Details
Title
Heating control of a finite rod with a mobile sourceJournal title
Archives of Control SciencesYearbook
2021Volume
vol. 31Issue
No 2Affiliation
Jilavyan, Samvel H. : Faculty of Mathematics and Mechanics, Yerevan State University, 1 Alex Manoogian, 0025 Yerevan, Armenia ; Grigoryan, Edmon R. : Faculty of Mathematics and Mechanics, Yerevan State University, 1 Alex Manoogian, 0025 Yerevan, Armenia ; Khurshudyan, Asatur Zh. : Dynamicsof Deformable Systems and Coupled Fields, Institute of Mechanics, National Academy of Sciences of Armenia, 0019 Yerevan, ArmeniaAuthors
Keywords
null-controllability ; mobile control ; nonlinear constraints ; triangular wave ; rectangular wave ; Green’s function approach ; heuristic control ; lack of exact controllabilityDivisions of PAS
Nauki TechniczneCoverage
417-430Publisher
Committee of Automatic Control and Robotics PASBibliography
[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.