fractional calculus on time scales and inequalities. Mathematical and Computer Modelling, 52(3-4), (2010), 556– 566, DOI: 10.1016/j.mcm.2010.03.055.
[9] T. Abdeljawad: On Riemann and Caputo fractional differences. Computers and Mathematics with Applications, 62(3), (2011), 1602–1611, DOI: 10.1016/j.camwa.2011.03.036.
[10] M. Edelman, E.E.N. Macau, and M.A.F. Sanjun (Eds.): Chaotic, Fractional, and Complex Dynamics: New Insights and Perspectives. Springer International Publishing, 2018.
[11] G.C. Wu, D. Baleanu, and S.D. Zeng: Discrete chaos in fractional sine and standard maps. Physics Letters A, 378(5-6), (2014), 484–487, DOI: 10.1016/j.physleta.2013.12.010.
[12] G.C. Wu and D. Baleanu: Discrete fractional logistic map and its chaos. Nonlinear Dynamics, 75(1-2), (2014), 283–287, DOI: 10.1007/s11071-013-1065-7.
[13] T. Hu: Discrete chaos in fractional Henon map. Applied Mathematics, 5(15), (2014), 2243–2248, DOI: 10.4236/am.2014.515218.
[14] G.C. Wu and D. Baleanu: Discrete chaos in fractional delayed logistic maps. Nonlinear Dynamics, 80 (2015), 1697–1703, DOI: 10.1007/s11071-014-1250-3.
[15] M.K. Shukla and B.B. Sharma: Investigation of chaos in fractional order generalized hyperchaotic Henon map. International Journal of Electronics and Communications, 78 (2017), 265–273, DOI: 10.1016/j.aeue.2017.05.009.
[16] A. Ouannas, A.A. Khennaoui, S. Bendoukha, and G. Grassi: On the dynamics and control of a fractional form of the discrete double scroll. International Journal of Bifurcation and Chaos, 29(6), (2019), DOI: 10.1142/S0218127419500780.
[17] L. Jouini, A. Ouannas, A.A. Khennaoui, X. Wang, G. Grassi, and V.T. Pham: The fractional form of a new three-dimensional generalized Henon map. Advances in Difference Equations, 122 (2019), DOI: 10.1186/s13662-019-2064-x.
[18] F. Hadjabi, A. Ouannas,N. Shawagfeh, A.A. Khennaoui, and G. Grassi: On two-dimensional fractional chaotic maps with symmetries. Symmetry, 12(5), (2020), DOI: 10.3390/sym12050756.
[19] D. Baleanu, G.C. Wu, Y.R. Bai, and F.L. Chen: Stability analysis of Caputo-like discrete fractional systems. Communications in Nonlinear Science and Numerical Simulation, 48 (2017), 520–530, DOI: 10.1016/j.cnsns.2017.01.002.
[20] A-A. Khennaoui, A. Ouannas, S. Bendoukha, G. Grassi, X. Wang, V-T. Pham, and F.E. Alsaadi: Chaos, control, and synchronization in some fractional-order difference equations. Advances in Difference Equations, 412 (2019), DOI: 10.1186/s13662-019-2343-6.
[21] A. Ouannas, A.A. Khennaoui, G. Grassi, and S. Bendoukha: On chaos in the fractional-order Grassi-Miller map and its control. Journal of Computational and Applied Mathematics, 358(2019), 293–305, DOI: 10.1016/j.cam.2019.03.031.
[22] A. Ouannas, A.A. Khennaoui, S. Momani, G. Grassi and V.T. Pham: Chaos and control of a three-dimensional fractional order discrete-time system with no equilibrium and its synchronization. AIP Advances, 10 (2020), DOI: 10.1063/5.0004884.
[23] A. Ouannas, A-A. Khennaoui, S. Momani, G. Grassi, V-T. Pham, R. El- Khazali, and D. Vo Hoang: A quadratic fractional map without equilibria: Bifurcation, 0–1 test, complexity, entropy, and control. Electronics, 9 (2020), DOI: 10.3390/electronics9050748.
[24] A. Ouannas, A-A. Khennaoui, S. Bendoukha, Z.Wang, and V-T. Pham: The dynamics and control of the fractional forms of some rational chaotic maps. Journal of Systems Science and Complexity, 33 (2020), 584–603, DOI: 10.1007/s11424-020-8326-6.
[25] A-A. Khennaoui, A. Ouannas, S. Bendoukha, G. Grassi, R.P. Lozi, and V-T. Pham: On fractional-order discrete-time systems: Chaos, stabilization and synchronization. Chaos, Solitons and Fractals, 119(C), (2019), 150– 162, DOI: 10.1016/j.chaos.2018.12.019.
[26] A. Ouannas, A-A. Khennaoui, Z. Odibat, V-T. Pham, and G. Grassi: On the dynamics, control and synchronization of fractional-order Ikeda map. Chaos, Solitons and Fractals, 123(C), (2015), 108–115, DOI: 10.1016/j.chaos.2019.04.002.
[27] A. Ouannas, F. Mesdoui, S. Momani, I. Batiha, and G. Grassi: Synchronization of FitzHugh-Nagumo reaction-diffusion systems via onedimensional linear control law. Archives of Control Sciences, 31(2), 2021, 333–345, DOI: 10.24425/acs.2021.137421.
[28] Y. Li, C. Sun, H. Ling, A. Lu, and Y. Liu: Oligopolies price game in fractional order system. Chaos, Solitons and Fractals, 132(C), (2020), DOI: 10.1016/j.chaos.2019.109583.
[29] D. Mozyrska and E. Girejko: Overview of fractional h-difference operators. In Advances in harmonic analysis and operator theory. Birkhäuser, Basel, 2013, 253–268.
Go to article

Authors and Affiliations

A. Othman Almatroud
1
Adel Ouannas
2
Giuseppe Grassi
3
Iqbal M. Batiha
4
Ahlem Gasri
5
M. Mossa Al-Sawalha
1

  1. Department of Mathematics, Faculty of Science, University of Ha'il, Ha'il 81451, Saudi Arabia
  2. Department of Mathematics and Computer Science, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria
  3. Dipartimento Ingegneria Innovazione, Universita del Salento, 73100 Lecce, Italy
  4. Department of Mathematics, Faculty of Science and Information Technology, Irbid National University, Irbid, Jordan and Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE
  5. Department of Mathematics, University of Larbi Tebessi, Tebessa 12002, Algeria
Download PDF Download RIS Download Bibtex

Abstract

Hybrid systems (HS) are roughly described as a set of discrete state transitions and continuous dynamics modeled by differential equations. Parametric HS may be constructed by having parameters on the differential equations, initial conditions, jump conditions, or a combination of the previous ones. In real applications, the best solution is obtained by a set of metrics functional over the set of solutions generated from a finite set of parameters. This paper examines the choice of parameters on delta-reachability bounded hybrid systems.We present an efficient model based on the tool pHL-MT to benchmark the HS solutions (based on dReach), and a non-parametric frontier analysis approach, relying on multidirectional efficiency analysis (MEA). Three numerical examples of epidemic models with variable growth infectivity are presented, namely: when the variable of infected individuals oscillates around some endemic (non-autonomous) equilibrium; when there is an asymptotically stable non-trivial attractor; and in the presence of bump functions.
Go to article

Bibliography

[1] M. Althoff and J.M. Dolan: Online verification of automated road vehicles using reachability analysis. IEEE Trans. on Robotics, 30(4), (2014), 903– 918, DOI: 10.1109/TRO.2014.2312453.
[2] P. Bogetoft and J.L. Hougaard: Efficiency evaluations based on potential (non-proportional) improvements. Journal of Productivity Analysis, 12(3), (1999), 233–247, DOI: 10.1023/A:1007848222681.
[3] X. Chen, E. Abraham and S. Sankaranarayanan: Flow*: An analyzer for non-linear hybrid systems. In: Proc. of CAV’13. LNCS, 8044, 258–263, Springer, 2013.
[4] E.M. Clarke and S. Gao: Model checking hybrid systems. In: Margaria T., Steffen B. (eds): Leveraging Applications of Formal Methods, Verification and Validation. Specialized Techniques and Applications. ISoLA 2014. Lecture Notes in Computer Science, 8803, 385–386, Springer, Berlin, Heidelberg, 2014.
[5] M. Franzle, C. Herde, S. Ratschan, T. Schubert and T. Teige: Efficient solving of large non-linear arithmetic constraint systems with complex Boolean structure. Journal on Satisfiability, Boolean Modeling and Computation, 1 (2007), 209–236, DOI: 10.3233/SAT190012.
[6] G. Frehse, C.L. Guernic, A. Donze, R. Ray, O. Lebeltel, R. Ripado, A. Girard, T. Dang and O. Maler: SpaceEx: Scalable verification of hybrid systems. In: Proc. of CAV’11. LNCS, 6806, 379–395, Springer, 2011.
[7] S. Gao: Computable analysis, decision procedures, and hybrid automata: A new framework for the formal verification of cyber-physical systems. Ph.D. thesis, Carnegie Mellon University, 2012.
[8] S. Gao, S. Kong and E.M. Clarke: dReal: An SMT solver for nonlinear theories over the reals. In: M.P. Bonacina (ed.) CADE 2013. LNCS (LNAI), 7898, 208–214, Springer, Heidelberg (2013). DOI: 10.1007/978-3-642-38574-2.
[9] HyCreate: A tool for overapproximating reachability of hybrid automata, http://stanleybak.com/projects/hycreate/hycreate.html.
[10] S. Kong, S. Gao, W. Chen and E. Clarke: dReach: δ-reachability analysis for hybrid systems. In Proc. International Conference on Tools and Algorithms for the Construction and Analysis of Systems, 2015. Available: http://link.springer.com/10.1007/978-3-662-46681-0.
[11] J. Lygeros, C. Tomlin and S. Sastry: Hybrid systems: modeling analysis and control. Electronic Research Laboratory, University of California, Berkeley, CA, Tech. Rep. UCB/ERL M, 2008.
[12] A. Platzer and J. Quesel: Keymaera: A hybrid theorem prover for hybrid systems (system description). In: Proc. of IJCAR’08.LNCS, 5195, 171–178, Springer, 2008.
[13] S. Ratschan and Z. She: Safety verification of hybrid systems by constraint propagation based abstraction refinement. In: Proc. of HSCC’05. LNCS, 3414, 573–589, Springer, 2005.
[14] E.M. Rocha: Oscillatory behaviour on a non-autonomous hybrid SIRmodel. In: M. Chaves and M. Martins (eds.), Molecular Logic and Computational Synthetic Biology. MLCSB 2018. Lecture Notes in Computer Science, 11415, Springer, Cham, 2019.
[15] L. Zhang, Z. She, S. Ratschan, H. Hermanns and E. Hahn: Safety verification for probabilistic hybrid systems. In: Proc. International Conference on Computer Aided Verification, (2010), 196–211.
Go to article

