This paper addresses the constrained receding horizon control scheme for a class of discrete-time Markovian jump linear systems with partly unknown transition probabilities and persistent bounded disturbances. The proposed method adopts paradigm that utilizes nominal closed-loop feedback controller plus an additional online optimized variable. Both the state feedback approach and the observer based approach are given. The obtained predictive controller guarantees constraint fulfillment and asymptotic state regulation in the mean square sense for all admissible disturbances. The system state and estimated state converge into a stochastic disturbance invariant set provided that the initial state and initial estimation error are feasible. A numerical example is given to verify the effectiveness of the proposed method.
Issue Section:
Research Papers
1.
Park
, B. G.
, Kwon
, W. H.
, and Lee
, J. W.
, 2001, “Robust Receding Horizon Control of Discrete-Time Markovian Jump Uncertain Systems
,” IEICE Trans. Fundamentals
0916-8508, 84-A
(9
), pp. 2272
–2279
.2.
Ji
, Y.
, Chezick
, H. J.
, Feng
, X.
, and Loparo
, K. A.
, 1991, “Stability and Control of Discrete-Time Jump Linear Systems
,” Control Theory Adv. Technol.
0911-0704, 7
(2
), pp. 247
–270
.3.
Costa
, O. L. V.
, and Fragoso
, M. D.
, 1993, “Stability Results for Discrete Time Linear Systems With Markovian Jumping Parameters
,” J. Math. Anal. Appl.
0022-247X, 179
(1
), pp. 154
–178
.4.
Pan
, G.
, and Bar-Shalom
, Y.
, 1996, “Stabilization of Jump Linear Gaussian Systems Without Mode Observation
,” Int. J. Control
0020-7179, 64
(4
), pp. 631
–661
.5.
Cao
, Y. Y.
, and Lam
, J.
, 1999, “Stochastic Stabilizability and H∞ Control for Discrete-Time Jump Linear Systems With Time Delay
,” J. Franklin Inst.
0016-0032, 336
(8
), pp. 1263
–1281
.6.
Costa
, O. L. V.
, Val
, J. B. R. D.
, and Geromel
, J. C.
, 1997, “A Convex Programming Approach to H2-Control of Discrete-Time Markovian Jump Linear Systems
,” Int. J. Control
0020-7179, 66
(4
), pp. 557
–579
.7.
Costa
, O. L. V.
, and Marques
, R. P.
, 1998, “Mixed H2/H∞ Control of Discrete-Time Markovian Jump Linear Systems
,” IEEE Trans. Autom. Control
0018-9286, 43
(1
), pp. 95
–100
.8.
Seiler
, P.
, and Sengupta
, R.
, 2003, “A Bounded Real Lemma for Jump Systems
,” IEEE Trans. Autom. Control
0018-9286, 48
(9
), pp. 1651
–1654
.9.
Ghaoui
, L. E.
, and Aitrami
, M.
, 1996, “Robust State Feedback Stabilization of Jump Linear Systems via LMIs
,” Int. J. Robust Nonlinear Control
1049-8923, 6
(9–10
), pp. 1015
–1022
.10.
Shi
, P.
, and Boukas
, E. K.
, 1997, “H∞ Control for Markovian Jumping Linear Systems With Parametric Uncertainty
,” J. Optim. Theory Appl.
0022-3239, 95
(1
), pp. 75
–99
.11.
Boukas
, E. K.
, and Shi
, P.
, 1998, “Stochastic Stability and Guaranteed Cost Control of Discrete-Time Uncertain Systems With Markovian Jumping Parameters
,” Int. J. Robust Nonlinear Control
1049-8923, 8
(13
), pp. 1155
–1167
.12.
Shi
, P.
, Boukas
, E. K.
, and Agarwal
, R. K.
, 1990, “Robust Control for Markovian Jump Discrete-Time Systems
,” Int. J. Syst. Sci.
0020-7721, 30
(8
), pp. 787
–797
.13.
Costa
, O. L. V.
, Fragoso
, M. D.
, and Marques
, R. P.
, 2005, Discrete Time Markovian Jump Linear Systems
, Springer-Verlag
, London
.14.
Karan
, M.
, Shi
, P.
, and Kaya
, C. Y.
, 2006, “Transition Probability Bounds for the Stochastic Stability Robustness of Continuous- and Discrete-Time Markovian Jump Linear Systems
,” Automatica
0005-1098, 42
(12
), pp. 2159
–2168
.15.
Xiong
, J. L.
, Lam
, J.
, Gao
, H. J.
, and Daniel
, W. C.
