Details
Title
On optimal control problem subject to fractional order discrete time singular systemsJournal title
Archives of Control SciencesYearbook
2021Volume
vol. 31Issue
No 4Authors
Affiliation
Chiranjeevi, Tirumalasetty : Department of Electrical Engineering, Rajkiya Engineering College Sonbhadra, U. P., India ; Biswas, Raj Kumar : Department of Electrical Engineering, National Institute of Technology, Silchar, India ; Devarapalli, Ramesh : Department of Electrical Engineering, BIT Sindri, Dhanbad 828123, Jharkhand, India ; Babu, Naladi Ram : Department of Electrical Engineering, National Institute of Technology, Silchar, India ; García Márquez, Fausto Pedro : Ingenium Research Group, University of Castilla-La Mancha, SpainKeywords
fractional optimal control problem ; discrete time singular system ; fractional derivative ; Hamiltonian techniqueDivisions of PAS
Nauki TechniczneCoverage
849-863Publisher
Committee of Automatic Control and Robotics PASBibliography
[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.