Authors and Affiliations

Eugénio Miguel Alexandre Rocha
1
Kelly Patricia Murillo
1

  1. Center for Research and Development in Mathematics and Applications, and Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
Download PDF Download RIS Download Bibtex

Abstract

The paper is concerned with the presentation and analysis of the Dynamic Matrix Control (DMC) model predictive control algorithm with the representation of the process input trajectories by parametrised sums of Laguerre functions. First the formulation of the DMCL (DMC with Laguerre functions) algorithm is presented. The algorithm differs from the standard DMC one in the formulation of the decision variables of the optimization problem – coefficients of approximations by the Laguerre functions instead of control input values are these variables. Then the DMCL algorithm is applied to two multivariable benchmark problems to investigate properties of the algorithm and to provide a concise comparison with the standard DMC one. The problems with difficult dynamics are selected, which usually leads to longer prediction and control horizons. Benefits from using Laguerre functions were shown, especially evident for smaller sampling intervals.
Go to article

Bibliography

[1] T.L. Blevins, G.K. McMillan, W.K. Wojsznis, and M.W. Brown: Advanced Control Unleashed. The ISA Society, Research Triangle Park, NC, 2003.
[2] T.L. Blevins,W.K.Wojsznis and M.Nixon: Advanced ControlFoundation. The ISA Society, Research Triangle Park, NC, 2013.
[3] E.F. Camacho and C. Bordons: Model Predictive Control. Springer Verlag, London, 1999.
[4] M. Ławrynczuk: Computationally Efficient Model Predictive Control Algorithms: A Neural Network Approach, Studies in Systems, Decision and Control. Vol. 3. Springer Verlag, Heidelberg, 2014.
[5] M. Ławrynczuk: Nonlinear model predictive control for processes with complex dynamics: parametrisation approach using Laguerre functions. International Journal of Applied Mathematics and Computer Science, 30(1), (2020), 35–46, DOI: 10.34768/amcs-2020-0003.
[6] J.M. Maciejowski: Predictive Control. Prentice Hall, Harlow, England, 2002.
[7] R. Nebeluk and P. Marusak: Efficient MPC algorithms with variable trajectories of parameters weighting predicted control errors. Archives of Control Sciences, 30(2), (2020), 325–363, DOI: 10.24425/acs.2020.133502.
[8] S.J. Qin and T.A.Badgwell:Asurvey of industrial model predictive control technology. Control Engineering Practice, 11(7), (2003), 733–764, DOI: 10.1016/S0967-0661(02)00186-7.
[9] J. B. Rawlings and D. Q. Mayne: Model Predictive Control: Theory and Design. Nob Hill Publishing, Madison, 2009.
[10] J.A. Rossiter: Model-Based Predictive Control. CRC Press, Boca Raton – London – New York – Washington, D.C., 2003.
[11] P. Tatjewski: Advanced Control of Industrial Processes. Springer Verlag, London, 2007.
[12] P. Tatjewski: Advanced control and on-line process optimization in multilayer structures. Annual Reviews in Control, 32(1), (2008), 71–85, DOI: 10.1016/j.arcontrol.2008.03.003.
[13] P. Tatjewski: Disturbance modeling and state estimation for offset-free predictive control with state-spaced process models. International Journal of Applied Mathematics and Computer Science, 24(2), (2014), 313–323, DOI: 10.2478/amcs-2014-0023.
[14] P. Tatjewski: Offset-free nonlinear Model Predictive Control with statespace process models. Archives of Control Sciences, 27(4), (2017), 595–615, DOI: 10.1515/acsc-2017-0035.
[15] P. Tatjewski: DMC algorithm with Laguerre functions. In Advanced, Contemporary Control, Proceedings of the 20th Polish Control Conference, pages 1006–1017, Łódz, Poland, (2020).
[16] G. Valencia-Palomo and J.A. Rossiter: Using Laguerre functions to improve efficiency of multi-parametric predictive control. In Proceedings of the 2010 American Control Conference, Baltimore, (2010).
[17] B. Wahlberg: System identification using the Laguerre models. IEEE Transactions on Automatic Control, 36(5), (1991), 551–562, DOI: 10.1109/9.76361.
[18] L. Wang: Discrete model predictive controller design using Laguerre functions. Journal of Process Control, 14(2), (2004), 131–142, DOI: 10.1016/S0959-1524(03)00028-3.
[19] L. Wang: Model Predictive Control System Design and Implementation using MATLAB. Springer Verlag, London, 2009.
[20] R. Wood and M. Berry: Terminal composition control of a binary distillation column. Chemical Engineering Science, 28(9), (1973), 1707–1717, DOI: 10.1016/0009-2509(73)80025-9.
Go to article

Authors and Affiliations

Piotr Tatjewski
1

  1. Warsaw University of Technology, Nowowiejska15/19, 00-665 Warszawa, Poland
Download PDF Download RIS Download Bibtex

Abstract

The paper studies the fault identification problem for linear control systems under the unmatched disturbances. A novel approach to the construction of a sliding mode observer is proposed for systems that do not satisfy common conditions required for fault estimation, in particular matching condition, minimum phase condition, and detectability condition. The suggested approach is based on the reduced order model of the original system. This allows to reduce complexity of sliding mode observer and relax the limitations imposed on the original system.
Go to article

Bibliography

[1] H. Alwi and C. Edwards: Fault tolerant control using sliding modes with on-line control allocation. Automatica, 44 (2008), 1859–1866, DOI: 10.1016/j.automatica.2007.10.034.
[2] H. Alwi, C. Edwards, and C. Tan: Sliding mode estimation schemes for incipient sensor faults. Automatica, 45 (2009), 1679–1685, DOI: 10.1016/j.automatica.2009.02.031.
[3] F. Bejarano, L. Fridman, and A. Pozhyak: Unknown input and state estimation for unobservable systems. SIAM J. Control and Optimization, 48 (2009), 1155–1178. DOI: 10.1137/070700322.
[4] F. Bejarano and L. Fridman: High-order sliding mode observer for linear systems with unbounded unknown inputs. Int. J. Control, 83 (2010), 1920– 1929, DOI: 10.1080/00207179.2010.501386.
[5] M. Blanke, M. Kinnaert, J. Lunze, and M. Staroswiecki: Diagnosis and Fault-Tolerant Control. Berlin: Springer-Verlag, 2006.
[6] A. Brahim, S. Dhahri, F. Hmida, and A. Sellami: Simultaneous actuator and sensor faults reconstruction based on robust sliding mode observer for a class of nonlinear systems. Asian J. Control, 19 (2017), 362–371, DOI: 10.1002/asjc.1359.
[7] J. Chan, C. Tan, and H. Trinh: Robust fault reconstruction for a class of infinitely unobservable descriptor systems. Int. J. Systems Science, (2017), 1–10. DOI: 10.1080/00207721.2017.1280552.
[8] L. Chen, C. Edwards, H. Alwi, and M. Sato: Flight evaluation of a sliding mode online control allocation scheme for fault tolerant control. Automatica, 144 (2020), DOI: 10.1016/j.automatica.2020.108829.
[9] M. Defoort, K. Veluvolu, J. Rath, and M. Djemai: Adaptive sensor and actuator fault estimation for a class of uncertain Lipschitz nonlinear systems. Int. J. Adaptive Control and Signal Processing, 30 (2016), 271–283, DOI: 10.1002/acs.2556.
[10] S. Ding: Data-driven Design of Fault Diagnosis and Fault-tolerant Control Systems. London: Springer-Verlag, 2014.
[11] C. Edwards and S. Spurgeon: On the development of discontinuous observers . Int. J. Control, 59 (1994), 1211–1229, DOI: 10.1080/ 00207179408923128.
[12] C. Edwards, S. Spurgeon, and R. Patton: Sliding mode observers for fault detection and isolation. Automatica, 36 (2000), 541–553, DOI: 10.1016/S0005-1098(99)00177-6.
[13] C. Edwards, H. Alwi, and C. Tan: Sliding mode methods for fault detection and fault tolerant control with application to aerospace systems. Int. J. Applied Mathematics and Computer Science, 22 (2012), 109–124, DOI: 10.2478/v10006-012-0008-7.
[14] V. Filaretov, A. Zuev, A. Zhirabok, and A. Protcenko: Development of fault identification system for electric servo actuators of multilink manipulators using logic-dynamic approach. J. Control Science and Engineering, 2017 (2017), 1–8, DOI: 10.1155/2017/8168627.
[15] T. Floquet, C. Edwards, and S. Spurgeon: On sliding mode observers for systems with unknown inputs. Int. J. Adaptive Control and Signal Processing, 21 (2007), 638–65, DOI: 10.1002/acs.958.
[16] L. Fridman, A. Levant, and J. Davila: Observation of linear systems with unknown inputs via high-order sliding-modes. Int. J. Systems Science, 38 (2007), 773–791, DOI: 10.1080/00207720701409538.
[17] L. Fridman, Yu. Shtessel, C. Edwards, and X. Yan: High-order slidingmode observer for state estimation and input reconstruction in nonlinear systems. Int. J. Robust and Nonlinear Control, 18 (2008), 399–412, DOI: 10.1002/rnc.1198.
[18] R. Hmidi, A. Brahim, F. Hmida, and A. Sellami: Robust fault tolerant control design for nonlinear systems not satisfying matching and minimum phase conditions. Int. J. Control, Automation and Systems, 18 (2020), 1–14, DOI: 10.1007/s12555-019-0516-4.
[19] H. Rios, D. Efimov, J. Davila, T. Raissi, L. Fridman, and A. Zolghadri: Non-minimum phase switched systems: HOSM based fault detection and fault identification via Volterra integral equation. Int. J. Adaptive Control and Signal Processing, 28 (2014), 1372–1397, DOI: 10.1002/acs.2448.
[20] I. Samy, I. Postlethwaite, and D. Gu: Survey and application of sensor fault detection and isolation schemes. Control Engineering Practice, 19 (2011), 658–674, DOI: 10.1016/j.conengprac.2011.03.002.
[21] C. Tan and C. Edwards: Sliding mode observers for robust detection and reconstruction of actuator and sensor faults. Int. J. Robust Nonlinear Control, 13 (2003), 443–463, DOI: 10.1002/rnc.723.
[22] C. Tan and C. Edwards: Robust fault reconstruction using multiple sliding mode observers in cascade: development and design. Proc. 2009 American Control Conf., St. Louis, USA, (2009), DOI: 10.1109/ACC.2009.5160176.
[23] V. Utkin: Sliding Modes in Control Optimization, Berlin: Springer, 1992.
[24] X. Wang, C. Tan, and G. Zhou: A novel sliding mode observer for state and fault estimation in systems not satisfying matching and minimum phase conditions. Automatica, 79 (2017), 290–295, DOI: 10.1016/ j.automatica.2017.01.027.
[25] X. Yan and C. Edwards: Nonlinear robust fault reconstruction and estimation using a sliding modes observer. Automatica, 43 (2007), 1605–1614, DOI: 10.1016/j.automatica.2007.02.008.
[26] J. Yang, F. Zhu, and X. Sun: State estimation and simultaneous unknown input and measurement noise reconstruction based on associated observers. Int. J. Adaptive Control and Signal Processing, 27 (2013), 846–858, DOI: 10.1002/acs.2360.
[27] A. Zhirabok: Nonlinear parity relation: A logic-dynamic approach. Automation and Remote Control, 69 (2008), 1051-1064, DOI: 10.1134/ S0005117908060155.
[28] A. Zhirabok, A. Shumsky, and S. Pavlov: Diagnosis of linear dynamic systems by the nonparametric method. Automation and Remote Control, 78 (2017), 1173–1188, DOI: 10.1134/S0005117917070013.
[29] A. Zhirabok, A. Shumsky, S. Solyanik, and A. Suvorov: Fault detection in nonlinear systems via linear methods. Int. J. Applied Mathematics and Computer Science, 27 (2017), 261–272, DOI: 10.1515/amcs-2017-0019.
[30] A. Zhirabok, A. Zuev, and A. Shumsky: Methods of diagnosis in linear systems based on sliding mode observers. J. Computer and Systems Sciences Int., 58 (2019), 898–914, DOI: 10.1134/S1064230719040166.
[31] A. Zhirabok, A. Zuev, andV. Filaretov: Fault identification in underwater vehicle thrusters via sliding mode observers. Int. J. Applied Mathematics and Computer Science, 30 (2020), 679–688, DOI: 10.34768/amcs-2020-0050.
Go to article