, 2005, “On Robust Stabilization of Markovian Jump Systems With Uncertain Switching Probabilities
,” Automatica
0005-1098, 41
(5
), pp. 897
–903
.16.
Zhang
, L. X.
, and Boukas
, E. K.
, 2009, “Stability and Stabilization of Markovian Jump Linear Systems With Partly Unknown Transition Probabilities
,” Automatica
0005-1098, 45
(2
), pp. 463
–468
.17.
Zhang
, L. X.
, and Boukas
, E. K.
, 2009, “Mode-Dependent H∞ Filtering for Discrete-Time Markovian Jump Linear Systems With Partly Unknown Transition Probabilities
,” Automatica
0005-1098, 45
(6
), pp. 1462
–1467
.18.
Kothare
, M. V.
, Balakrishnan
, V.
, and Morari
, M.
, 1996, “Robust Constrained Model Predictive Control Using Linear Matrix Inequalities
,” Automatica
0005-1098, 32
(10
), pp. 1361
–1379
.19.
Mayne
, D. Q.
, Rawlings
, J. B.
, and Rao
, C. V.
, 2000, “Constrained Model Predictive Control: Stability And Optimality
,” Automatica
0005-1098, 36
(6
), pp. 789
–814
.20.
Lee
, Y. L.
, and Kouvaritakis
, B.
, 2001, “Receding Horizon Output Feedback Control for Linear Systems With Input Saturation
,” IEE Proc.: Control Theory Appl.
1350-2379, 148
(2
), pp. 109
–115
.21.
Chisci
, L.
, Rossiter
, J. A.
, and Zappa
, G.
, 2001, “System With Persistent Disturbance: Predictive Control With Restricted Constraints
,” Automatica
0005-1098, 37
(7
), pp. 1019
–1028
.22.
Mayne
, D. Q.
, Seron
, M. M.
, and Raković
, S. V.
, 2005, “Robust Model Predictive Control of Constrained Linear Systems With Bounded Disturbances
,” Automatica
0005-1098, 41
(2
), pp. 219
–224
.23.
Mayne
, D. Q.
, Raković
, S. V.
, Findeisen
, R.
, and Allgöwer
, F.
, 2006, “Robust Output Feedback Model Predictive Control of Constrained Linear Systems
,” Automatica
0005-1098, 42
(7
), pp. 1217
–1222
.24.
Raković
, S. V.
, Kerrigan
, E. C.
, Mayne
, D. Q.
, and Kouramas
, K. I.
, 2007, “Optimized Robust Control Invariance for Linear Discrete-Time Systems: Theoretical Foundation
,” Automatica
0005-1098, 43
(5
), pp. 831
–841
.25.
Park
, B. G.
, and Kwon
, W. H.
, 2002, “Robust One-Step Receding Horizon Control of Discrete Time Markovian Jump Uncertain Systems
,” Automatica
0005-1098, 38
(7
), pp. 1229
–1235
.26.
Val
, J. B. R. D.
, and Basar
, T.
, 1997, “Receding Horizon Control of Markov Jump Linear Systems
,” Proceedings of the 1997American Control Conference
, Albuquerque, Vol. 5
, pp. 3195
–3199
.27.
Park
, B. G.
, Lee
, J. W.
, and Kwon
, W. H.
, 1997, “Receding Horizon Control for Linear Discrete Systems With Jump Parameters
,” Proceedings of the 36th Conference on Decision and Control
, San Diego, Vol. 4
, pp. 3956
–3957
.28.
Chen
, J. R.
, and Liu
, F.
, 2008, “Robust Model Predictive Control for Markov Jump Systems Subject Actuator Saturation,” Journal of Systems Engineering and Electronics, 30(4), pp. 696–699.29.
Cai
, Y.
, and Liu
, F.
, 2007, “Constrained One Step Predictive Control of Discrete Time Markovian Jump Linear System,” Journal of Systems Engineering and Electronics, 29(6), pp. 950–954.30.
Liu
, F.
, and Cai
, Y.
, 2008, “Constrained Predictive Control of Markov Jump Linear Systems Based on Terminal Invariant Sets
,” Acta Automatica Sin.
, 34
(4
), pp. 496
–499
.31.
Kwon
, W. H.
, and Han
, S.
, 2005, Receding Horizon Control
, Springer-Verlag
, London
.32.
Kolmanovsky
, I.
, and Gilbert
, E. G.
, 1995, “Maximal Output Admissible SET for Discrete-Time Systems With Disturbance Inputs
,” Proceedings of the 1995 American Control Conference
, Seattle, Vol. 3, pp. 1995–1999.Copyright © 2011
by American Society of Mechanical Engineers
You do not currently have access to this content.
