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On optimal control problem subject to fractional order discrete time singular systems

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Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Strony
849--863
Opis fizyczny
Bibliogr. 37 poz., rys., wzory
Twórcy
  • Department of Electrical Engineering, Rajkiya Engineering College Sonbhadra, U. P., India
  • Department of Electrical Engineering, National Institute of Technology, Silchar, India
  • Department of Electrical Engineering, BIT Sindri, Dhanbad 828123, Jharkhand, India
  • Department of Electrical Engineering, National Institute of Technology, Silchar, India
  • Ingenium Research Group, University of Castilla-La Mancha, Spain
Bibliografia
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  • [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 HIV-immune 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 discrete-time 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.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-d3e14aca-eecc-4c33-a17d-8714717b2063
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