Authors and Affiliations

Alexey Zhirabok
1 2
Alexander Zuev
2
Vladimir Filaretov
3
Alexey Shumsky
1

  1. Far Eastern Federal University, Vladivostok 690091, Russia
  2. Institute of Marine Technology Problems, Vladivostok, 690091, Russia
  3. Institute of Automation and Processes of Control, Vladivostok, 690014, Russia
Download PDF Download RIS Download Bibtex

Abstract

In this paper, model reference output feedback tracking control of an aircraft subject to additive, uncertain, nonlinear disturbances is considered. In order to present the design steps in a clear fashion: first, the aircraft dynamics is temporarily assumed as known with all the states of the system available. Then a feedback linearizing controller minimizing a performance index while only requiring the output measurements of the system is proposed. As the aircraft dynamics is uncertain and only the output is available, the proposed controller makes use of a novel uncertainty estimator. The stability of the closed loop system and global asymptotic tracking of the proposed method are ensured via Lyapunov based arguments, asymptotic convergence of the controller to an optimal controller is also established. Numerical simulations are presented in order to demonstrate the feasibility and performance of the proposed control strategy.
Go to article

Bibliography

[1] S.N. Balakrishnan and V. Biega: Adaptive-critic-based neural networks for aircraft optimal control. J. of Guidance, Control, and Dynamics, 19(4), (1996), 893–898, DOI : 10.2514/3.21715.
[2] B. Bidikli, E. Tatlicioglu, E. Zergeroglu, and A. Bayrak: An asymptotically stable robust controller formulation for a class of MIMO nonlinear systems with uncertain dynamics. Int. J. of Systems Science, 47(12), (2016), 2913–2924, DOI: 10.1080/00207721.2015.1039627.
[3] B. Bidikli, E. Tatlicioglu, A. Bayrak, and E. Zergeroglu: A new robust integral of sign of error feedback controller with adaptive compensation gain. In IEEE Int. Conf. on Decision and Control, (2013), 3782–3787, DOI: 10.1109/CDC.2013.6760466.
[4] B. Bidikli, E. Tatlicioglu, and E. Zergeroglu: A self tuning RISE controller formulation. In American Control Conf., (2014), 5608–5613, DOI: 10.1109/ACC.2014.6859217.
[5] M. Bouchoucha, M. Tadjine, A. Tayebi, P. Mullhaupt, and S. Bouab- dallah: Robust nonlinear pi for attitude stabilization of a four-rotor miniaircraft: From theory to experiment. Archives of Control Sciences, 18(1), (2008), 99–120.
[6] A.E. Bryson and Yu-Chi Ho: Applied Optimal Control: Optimization, Estimation, and Control. Hemisphere, Washington, DC, WA, USA, 1975.
[7] Agus Budiyono and Singgih S. Wibowo: Optimal tracking controller design for a small scale helicopter. J. of Bionic Engineering, 4 (2007), 271–280, DOI: 10.1016/S1672-6529(07)60041-9.
[8] Y.N. Chelnokov, I.A. Pankratov, and Y.G. Sapunkov: Optimal reorientation of spacecraft orbit. Archives of Control Sciences, 24(2), (2014), 119–128, DOI: 10.2478/acsc-2014-0008.
[9] W.-H. Chen, D.J. Ballance, P.J. Gawthrop, and J. O’Reilly: A nonlinear disturbance observer for robotic manipulators. IEEE Tr. on Industrial Electronics, 47(4), (2000), 932–938, DOI: 10.1109/41.857974.
[10] R. Czyba and L. Stajer: Dynamic contraction method approach to digital longitudinal aircraft flight controller design. Archives of Control Sciences, 29(1), (2019), 97–109, DOI: 10.24425/acs.2019.127525.
[11] Z.T. Dydek, A.M. Annaswamy, and E. Lavretsky: Adaptive control and the NASA X-15-3 flight revisited. IEEE Control Systems, 30(3), (2010), 32–48, DOI: 10.1109/MCS.2010.936292.
[12] E.N. Johnson and A.J. Calise: Pseudo-control hedging: a new method for adaptive control. In Workshop on advances in navigation guidance and control technology, pages 1–23, (2000).
[13] H.K. Khalil and J.W. Grizzle: Nonlinear systems. Prentice Hall, New York, NY, USA, 2002.
[14] D.E. Kirk: Optimal Control Theory: An Introduction. Dover, 2012.
[15] L.-V. Lai, C.-C. Yang, and C.-J. Wu: Time-optimal control of a hovering quadrotor helicopter. J. of Intelligent and Robotic Systems, 45 (2006), 115– 135, DOI: 10.1007/s10846-005-9015-3.
[16] J. Leitner, A. Calise, and JV.R. Prasad: Analysis of adaptive neural networks for helicopter flight control. J. of Guidance, Control, and Dynamics, 20(5), (1997), 972–979, DOI: 10.2514/2.4142.
[17] F.L. Lewis, D. Vrabie, and V.L. Syrmos: Optimal Control. John Wiley & Sons, 2012.
[18] W. MacKunis: Nonlinear Control for Systems Containing Input Uncertainty via a Lyapunov-based Approach. PhD thesis, University of Florida, Gainesville, FL, USA, 2009.
[19] W. MacKunis, P.M. Patre, M.K. Kaiser, and W.E. Dixon: Asymptotic tracking for aircraft via robust and adaptive dynamic inversion methods. IEEE Tr. on Control Systems Technology, 18(6), (2010), 1448–1456, DOI: 10.1109/TCST.2009.2039572.
[20] S. Mishra, T. Rakstad, andW. Zhang: Robust attitude control for quadrotors based on parameter optimization of a nonlinear disturbance observer. J. of Dynamic Systems, Measurement and Control, 141(8), (2019), 081003, DOI: 10.1115/1.4042741.
[21] R.M. Murray: Recent research in cooperative control of multivehicle systems. J. of Dynamic Systems, Measurement and Control, 129 (2007), 571– 583, DOI: 10.1115/1.2766721.
[22] D. Nodland, H. Zargarzadeh, and S. Jagannathan: Neural networkbased optimal adaptive output feedback control of a helicopter UAV. IEEE Trans. on Neural Networks and Learning Systems, 24(7), (2013), 1061– 1073, DOI: 10.1109/TNNLS.2013.2251747.
[23] A. Phillips and F. Sahin: Optimal control of a twin rotor MIMO system using LQR with integral action. In IEEE World Automation Cong., (2014), 114–119, DOI: 10.1109/WAC.2014.6935709.
[24] Federal Aviation Administration. Federal aviation regulations. part 25: Airworthiness standards: Transport category airplanes, 2002.
[25] R.R. Costa, L. Hsu, A.K. Imai, and P. Kokotovic: Lyapunov-based adaptive control ofMIMOsystems. Automatica, 39(7), (2003), 1251–1257, DOI: 10.1016/S0005-1098(03)00085-2.
[26] A.C. Satici, H. Poonawala, and M.W. Spong: Robust optimal control of quadrotor UAVs. IEEE Access, 1 (2013), 79–93, DOI: 10.1109/ACCESS. 2013.2260794.
[27] R.F. Stengel: Optimal Control and Estimation. Dover, 1994.
[28] V. Stepanyan and A. Kurdila: Asymptotic tracking of uncertain systems with continuous control using adaptive bounding. IEEE Trans. on Neural Networks, 20(8), (2009), 1320–1329, DOI: 10.1109/TNN.2009.2023214.
[29] B.L. Stevens and F.L. Lewis: Aircraft control and simulation. John Wiley & Sons, New York, NY, USA, 2003.
[30] I. Tanyer, E. Tatlicioglu, and E. Zergeroglu: A robust adaptive tracking controller for an aircraft with uncertain dynamical terms. In IFAC World Cong., (2014), 3202–3207, DOI: 10.3182/20140824-6-ZA-1003.01515.
[31] I. Tanyer, E. Tatlicioglu, and E. Zergeroglu: Neural network based robust control of an aircraft. Int. J. of Robotics& Automation, 35(1), (2020), DOI: 10.2316/J.2020.206-0074.
[32] I. Tanyer, E. Tatlicioglu, E. Zergeroglu, M. Deniz, A. Bayrak, and B. Ozdemirel: Robust output tracking control of an unmanned aerial vehicle subject to additive state-dependent disturbance. IET Control Theory & Applications, 10(14), (2016), 1612–1619, DOI: 10.1049/iet-cta.2015.1304.
[33] G. Tao: Adaptive control design and analysis. John Wiley & Sons, New York, NY, USA, 2003.
[34] Q. Wang and R.F. Stengel: Robust nonlinear flight control of a highperformance aircraft. IEEE Tr. on Control Systems Technology, 13(1), (2005), 15–26, DOI: 10.1109/TCST.2004.833651.
[35] H-N. Wu, M-M. Li, and L. Guo: Finite-horizon approximate optimal guaranteed cost control of uncertain nonlinear systems with application to Mars entry guidance. IEEE Trans. on Neural Networks and Learning Systems, 26(7), (2015), 1456–1467, DOI: 10.1109/TNNLS.2014.2346233.
[36] Q. Xie, B. Luo, F. Tan, and X. Guan: Optimal control for vertical take-off and landing aircraft non-linear system by online kernel-based dual heuristic programming learning. IET Control Theory & Applications, 9(6), (2015), 981–987, DOI: 10.1049/iet-cta.2013.0889.



