Integral linear quadratic regulator for Markovian jump linear systems subject with exogenous inputs
DOI:
https://doi.org/10.22481/intermaths.v5i1.14689Keywords:
Regulator, Optimal Control, Markovian Systems, Discrete-time, Disturbances, Integral ActionAbstract
In this paper, the problem of linear quadratic regulation with integral action and external
disturbances rejection is addressed for Markovian Jump Linear Systems. Problem solu-
tion is based on augmented state and the method of constrained weighted least squares.
Numerical examples are presented to demonstrated to efficiency of the proposed regulator.
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A.A. Siqueira, M.H. Terra, ”A fault tolerant manipulator robot based on H2, H∞, and mixed H2/H∞ Markovian controls”, Proceedings of the IEEE International Conference on Control Applications, vol. 1, pp. 309 - 314, 2004.
A. N. Vargas, E. F. Costa, J.B.R. do Val, ”Finite-time stability, homogeneity, homogeneous systems, implicit Lyapunov function, non-aymptotic stabilization, sliding mode control, uncertain systems”, International Journal of Robust and Nonlinear Control, vol. 23, no. 10, pp. 1136 - 1150, 2013.
Z. Matjacicand T. Bajd, ”Arm-free paraplegic standing–Part I: Control model synthesis and simulation”, IEEE Transactions on Rehabilitation Engineering, vol. 6, no. 2, p. 125 - 138, 1998.
A. P. Blake, F. Zampolli, ”Optimal policy in Markov-switching rational expectations models”, Journal of Economic Dynamics and Control, vol. 35, no. 10, p. 1626 - 1651, 2011.
D. Sworder, ”Feedback control of a class of linear systems with jump parameters”, IEEE Transactions on Automatic Control, vol. 14, no. 1, p. 9 - 14, 1969.
H. J. Chizeck, A. S. Willsky, D. Castanon, ”Markovian Jump Linear Quadratic Optimal Control in Discrete Time”, Proceedings of the IEEE Conference on Decision and Control, vol. 3, p. 1138-1142, 1983.
H. J. Chizeck, A. S. Willsky, D. Castanon, ”Discrete-time markovian-jump linear quadratic optimal control”, International Journal of Control, vol. 43, no. 1, p. 213 - 231, 1986.
H. Abou-Kandil, G. Freiling, G. Jank, ”On the solution of discrete-time Markovian jump linear quadratic control problems”, Automatica, vol. 31, no. 5, p. 765 - 768, 1995.
A. K. Singh, B. C. Pal, ”An extended linear quadratic regulator for LTI systems with exogenous inputs”, Automatica, vol. 76, p. 10 - 16, 2017.
G. Ma, X. Liu, P. R. Pagilla, ”Repetitive Control of Discrete-Time Markov Jump Linear Systems”, Proceedings of the American Control Conference, vol. 6, p. 4546 - 4551, 2018.
G. Nakura, ”Stochastic optimal tracking with preview by state feedback for linear discrete
time markovian jump systems”, International Journal of Innovative Computing, Information and Control, vol. 6, no. 1, p. 15 - 27, 2010.
G. Nakura, ”Stochastic Optimal Tracking with Preview for Linear Continuous-Time Markovian Jump Systems by Output Feedback”, Proceedings of the ISCIE International Symposium on Stochastic Systems Theory and its Applications, p. 13 - 21, 2015.
N. Birla, A. Swarup, ”Optimal preview control: A review”, Optimal Control Applications and Methods, vol. 36, no. 2, p. 241 - 268, 2015.
J. Wu, F. Liao Z. Xu, ”Preview control for a class of linear stochastic systems with multiplicative noise”, International Journal of Systems Science, vol. 50, no. 14, p. 2592 - 2603,
T. Holzhuter, ”Optimal regulator for the inverted pendulum via Euler-Lagrange backward integration”, Automatica, vol. 40, no. 9, p. 1613 - 1620, 2004.
M. Akhtaruzzaman, A. A. Shafie, ”Modeling and control of a rotary inverted pendulum using various methods, comparative assessment and result analysis”, Proceedings of 2010 IEEE International Conference on Mechatronics and Automation, ICMA 2010, p. 1342 -1347, 2010.
K. Yoshida, ”Swing-up control of an inverted pendulum by energy-based methods”, Proceedings of the American Control Conference, vol. 6, no. 6, p. 4045 - 4047, 1999.
C. M. Mitschka and , M. H. Terra, A. A. G. Siqueira, , ”Derivation of a Markovian controller for an exo-skeleton by overcome the benchmarks of a single and double inverted pendulum” Proceedings of the IEEE Conference on Decision and Control, p. 5061 - 5066, 2015.
A. T. Safa, A. Nouriani, A. Alasty, ”Stable handspring maneuvers with passive flight phases: Results from an inverted pendulum-like template”, International Journal of Non-Linear Mechanics, vol. 128, p. 103606, 2021.
K. Furuta, M. Yamakita, S. Kobayashi, ”Swing-up Control of Inverted Pendulum Using Pseudo-State Feedback”, Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, vol. 206, no. 4, p. 263 - 269, 1992.
J. P. Cerri and M. H. Terra, ”Recursive Robust Regulator for Discrete-Time Markovian Jump Linear Systems,”IEEE Transactions on Automatic Control, vol. 62, no. 11, p. 6004 - 6011, 2017.
V. S. Madureira, T.P. das Chagas, G. Q. de Jesus, ”Integral linear quadratic Gaussian regulator subject to unknown inputs: application in photovoltaic systems”, International Journal Dynamic Control, 2023.
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