Go to article

Authors and Affiliations

Ilker Tanyer
1
Enver Tatlicioglu
2
Erkan Zergeroglu
3

  1. Gezgini Inc., Folkart Towers, BBuilding, Floor: 36, Office: 3608, Izmir, 35580, Turkey
  2. Department of Electrical and Electronics Engineering, Ege University, Izmir, 35100, Turkey
  3. Department of Computer Engineering, Gebze Technical University, Kocaeli, 41400, Turkey
Download PDF Download RIS Download Bibtex

Abstract

The article presents "-approximation of hydrodynamics equations’ stationary model along with the proof of a theorem about existence of a hydrodynamics equations’ strongly generalized solution. It was proved by a theorem on the existence of uniqueness of the hydrodynamics equations’ temperature model’s solution, taking into account energy dissipation. There was implemented the Galerkin method to study the Navier–Stokes equations, which provides the study of the boundary value problems correctness for an incompressible viscous flow both numerically and analytically. Approximations of stationary and non-stationary models of the hydrodynamics equations were constructed by a system of Cauchy–Kovalevsky equations with a small parameter ". There was developed an algorithm for numerical modelling of the Navier– Stokes equations by the finite difference method.
Go to article

Bibliography

[1] C. Conca: On the application of the homogenization theory to a class of problems arising in fluid mechanics. J. Math. Purs at Appl., 64(1), (1985), 31–35.
[2] M.R. Malik, T.A. Zang, and M.Y. Hussaini:Aspectral collocation method for the Navier–Stokes equations. J. Comput. Phys., 61(1), (1985), 64–68.
[3] P.M. Gresho: Incompressible fluid dynamics: some fundamental formulation issues. Annu. Rev. Fluid Mech., 23, Palo Alto, Calif., (1991), 413-453.
[4] R. Lakshminarayana, K. Dadzie, R. Ocone, M. Borg, and J. Reese: Recasting Navier–Stokes equations. J. Phys. Commun., 3(10), (2019), 13– 18, DOI: 10.1088/2399-6528/ab4b86.
[5] S.Sh. Kazhikenova, S.N. Shaltakov, D. Belomestny, and G.S. Shai- hova: Finite difference method implementation for numerical integration hydrodynamic equations melts. Eurasian Physical Technical Journal, 17(1), (2020), 50–56.
[6] O.A. Ladijenskaya: Boundary Value Problems of Mathematical Physics. Nauka, Moscow, 1973.
[7] Z.R. Safarova: On a finding the coefficient of one nonlinear wave equation in the mixed problem. Archives of Control Sciences, 30(2), (2020), 199–212, DOI: 10.24425/acs.2020.133497.
[8] A. Abramov and L.F. Yukhno: Solving some problems for systems of linear ordinary differential equations with redundant conditions. Comput. Math. and Math. Phys., 57 (2017), 1285–1293, DOI: 10.7868/ S0044466917080026.
[9] K. Yasumasa and T. Takahico: Finite-element method for three-dimensional incompressible viscous flow using simultaneous relaxation of velocity and Bernoulli function. 1st report flow in a lid-driven cubic cavity at Re = 5000. Trans. Jap. Soc. Mech. Eng., 57(540), (1991), 2640–2647.
[10] H. Itsuro, Î. Hideki, T. Yuji, and N. Tetsuji: Numerical analysis of a flow in a three-dimensional cubic cavity. Trans. Jap. Soc. Mech. Eng., 57(540), (1991), 2627–2631.
[11] X. Yan, L. Wei, Y. Lei, X. Xue, Y.Wang, G. Zhao, J. Li, and X. Qingyan: Numerical simulation of Meso-Micro structure in Ni-based superalloy during liquid metal cooling. Proceedings of the 4th World Congress on Integrated Computational Materials Engineering. The Minerals, Metals & Materials Series. Ð. 249–259, DOI: 10.1007/978-3-319-57864-4_23.
[12] T.A. Barannyk, A.F. Barannyk, and I.I. Yuryk: Exact Solutions of the nonliear equation. Ukrains’kyi Matematychnyi Zhurnal, 69(9), (2017), 1180–1186, http://umj.imath.kiev.ua/index.php/umj/article/view/1768.
[13] S. Tleugabulov, D. Ryzhonkov, N. Aytbayev, G. Koishina, and G. Sul- tamurat: The reduction smelting of metal-containing industrial wastes. News of the Academy of Sciences of the Republic of Kazakhstan, 1(433), (2019), 32–37, DOI: 10.32014/2019.2518-170X.3.
[14] S.L. Skorokhodov and N.P. Kuzmina: Analytical-numerical method for solving an Orr–Sommerfeld-type problem for analysis of instability of ocean currents. Zh. Vychisl. Mat. Mat. Fiz., 58(6), (2018), 1022–1039, DOI: 10.7868/S0044466918060133.
[15] N.B. Iskakova, A.T. Assanova, and E.A. Bakirova: Numerical method for the solution of linear boundary-value problem for integrodifferential equations based on spline approximations. Ukrains’kyi Matematychnyi Zhurnal, 71(9), (2019), 1176–1191, http://umj.imath.kiev.ua/index.php/ umj/article/view/1508.
[16] S.Sh. Kazhikenova, M.I. Ramazanov, and A.A. Khairkulova: epsilon- Approximation of the temperatures model of inhomogeneous melts with allowance for energy dissipation. Bulletin of the Karaganda University- Mathematics, 90(2), (2018), 93–100, DOI: 10.31489/2018M2/93-100.
[17] J.A. Iskenderova and Sh. Smagulov: The Cauchy problem for the equations of a viscous heat-conducting gas with degenerate density. Comput. Maths Math. Phys. Great Britain, 33(8), (1993), 1109–1117.
[18] A.M. Molchanov: Numerical Methods for Solving the Navier–Stokes Equations. Moscow, 2018.
[19] Y. Achdou and J.-L. Guermond: Convergence Analysis of a finite element projection / Lagrange-Galerkin method for the incompressible Navier–Stokes equations. SIAM Journal of Numerical Analysis, 37 (2000), 799–826.
[20] M.P. de Carvalho, V.L. Scalon, and A. Padilha: Analysis of CBS numerical algorithm execution to flow simulation using the finite element method. Ingeniare Revista chilena de Ingeniería, 17(2), (2009), 166–174, DOI: 10.4067/S0718-33052009000200005.
[21] G. Muratova, T. Martynova, E. Andreeva, V. Bavin, and Z-Q. Wang: Numerical solution of the Navier–Stokes equations using multigrid methods with HSS-based and STS-based smoother. Symmetry, 12(2), (2020), DOI: 10.3390/sym12020233.
[22] M. Rosenfeld and M. Israeli: Numerical solution of incompressible flows by a marching multigrid nonlinear method. AIAA 7th Comput. Fluid Dyn. Conf.: Collect. Techn. Pap., New-York, (1985), 108–116.92.


Go to article

Authors and Affiliations

Saule Sh. Kazhikenova
1
ORCID: ORCID

  1. Head of the Department of Higher Mathematics, Karaganda Technical University, Kazakhstan
Download PDF Download RIS Download Bibtex

Abstract

The Fitzhugh-Nagumo model (FN model), which is successfully employed in modeling the function of the so-called membrane potential, exhibits various formations in neuronal networks and rich complex dynamics. This work deals with the problem of control and synchronization of the FN reaction-diffusion model. The proposed control law in this study is designed to be uni-dimensional and linear law for the purpose of reducing the cost of implementation. In order to analytically prove this assertion, Lyapunov’s second method is utilized and illustrated numerically in one- and/or two-spatial dimensions.
Go to article

Bibliography

[1] S.K. Agrawal and S. Das: A modified adaptive control method for synchronization of some fractional chaotic systems with unknown parameters. Nonlinear Dynamics, 73(1), (2013), 907–919, DOI: 10.1007/s11071-013- 0842-7.
[2] B. Ambrosio and M.A. Aziz-Alaoui: Synchronization and control of coupled reaction–diffusion systems of the FitzHugh–Nagumo type. Computers & Mathematics with Applications, 64(5), (2012), 934–943, DOI: 10.1016/j.camwa.2012.01.056.
[3] B. Ambrosio, M.A. Aziz-Alaoui, and V.L.E. Phan: Global attractor of complex networks of reaction-diffusion systems of Fitzhugh-Nagumo type. Discrete & Continuous Dynamical Systems, 23(9), (2018), 3787–3797, DOI: 10.3934/dcdsb.2018077.
[4] B. Ambrosio, M. A. Aziz-Alaoui, and V.L.E. Phan: Large time behaviour and synchronization of complex networks of reaction–diffusion systems of FitzHugh–Nagumo type. IMA Journal of Applied Mathematics, 84(2), (2019), 416–443, DOI: 10.1093/imamat/hxy064.
[5] M. Aqil, K.-S. Hong, and M.-Y. Jeong: Synchronization of coupled chaotic FitzHugh–Nagumo systems. Communications in Nonlinear Science and Numerical Simulation, 17(4), (2012), 1615–1627, DOI: 10.1016/j.cnsns. 2011.09.028.
[6] S. Bendoukha, S. Abdelmalek, and M. Kirane: The global existence and asymptotic stability of solutions for a reaction–diffusion system. Nonlinear Analysis: Real World Applications. 53, (2020), 103052, DOI: 10.1016/j.nonrwa.2019.103052.
[7] X.R. Chen and C.X. Liu: Chaos synchronization of fractional order unified chaotic system via nonlinear control. International Journal of Modern Physics B, 25(03), (2011), 407–415, DOI: 10.1142/S0217979211058018.
[8] D. Eroglu, J.S.W. Lamb, and Y. Pereira: Synchronisation of chaos and its applications. Contemporary Physics, 58(3), (2017), 207–243, DOI: 10.1080/00107514.2017.1345844.
[9] R. Fitzhugh: Thresholds and Plateaus in the Hodgkin-Huxley Nerve Equations. The Journal of General Physiology, 43(5), (1960), 867–896, DOI: 10.1085/jgp.43.5.867.
[10] P.Garcia, A.Acosta, and H. Leiva: Synchronization conditions for masterslave reaction diffusion systems . EPL, 88(6), (2009), 60006.
[11] A.L. Hodgkin and A.F. Huxley: A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol, 117, (1952), 500–544, DOI: 10.1113/jphysiol.1952.sp004764.
[12] T. Kapitaniak: Continuous control and synchronization in chaotic systems. Chaos, Solitons & Fractals, 6 (1995), 237–244, DOI: 10.1016/0960- 0779(95)80030-K.
[13] A.C.J. Luo: Dynamical System Synchronization. Springer-Verlag, New York. 2013.
[14] D. Mansouri, S. Bendoukha, S. Abdelmalek, and A. Youkana: On the complete synchronization of a time-fractional reaction–diffusion system with the Newton–Leipnik nonlinearity. Applicable Analysis, 100(3), (2021), 675–694, DOI: 10.1080/00036811.2019.1616694.
[15] F. Mesdoui, A. Ouannas, N. Shawagfeh, G. Grassi, and V.-T. Pham: Synchronization Methods for the Degn-Harrison Reaction-Diffusion Systems. IEEE Access., 8 (2020), 91829–91836, DOI: 10.1109/ACCESS. 2020.2993784.
[16] F. Mesdoui, N. Shawagfeh, and A. Ouannas: Global synchronization of fractional-order and integer-order N component reaction diffusion systems: Application to biochemical models. Mathematical Methods in the Applied Sciences, 44(1), (2021), 1003–1012, DOI: 10.1002/mma.6807.
[17] J. Nagumo, S. Arimoto, and S. Yoshizawa: An active pulse transmission line simulating nerve axon. Proceedings of the IRE, 50(10), (1962), 2061– 2070, DOI: 10.1109/JRPROC.1962.288235.
[18] L.H. Nguyen and K.-S. Hong: Synchronization of coupled chaotic FitzHugh–Nagumo neurons via Lyapunov functions. Mathematics and Computers in Simulation, 82(4), (2011), 590–603, DOI: 10.1016/j.matcom. 2011.10.005.
[19] Z.M. Odibat: Adaptive feedback control and synchronization of nonidentical chaotic fractional order systems. Nonlinear Dynamics, 60(4), (2010), 479–487, DOI: 10.1007/s11071-009-9609-6.
[20] Z.M. Odibat, N. Corson, M.A. Aziz-Alaoui, and C. Bertelle: Synchronization of chaotic fractional-order systems via linear control. International Journal of Bifurcation and Chaos, 20(1), (2010), 81–97, DOI: 10.1142/S0218127410025429.
[21] A. Ouannas, M. Abdelli, Z. Odibat, X. Wang, V.-T. Pham, G. Grassi, and A. Alsaedi: Synchronization Control in Reaction-Diffusion Systems: Application to Lengyel-Epstein System. Complexity, (2019), Article ID 2832781, DOI: 10.1155/2019/2832781.
[22] A. Ouannas, Z. Odibat, N. Shawagfeh, A. Alsaedi, and B. Ahmad: Universal chaos synchronization control laws for general quadratic discrete systems. Applied Mathematical Modelling, 45 (2017), 636–641, DOI: 10.1016/j.apm.2017.01.012.
[23] A. Ouannas, Z. Odibat, and N. Shawagfeh: A new Q–S synchronization results for discrete chaotic systems. Differential Equations and Dynamical Systems, 27(4), (2019), 413–422, DOI: 10.1007/s12591-016-0278-x.
[24] N. Parekh, V.R. Kumar, and B.D. Kulkarni: Control of spatiotemporal chaos: A study with an autocatalytic reaction-diffusion system. Pramana – J. Phys., 48(1), (1997), 303–323, DOI: 10.1007/BF02845637.
[25] L.M. Pecora and T.L. Carroll: Synchronization in chaotic systems. Physical Review Letter, bf 64(8), (1990), 821–824, DOI: 10.1103/Phys- RevLett.64.821.
[26] M. Srivastava, S.P. Ansari, S.K. Agrawal, S. Das, and A.Y.T. Le- ung: Anti-synchronization between identical and non-identical fractionalorder chaotic systems using active control method. Nonlinear Dynamics, 76 (2014), 905–914, DOI: 10.1007/s11071-013-1177-0.
[27] J. Wang, T. Zhang, and B. Deng: Synchronization of FitzHugh–Nagumo neurons in external electrical stimulation via nonlinear control. Chaos, Solitons & Fractals, 31(1), (2007), 30–38, DOI: 10.1016/j.chaos.2005.09.006.
[28] J. Wang, Z. Zhang, and H. Li: Synchronization of FitzHugh–Nagumo systems in EES via H1 variable universe adaptive fuzzy control. Chaos, Solitons & Fractals, 36(5), (2008), 1332–1339, DOI: 10.1016/j.chaos. 2006.08.012.
[29] L. Wang and H. Zhao: Synchronized stability in a reaction–diffusion neural network model. Physics Letters A, 378(48), (2014), 3586–3599, DOI: 10.1016/j.physleta.2014.10.019.
[30] J. Wei and M. Winter: Standingwaves in the FitzHugh-Nagumo system and a problem in combinatorial geometry. Mathematische Zeitschrift, 254(2), (2006), 359–383, DOI: 10.1007/s00209-006-0952-8.
[31] X. Wei, J.Wang, and B. Deng: Introducing internal model to robust output synchronization of FitzHugh–Nagumo neurons in external electrical stimulation. Communications in Nonlinear Science and Numerical Simulation, 14(7), (2009), 3108–3119, DOI: 10.1016/j.cnsns.2008.10.016.
[32] F. Wu, Y. Wang, J. Ma, W. Jin, and A. Hobiny: Multi-channels couplinginduced pattern transition in a tri-layer neuronal network. Physica A: Statistical Mechanics and its Applications, 493 (2018), 54–68, DOI: 10.1016/j.physa.2017.10.041.
[33] K.-N. Wu, T. Tian, and L. Wang: Synchronization for a class of coupled linear partial differential systems via boundary control. Journal of the Franklin Institute, 353(16), (2016), 4062–4073, DOI: 10.1016/ j.jfranklin.2016.07.019.


Go to article

Authors and Affiliations

Adel Ouannas
1
Fatiha Mesdoui
2
Shaher Momani
2 3
Iqbal Batiha
4 3
Giuseppe Grassi
5

  1. Laboratory of Dynamical Systems and Control, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria
  2. Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, Jordan
  3. Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE
  4. Department of Mathematics, Faculty of Science and Technology, Irbid National University, 2600 Irbid, Jordan
  5. Dipartimento Ingegneria Innovazione, Universitadel Salento, 73100 Lecce, Italy
Download PDF Download RIS Download Bibtex

Abstract

In recent, modeling practical systems as interval systems is gaining more attention of control researchers due to various advantages of interval systems. This research work presents a new approach for reducing the high-order continuous interval system (HOCIS) utilizing improved Gamma approximation. The denominator polynomial of reduced-order continuous interval model (ROCIM) is obtained using modified Routh table, while the numerator polynomial is derived using Gamma parameters. The distinctive features of this approach are: (i) It always generates a stable model for stable HOCIS in contrast to other recent existing techniques; (ii) It always produces interval models for interval systems in contrast to other relevant methods, and, (iii) The proposed technique can be applied to any system in opposite to some existing techniques which are applicable to second-order and third-order systems only. The accuracy and effectiveness of the proposed method are demonstrated by considering test cases of single-inputsingle- output (SISO) and multi-input-multi-output (MIMO) continuous interval systems. The robust stability analysis for ROCIM is also presented to support the effectiveness of proposed technique.
Go to article

Bibliography

[1] A.S.S. Abadi, P.A. Hosseinabadi, S.Mekhilef and A. Ordys: A new strongly predefined time sliding mode controller for a class of cascade high-order nonlinear systems. Archives of Control Sciences, 30(3), (2020), 599–620, DOI: 10.24425/acs.2020.134679.
[2] A. Gupta, R. Saini, and M. Sharma: Modelling of hybrid energy system— part i: Problem formulation and model development. Renewable Energy, 36(2), (2011), 459–465, DOI: 10.1016/j.renene.2010.06.035.
[3] S. Singh, V. Singh, and V. Singh: Analytic hierarchy process based approximation of high-order continuous systems using tlbo algorithm. International Journal of Dynamics and Control, 7(1), (2019), 53–60, DOI: 10.1504/IJSCC.2020.105393.
[4] J. Hu, Y. Yang, M. Jia, Y. Guan, C. Fu, and S. Liao: Research on harmonic torque reduction strategy for integrated electric drive system in pure electric vehicle. Electronics, 9(8), (2020), DOI: 10.3390/electronics9081241.
[5] K. Takahashi, N. Jargalsaikhan, S. Rangarajan, A. M. Hemeida, H. Takahashi and T. Senjyu: Output control of three-axis pmsg wind turbine considering torsional vibration using h infinity control. Energies, 13(13), (2020), DOI: 10.3390/en13133474.
[6] V. Singh, D.P.S. Chauhan, S.P. Singh, and T. Prakash: On time moments and markov parameters of continuous interval systems. Journal of Circuits, Systems and Computers, 26(3), (2017), DOI: 10.1142/S0218126617500384.
[7] B. Pariyar and R.Wagle: Mathematical modeling of isolated wind-dieselsolar photo voltaic hybrid power system for load frequency control. arXiv preprint arXiv:2004.05616, (2020).
[8] N. Karkar, K. Benmhammed, and A. Bartil: Parameter estimation of planar robot manipulator using interval arithmetic approach. Arabian Journal for Science and Engineering, 39(6), (2014), 5289–5295, DOI: 10.1007/s13369-014-1199-z.
[9] F.P.G. Marquez: A new method for maintenance management employing principal component analysis. Structural Durability & Health Monitoring, 6(2), (2010), DOI: 10.3970/sdhm.2010.006.089.
[10] F.P.G. Marquez: An approach to remote condition monitoring systems management. IET International Conference on Railway Condition Monitoring, (2006), 156–160, DOI: 10.1049/ic:20060061.
[11] D. Li, S. Zhang, andY. Xiao: Interval optimization-based optimal design of distributed energy resource systems under uncertainties. Energies, 13(13), (2020), DOI: 10.3390/en13133465.
[12] A.K. Choudhary and S.K. Nagar: Order reduction in z-domain for interval system using an arithmetic operator. Circuits, Systems, and Signal Processing, 38(3), (2019), 1023–1038, DOI: 10.1007/s00034-018-0912-7.
[13] A.K. Choudhary and S.K. Nagar: Order reduction techniques via routh approximation: a critical survey. IETE Journal of Research, 65(3), (2019), 365–379, DOI: 10.1080/03772063.2017.1419836.
[14] V.P. Singh and D. Chandra: Model reduction of discrete interval system using dominant poles retention and direct series expansion method. In 5th International Power Engineering and Optimization Conference, (2011), 27– 30, DOI: 10.1109/PEOCO.2011.5970421.
[15] V. Singh and D. Chandra: Reduction of discrete interval system using clustering of poles with Padé approximation: a computer-aided approach. International Journal of Engineering, Science and Technology, 4(1), (2012), 97–105, DOI: 10.4314/ijest.v4i1.11S.
[16] Y. Dolgin and E. Zeheb: On Routh-Pade model reduction of interval systems. IEEE Transactions on Automatic Control, 48(9), (2003), 1610–1612, DOI: 10.1109/TAC.2003.816999.
[17] S.F. Yang: Comments on “On Routh-Pade model reduction of interval systems”. IEEE Transactions on Automatic Control, 50(2), (2005), 273– 274, DOI: 10.1109/TAC.2004.841885.
[18] Y. Dolgin: Author’s reply [to comments on ‘On Routh-Pade model reduction of interval systems’ . IEEE Transactions on Automatic Control, 50(2), (2005), 274–275, DOI: 10.1109/TAC.2005.843849.
[19] B. Bandyopadhyay, O. Ismail, and R. Gorez: Routh-Pade approximation for interval systems. IEEE Transactions on Automatic Control, 39(12), (1994), 2454–2456, DOI: 10.1109/9.362850.
[20] Y.V. Hote, A.N. Jha, and J.R. Gupta: Reduced order modelling for some class of interval systems. International Journal of Modelling and Simulation, 34(2), (2014), 63–69, DOI: 10.2316/Journal.205.2014.2.205-5785.
[21] B. Bandyopadhyay, A. Upadhye, and O. Ismail: /spl gamma/-/spl delta/routh approximation for interval systems. IEEE Transactions on Automatic Control, 42(8), (1997), 1127–1130, DOI: 10.1109/9.618241.
[22] J. Bokam, V. Singh, and S. Raw: Comments on large scale interval system modelling using routh approximants. Journal of Advanced Research in Dynamical and Control Systems, 9(18), (2017), 1571–1575.
[23] G. Sastry, G.R. Rao, and P.M. Rao: Large scale interval system modelling using Routh approximants. Electronics Letters, 36(8), (2000), 768–769, DOI: 10.1049/el:20000571.
[24] M.S. Kumar and G. Begum: Model order reduction of linear time interval system using stability equation method and a soft computing technique. Advances in Electrical and Electronic Engineering, 14(2), (2016), 153– 161, DOI: 10.15598/aeee.v14i2.1432.
[25] S.R. Potturu and R. Prasad: Qualitative analysis of stable reduced order models for interval systems using mixed methods. IETE Journal of Research, (2018), 1–9, DOI: 10.1080/03772063.2018.1528185.
[26] N. Vijaya Anand, M. Siva Kumar, and R. Srinivasa Rao: A novel reduced order modeling of interval system using soft computing optimization approach. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 232(7), (2018), 879–894, DOI: 10.1177/0959651818766811.
[27] A. Abdelhak and M. Rachik: Model reduction problem of linear discrete systems: Admissibles initial states. Archives of Control Sciences, 29(1), (2019), 41–55, DOI: 10.24425/acs.2019.127522.
[28] M. Buslowicz: Robust stability of a class of uncertain fractional order linear systems with pure delay. Archives of Control Sciences, 25(2), (2015), 177–187.
[29] S.R. Potturu and R. Prasad: Model order reduction of LTI interval systems using differentiation method based on Kharitonov’s theorem. IETE Journal of Research, (2019), 1–17, DOI: 10.1080/03772063.2019.1686663.
[30] E.-H. Dulf: Simplified fractional order controller design algorithm. Mathematics, 7(12), (2019), DOI: 10.3390/math7121166.
[31] Y. Menasria, H. Bouras, and N. Debbache: An interval observer design for uncertain nonlinear systems based on the ts fuzzy model. Archives of Control Sciences, 27(3), (2017), 397–407, DOI: 10.1515/acsc-2017-0025.
[32] A. Khan, W. Xie, L. Zhang, and Ihsanullah: Interval state estimation for linear time-varying (LTV) discrete-time systems subject to component faults and uncertainties. Archives of Control Sciences, 29(2), (2019), 289- 305, DOI: 10.24425/acs.2019.129383.
[33] N. Akram, M. Alam, R. Hussain, A. Ali, S. Muhammad, R. Malik, and A.U. Haq: Passivity preserving model order reduction using the reduce norm method. Electronics, 9(6), (2020), DOI: 10.3390/electronics9060964.
[34] K. Kumar Deveerasetty and S. Nagar: Model order reduction of interval systems using an arithmetic operation. International Journal of Systems Science, (2020), 1–17, DOI: 10.1080/00207721.2020.1746433.
[35] K.K. Deveerasetty,Y. Zhou, S. Kamal, and S.K.Nagar: Computation of impulse-response gramian for interval systems. IETE Journal of Research, (2019), 1–15, DOI: 10.1080/03772063.2019.1690592.
[36] P. Dewangan, V. Singh, and S. Sinha: Improved approximation for SISO and MIMO continuous interval systems ensuring stability. Circuits, Systems, and Signal Processing, (2020), 1–12, DOI: 10.1007/s00034-020-01387-w.
[37] M.S. Kumar, N.V. Anand, and R.S. Rao: Impulse energy approximation of higher-order interval systems using Kharitonov’s polynomials. Transactions of the Institute of Measurement and Control, 38(10), (2016), 1225–1235, DOI: 10.1177/0142331215583326.
[38] S.K. Mangipudi and G. Begum: A new biased model order reduction for higher order interval systems. Advances in Electrical and Electronic Engineering, (2016), DOI: 10.15598/aeee.v14i2.1395.
[39] V.L. Kharitonov: The asymptotic stability of the equilibrium state of a family of systems of linear differential equations. Differentsial’nye Uravneniya, 14(11), (1978), 2086–2088.
[40] M. Sharma, A. Sachan and D. Kumar: Order reduction of higher order interval systems by stability preservation approach. In 2014 International Conference on Power, Control and Embedded Systems (ICPCES), (2014), 1–6.
[41] G. Sastry and P.M. Rao: A new method for modelling of large scale interval systems. IETE Journal of Research, 49(6), (2003), 423–430, DOI: 10.1080/03772063.2003.11416366.



Go to article

Authors and Affiliations

Jagadish Kumar Bokam
1
Vinay Pratap Singh
2
Ramesh Devarapalli
3
ORCID: ORCID
Fausto Pedro García Márquez
4
ORCID: ORCID

  1. Department of Electrical Electronics and Communication Engineering, Gandhi Institute of Technology and Management (Deemed to be University), Visakhapatnam, 530045, Andhra Pradesh, India
  2. Department of Electrical Engineering, Malaviya National Institute of Technology Jaipur, India
  3. Department of Electrical Engineering, BITSindri, Dhanbad, Jharkhand
  4. Ingenium Research Group, University of Castilla-La Mancha, Spain
Download PDF Download RIS Download Bibtex

Abstract

Classical planning in Artificial Intelligence is a computationally expensive problem of finding a sequence of actions that transforms a given initial state of the problem to a desired goal situation. Lack of information about the initial state leads to conditional and conformant planning that is more difficult than classical one. A parallel plan is the plan in which some actions can be executed in parallel, usually leading to decrease of the plan execution time but increase of the difficulty of finding the plan. This paper is focused on three planning problems which are computationally difficult: conditional, conformant and parallel conformant. To avoid these difficulties a set of transformations to Linear Programming Problem (LPP), illustrated by examples, is proposed. The results show that solving LPP corresponding to the planning problem can be computationally easier than solving the planning problem by exploring the problem state space. The cost is that not always the LPP solution can be interpreted directly as a plan.
Go to article

Bibliography

[1] J.L. Ambite and C.A. Knoblock: Planning by rewriting. Journal of Artificial Intelligence Research, 15 (2001), 207–261, DOI: 10.1613/jair.754.
[2] Ch. Backstrom: Computational Aspects of Reordering Plans. Journal of Artificial Intelligence Research, 9 (1998), 99–137, DOI: 10.1613/jair.477.
[3] Ch. Baral, V. Kreinovich, and R. Trejo: Computational complexity of planning and approximate planning in the presence of incompleteness. Artificial Intelligence, 122 (2000), 241–267, DOI: 10.1007/3-540-44957-4_59.
[4] R. Bartak: Constraint satisfaction techniques in planning and scheduling: An introduction. Archives of Control Sciences, 18(2), (2008), DOI: 10.1007/s10845-008-0203-4.
[5] A. Bhattacharya and P. Vasant: Soft-sensing of level of satisfaction in TOC product-mix decision heuristic using robust fuzzy-LP, European Journal of Operational Research, 177(1), (2007), 55–70, DOI: 10.1016/j.ejor.2005.11.017.
[6] J. Blythe: An Overview of Planning Under Uncertainty. Pre-print from AI Magazine, 20(2), (1999), 37–54, DOI: 10.1007/3-540-48317-9_4.
[7] T. Bylander: The Computational Complexity of Propositional STRIPS Planning. Artificial Intelligence, 69 (1994), 165–204, DOI: 10.1016/0004- 3702(94)90081-7.
[8] T. Bylander: A Linear Programming Heuristic for Optimal Planning. In Proc. of AAAI Nat. Conf., (1997).
[9] L.G. Chaczijan: A polynomial algorithm for linear programming. Dokł. Akad. Nauk SSSR, 244 (1979), 1093–1096.
[10] E.R. Dougherty and Ch.R. Giardina: Mathematical Methods for Artificial Intelligence and Autonomous Systems, Prentice-Hall International, Inc. USA, 1988.
[11] I. Elamvazuthi, P. Vasant, and T. Ganesan: Fuzzy Linear Programming using Modified Logistic Membership Function, International Review of Automatic Control, 3(4), (2010), 370–377, DOI: 10.3923/jeasci.2010.239.245.
[12] A. Galuszka: On transformation of STRIPS planning to linear programming. Archives of Control Sciences, 21(3), (2011), 227–251, DOI: 10.2478/v10170-010-0042-3.
[13] A. Galuszka, W. Ilewicz, and A. Olczyk: On Translation of Conformant Action Planning to Linear Programming. Proc. 20th International Conference on Methods and Models in Automation & Robotics, 24–27 August, (2005), 353–357, DOI: 10.1109/MMAR.2015.7283901.
[14] A. Galuszka, T. Grzejszczak, J. Smieja, A. Olczyk, and J. Kocerka: On parallel conformant planning as an optimization problem. 32nd Annual European Simulation and Modelling Conference, Ghent, (2018), 17–22.
[15] M. Ghallab et al.: PDDL – the Planning Domain Definition Language, Version 1.2. Technical Report DCS TR-1165, Yale Center for Computational Vision and Control, (1998).
[16] A. Grastien and E. Scala: Sampling Strategies for Conformant Planning. Proc. Twenty-Eighth International Conference on Automated Planning and Scheduling, (2018), 97–105.
[17] A. Grastien and E. Scala: CPCES: A planning framework to solve conformant planning problems through a counterexample guided refinement. Artificial Intelligence, 284 (2020), 103271, DOI: 10.1016/j.artint.2020.103271.
[18] D. Hoeller, G. Behnke, P. Bercher, S. Biundo, H. Fiorino, D. Pellier, and R. Alford: HDDL: An extension to PDDL for expressing hierarchical planning problems. Proc. AAAI Conference on Artificial Intelligence, 34(6), (2020), 1–9, DOI: 10.1609/aaai.v34i06.6542.
[19] J. Koehler and K. Schuster: Elevator Control as a Planning Problem. AIPS-2000, (2000), 331–338.
[20] R. van der. Krogt: Modification strategies for SAT-based plan adaptation. Archives of Control Sciences, 18(2), (2008).
[21] M.D. Madronero, D. Peidro, and P. Vasant: Vendor selection problem by using an interactive fuzzy multi-objective approach with modified s-curve membership functions. Computers and Mathematics with Applications, 60 (2010), 1038–1048, DOI: 10.1016/j.camwa.2010.03.060.
[22] A. Nareyek, C. Freuder, R. Fourer, E. Giunchiglia, R.P. Goldman, H. Kautz, J. Rintanen, and A. Tate: Constraitns and AI Planning. IEEE Intelligent Systems, (2005), 62–72, DOI: 10.1109/MIS.2005.25.
[23] N.J. Nilson: Principles of Artificial Intelligence. Toga Publishing Company, Palo Alto, CA, 1980.
[24] E.P.D. Pednault: ADL and the state-transition model of action. Journal of Logic and Computation, 4(5), (1994), 467–512, DOI: 10.1093/logcom/4.5.467.
[25] D. Peidro and P. Vasant: Transportation planning with modified scurve membership functions using an interactive fuzzy multi-objective approach, Applied Soft Computing, 11 (2011), 2656–2663, DOI: 10.1016/j.asoc.2010.10.014.
[26] F. Pommerening, G. Roger, M. Helmert, H. Cambazard, L.M. Rousseau, and D. Salvagnin: Lagrangian decomposition for classical planning. Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence, (2020), 4770—4774, DOI: 10.24963/ijcai. 2020/663.
[27] T. Rosa, S. Jimenez, R. Fuentetaja, and D. Barrajo: Scaling up heuristic planning with relational decision trees. Journal of Artificial Intelligence Research, 40 (2011), 767–813, DOI: 10.1613/jair.3231.
[28] S.J. Russell and P. Norvig: Artificial Intelligence: A Modern Approach. Fourth Edition. Pearson, 2020.
[29] J. Seipp, T. Keller, and M. Helmert: Saturated post-hoc optimization for classical planning. Proceedings of the Thirty-Fifth AAAI Conference on Artificial Intelligence, (2021).
[30] D.E. Smith and D.S. Weld: Conformant Graphplan. Proc. 15th National Conf. on AI, (1998).
[31] D.S. Weld: Recent Advantages in AI Planning. AI Magazine, (1999), DOI: 10.1609/aimag.v20i2.1459.
[32] D.S. Weld, C.R. Anderson, and D.E. Smith: Extending graphplan to handle uncertainty & sensing actions. Proc. 15th National Conf. on AI, (1998), 897–904.
[33] X. Zhang, A. Grastien, and E. Scala: Computing superior counterexamples for conformant planning. Proc. AAAI Conference on Artificial Intelligence 34(6), (2020), 1–8, DOI: 10.1609/aaai.v34i06.6558.


Go to article

Authors and Affiliations

Adam Galuszka
1
Eryka Probierz
1

  1. Department of Automatic Control and Robotics, Silesian University of Technology, Akademicka 16, 44-100 Gliwice, Poland
Download PDF Download RIS Download Bibtex

Abstract

The Green’s function approach is applied for studying the exact and approximate nullcontrollability of a finite rod in finite time by means of a source moving along the rod with controllable trajectory. The intensity of the source remains constant. Applying the recently developed Green’s function approach, the analysis of the exact null-controllability is reduced to an infinite system of nonlinear constraints with respect to the control function. A sufficient condition for the approximate null-controllability of the rod is obtained. Since the exact solution of the system of constraints is a long-standing open problem, some heuristic solutions are used instead. The efficiency of these solutions is shown on particular cases of approximate controllability.
Go to article

Bibliography

[1] J. Klamka: Controllability of Dynamical Systems. Kluwer Academic, Dordrecht, 1991.
[2] S.A. Avdonin and S.A. Ivanov: Families of Exponentials. The Method of Moments in Controllability Problems for Distributed Parameter Systems. Cambridge University Press, New York, 1995.
[3] A. Fursikov and O.Yu. Imanuvilov: Controllability of Evolution Equations. Lecture Notes Series, vol. 34. Seoul National University, Research Institute of Mathematics, Global Analysis Research Center, Seoul, 1996.
[4] E. Zuazua: Controllability and Observability of Partial Differential Equations: Some Results and Open Problems. Handbook of Differential Equations: Evolutionary Differential Equations, vol. 3, Elsevier/North-Holland, Amsterdam, 2006.
[5] R. Glowinski, J.-L. Lions and J. He: Exact and Approximate Controllability for Distributed Parameter Systems: A Numerical Approach. Cambridge University Press, New York, 2008.
[6] A.S. Avetisyan and As.Zh. Khurshudyan: Controllability of Dynamic Systems: The Green’s Function Approach. Cambridge Scholars Publishing, Cambridge, 2018.
[7] S. Micu and E. Zuazua: On the lack of null-controllability of the heat equation on the half-line. Transactions of the American Mathematical Society, 353(4), (2001), 1635–1659.
[8] S. Micu and E. Zuazua: Null Controllability of the Heat Equation in Unbounded Domains. In “Unsolved Problems in Mathematical Systems and Control Theory”, edited by Blondel V.D., Megretski A., Princeton University Press, Princeton, 2004.
[9] V. Barbu: Exact null internal controllability for the heat equation on unbounded convex domain. ESAIM: Control, Optimisation and Calculus of Variations, 20 (2014), 222–235, DOI: 10.1051/cocv/2013062.
[10] As.Zh. Khurshudyan: (2019), Distributed controllability of heat equation in un-bounded domains: The Green’s function approach. Archives of Control Sciences, 29(1), (2019), 57–71, DOI: 10.24425/acs.2019.127523.
[11] S. Ivanov and L. Pandolfi: Heat equation with memory: Lack of controllability to rest. Journal of Mathematical Analysis and Applications, 355 (2009), 1–11, DOI: 10.1016/j.jmaa.2009.01.008.
[12] A. Halanay and L. Pandolfi: Approximate controllability and lack of controllability to zero of the heat equation with memory. Journal of Mathematical Analysis and Applications, 425 (2015), 194–211, DOI: 10.1016/j.jmaa.2014.12.021.
[13] B.S. Yilbas: Laser Heating Applications: Analytical Modelling. Elsevier, Waltham, 2012.
[14] A.G. Butkovskiy and L.M. Pustylnikov: Mobile Control of Distributed Parameter Systems. Chichester, Ellis Horwood, 1987.
[15] V.A. Kubyshkin and V.I. Finyagina: Moving control of systems with distributed parameters (in Russian). Moscow: SINTEG, 2005.
[16] Sh.Kh. Arakelyan and As.Zh. Khurshudyan: The Bubnov-Galerkin procedure for solving mobile control problems for systems with distributed parameters. Mechanics. PNAS Armenia, 68(3), (2015), 54–75.
[17] A.G. Butkovskiy: Some problems of control of the distributed-parameter systems. Automation and Remote Control, 72 (2011), 1237–1241, DOI: 10.1134/S0005117911060105.
[18] A.S. Avetisyan and As.Zh. Khurshudyan: Green’s function approach in approximate controllability problems. Proceedings of National Academy of Sciences of Armenia. Mechanics, vol. 69, issue 2, (2016), 3–22, DOI: 10.33018/69.2.1.
[19] A.S. Avetisyan and As.Zh. Khurshudyan: Green’s function approach in approximate controllability of nonlinear physical processes. Modern Physics Letters A, 32 1730015, (2017), DOI: 10.1142/S0217732317300154.
[20] As.Zh. Khurshudyan: Resolving controls for the exact and approximate controllabilities of the viscous Burgers’ equation: the Green’s function approach. International Journal of Modern Physics C, 29(6), 1850045, (2018), DOI: 10.1142/S0129183118500456.
[21] A.S. Avetisyan and As.Zh. Khurshudyan: Exact and approximate controllability of nonlinear dynamic systems in infinite time: The Green’s function approach. ZAMM, 98(11), (2018), 1992–2009, DOI: 10.1002/zamm.201800122.
[22] As.Zh. Khurshudyan: Exact and approximate controllability conditions for the micro-swimmers deflection governed by electric field on a plane: The Green’s function approach. Archives of Control Sciences, 28(3), (2018), 335–347. DOI: 10.24425/acs.2018.124706.
[23] J. Klamka and As.Zh. Khurshudyan: Averaged controllability of heat equation in unbounded domains with uncertain geometry and location of controls: The Green’s function approach. Archives of Control Sciences, 29(4), (2019), 573–584, DOI: 10.24425/acs.2018.124706.
[24] J. Klamka, A.S. Avetisyan and As.Zh. Khurshudyan: Exact and approximate distributed controllability of the KdV and Boussinesq equations: The Green’s function approach. Archives of Control Sciences, 30(1), (2020), 177–193, DOI: 10.24425/acs.2020.132591.
[25] J. Klamka and As.Zh. Khurshudyan: Approximate controllability of second order infinite dimensional systems. Archives of Control Sciences, 31(1), (2021), 165–184, DOI: 10.24425/acs.2021.136885.
[26] As.Zh. Khurshudyan: Heuristic determination of resolving controls for exact and approximate controllability of nonlinear dynamic systems. Mathematical Problems in Engineering, (2018), Article ID 9496371, DOI: 10.1155/2018/9496371.
[27] H. Hossain and As.Zh. Khurshudyan: Heuristic control of nonlinear power systems: Application to the infinite bus problem. Archives of Control Sciences, 29(2), (2019), 279–288, DOI: 10.24425/acs.2019.129382.
[28] A.G. Butkovskii and L.M. Pustyl’nikov: Characteristics of Distributed- Parameter Systems. Kluwer Academic Publishers, 1993.
Go to article

Authors and Affiliations

Samvel H. Jilavyan
1
Edmon R. Grigoryan
1
Asatur Zh. Khurshudyan
2

  1. Faculty of Mathematics and Mechanics, Yerevan State University, 1 Alex Manoogian, 0025 Yerevan, Armenia
  2. Dynamicsof Deformable Systems and Coupled Fields, Institute of Mechanics, National Academy of Sciences of Armenia, 0019 Yerevan, Armenia
Download PDF Download RIS Download Bibtex

Abstract

We devise a tool-supported framework for achieving power-efficiency of data-flowhardware circuits. Our approach relies on formal control techniques, where the goal is to compute a strategy that can be used to drive a given model so that it satisfies a set of control objectives. More specifically, we give an algorithm that derives abstract behavioral models directly in a symbolic form from original designs described at Register-transfer Level using a Hardware Description Language, and for formulating suitable scheduling constraints and power-efficiency objectives. We show how a resulting strategy can be translated into a piece of synchronous circuit that, when paired with the original design, ensures the aforementioned objectives. We illustrate and validate our approach experimentally using various hardware designs and objectives.
Go to article

Bibliography

[1] P. Babighian, L. Benini, and E. Macii: A scalable algorithm for RTL insertion of gated clocks based onODCscomputation. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 24(1), (2005), 29–42, DOI: 10.1109/TCAD.2004.839489.
[2] R. Bellman: Dynamic programming and stochastic control processes. Information and Control, 1(3), (1958), 228–239, DOI: 10.1016/S0019- 9958(58)80003-0.
[3] L. Benini, P. Siegel, and G. De Micheli: Saving power by synthesizing gated clocks for sequential circuits. IEEE Design & Test of Computers, 11(4), (1994), 32–41, DOI: 10.1109/54.329451.
[4] R. Bhutada and Y. Manoli: Complex clock gating with integrated clock gating logic cell. In 2007 International Conference on Design Technology of Integrated Systems in Nanoscale Era, (2007), 164–169, DOI: 10.1109/DTIS.2007.4449512.
[5] J. Billon: Perfect normal forms for discrete programs. Technical report, Bull, 1987.
[6] E.M. Clarke, E.A. Emerson, and A.P. Sistla: Automatic verification of finite-state concurrent systems using temporal logic specifications. ACM Transactions on Programming Languages and Systems, 8(2), (1986), 244– 263, DOI: 10.1145/5397.5399.
[7] E. Dumitrescu, A. Girault, H. Marchand, and E. Rutten: Multicriteria optimal reconfiguration of fault-tolerant real-time tasks. IFAC Proceedings Volumes, 43(12), (2010), 356–363, DOI: 10.3182/20100830-3-DE- 4013.00059.
[8] K. Gilles: The semantics of a simple language for parallel programming. Information Processing, 74 (1974), 471–475.
[9] E.A. Lee and T.M. Parks: Dataflow process networks. Proceedings of the IEEE, 83(5), (1995), 773–801, DOI: 10.1109/5.381846.
[10] H. Marchand and M.L. Borgne: On the optimal control of polynomial dynamical systems over z/pz. In 4th International Workshop on Discrete Event Systems, (1998), 385–390.
[11] H. Marchand, P. Bournai, M.L. Borgne, and P.L. Guernic: Synthesis of discrete-event controllers based on the signal environment. Discrete Event Dynamic System: Theory and Applications, 10(4), (2000), 325–346, DOI: 10.1023/A:1008311720696.
[12] S. Miremadi, B. Lennartson, and K. Akesson: A BDD-based approach for modeling plant and supervisor by extended finite automata. IEEE Transactions on Control Systems Technology, 20(6), (2012), 1421–1435, DOI: 10.1109/TCST.2011.2167150.
[13] M. Özbaltan: Achieving Power Efficiency in Hardware Circuits with Symbolic Discrete Control. PhD thesis, University of Liverpool, 2020.
[14] M. Özbaltan and N. Berthier: Exercising symbolic discrete control for designing low-power hardware circuits: an application to clock-gating. IFAC-PapersOnLine, 51(7), (2018), 120–126, DOI: 10.1016/j.ifacol.2018.06.289.
[15] M. Özbaltan and N. Berthier: A case for symbolic limited optimal discrete control: Energy management in reactive data-flow circuits. IFAC-PapersOnLine, 53(2), (2020), 10688–10694, DOI: 10.1016/j.ifacol. 2020.12.2842.
[16] M. Pedram and Q.Wu: Design considerations for battery-powered electronics. In Proceedings 1999 Design Automation Conference, (1999), 861–866, DOI: 10.1109/DAC.1999.782166.
[17] N. Raghavan, V. Akella, and S. Bakshi: Automatic insertion of gated clocks at register transfer level. In Proceedings of the 12th International Conference on VLSI Design, (1999), 48–54, DOI: 10.1109/ICVD.1999.745123.
[18] P. Ramadge and W. Wonham: The control of discrete event systems. Proceedings of the IEEE, 77(1), (1989), 81–98, DOI: 10.1109/5.21072.
[19] S. Tripakis, R. Limaye, K. Ravindran, G. Wang, H. Andrade, and A. Ghosal: Tokens vs. signals: On conformance between formal models of dataflow and hardware. Journal of Signal Processing Systems, 85(1), (2016), 23–43, DOI: 10.1007/s11265-015-0971-y.
Go to article

Authors and Affiliations

Mete Özbaltan
1
Nicolas Berthier
2

  1. Erzurum Technical University, Erzurum, Turkey
  2. University of Liverpool, Liverpool, England

This page uses 'cookies'. Learn more