Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-06T12:04:25.805Z Has data issue: false hasContentIssue false

FEEDBACK PREDICTIVE CONTROL OF NONHOMOGENEOUS MARKOV JUMP SYSTEMS WITH NONSYMMETRIC CONSTRAINTS

Published online by Cambridge University Press:  18 December 2014

YANQING LIU
Affiliation:
Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Institute of Automation, Jiangnan University, Wuxi, China email [email protected], [email protected]
FEI LIU*
Affiliation:
Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Institute of Automation, Jiangnan University, Wuxi, China email [email protected], [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We consider feedback predictive control of a discrete nonhomogeneous Markov jump system with nonsymmetric constraints. The probability transition of the Markov chain is modelled as a time-varying polytope. An ellipsoid set is utilized to construct an invariant set in the predictive controller design. However, when the constraints are nonsymmetric, this method leads to results which are over conserved due to the geometric characteristics of the ellipsoid set. Thus, a polyhedral invariant set is applied to enlarge the initial feasible area. The results obtained are for a more general class of dynamical systems, and the feasibility region is significantly enlarged. A numerical example is presented to illustrate the advantage of the proposed method.

Type
Research Article
Copyright
Copyright © 2014 Australian Mathematical Society 

References

Bemporad, A., Morari, M., Dua, V. and Pistikopoulos, E. N., “The explicit linear quadratic regulator for constrained systems”, Automatica J. IFAC 38 (2002) 320; doi:10.1016/S0005-1098(01)00174-1.Google Scholar
Hou, Z. and Wang, B., “Markov skeleton process approach to a class of partial differential–integral equation systems arising in operations research”, Int. J. Innov. Comput. I 7 (2011) 67996814; http://www.ijicic.org/ijicic-10-08090.pdf.Google Scholar
Huang, H., Li, D., Lin, Z. and Xi, Y., “An improved robust model predictive control design in the presence of actuator saturation”, Automatica J. IFAC 47 (2011) 861864; doi:10.1016/j.automatica.2011.01.045.Google Scholar
“Internet traffic report”, http://www.internettrafficreport.com(2008).Google Scholar
Iosifescu, M., Finite Markov processes and their applications (John Wiley, Bucharest, 1980).Google Scholar
Kemeny, J. and Snell, J., Finite Markov chains (Van Nostrand, Princeton, NJ, 1960).Google Scholar
Kothare, M. V., Balakrishnan, V. and Morari, M., “Robust constrained model predictive control using linear matrix inequalities”, Automatica J. IFAC 32 (1996) 13611379; doi:10.1016/0005-1098(96)00063-5.Google Scholar
Liu, J., Gu, Z. and Hu, S., “H-infinity filtering for Markovian jump systems with time-varying delays”, Int. J. Innov. Comput. I 7 (2011) 12991310; http://www.researchgate.net/publication/224151362.Google Scholar
Mayne, D. Q., Rawlings, J. B. and Rao, C. V., “Constrained model predictive control: stability and optimality”, Automatica J. IFAC 36 (2000) 789814; doi:10.1016/S0005-1098(00)00173-4.Google Scholar
Narendra, K. S. and Tripathi, S. S., “Identification and optimization of aircraft dynamics”, J. Aircraft 10 (1973) 193199; doi:10.2514/3.44364.Google Scholar
Pluymers, B., Rossiter, J. A., Suykens, J. A. K. and Moor, B. D., “The efficient computation of polyhedral invariant sets for linear systems with polytopic uncertainty”, in: Proceedings of the American Control Conference, Volume 2 (2005) 804809; doi:10.1109/ACC.2005.1470058.Google Scholar
Shi, P., Boukas, E. K. and Agarwal, R., “Kalman filtering for continuous-time uncertain systems with Markovian jumping parameters”, IEEE Trans. Automat. Control 44 (1999) 15921597; doi:10.1109/9.780431.Google Scholar
Shi, P., Boukas, E. K. and Agarwal, R., “Control of Markovian jump discrete-time systems with norm bounded uncertainty and unknown delay”, IEEE Trans. Automat. Control 44 (1999) 21392144; doi:10.1109/9.802932.Google Scholar
Shi, P., Xia, Y., Liu, G. and Rees, D., “On designing of sliding mode control for stochastic jump systems”, IEEE Trans. Automat. Control 51 (2006) 97103; doi:10.1109/TAC.2005.861716.CrossRefGoogle Scholar
Vouzis, P. D., Bleris, L. G., Arnold, M. G. and Kothare, M. V., “A system-on-a-chip implementation for embedded real-time model predictive control”, IEEE Trans. Control Syst. Technol. 17 (2009) 10061017; doi:10.1109/TCST.2008.2004503.CrossRefGoogle Scholar
Wakasa, Y., Tanaka, K. and Nishimura, Y., “Distributed output consensus via LMI-based model predictive control and dual decomposition”, Int. J. Innov. Comput. I 7 (2011) 58015812; http://www.ijicic.org/ijicic-10-08009.pdf.Google Scholar
Wan, Z. and Kothare, M. V., “An efficient off-line formulation of robust model predictive control using linear matrix inequalities”, Automatica J. IFAC 39 (1996) 837846; doi:10.1016/S0005-1098(02)00174-7.Google Scholar
Wan, Z. and Kothare, M. V., “Efficient scheduled stabilizing output feedback model predictive control for constrained nonlinear systems”, IEEE Trans. Automat. Control 49 (2004) 11721177; doi:10.1109/TAC.2004.831122.CrossRefGoogle Scholar
Yin, Y., Shi, P. and Liu, F., “Gain-scheduled robust fault detection on time-delay stochastic nonlinear systems”, IEEE Trans. Ind. Electron. 58 (2011) 13611379; doi:10.1109/TIE.2010.2103537.Google Scholar
Zhang, L. and Boukas, E. K., “Mode-dependent $H_{\infty }$ filtering for discrete-time Markovian jump linear systems with partly unknown transition probabilities”, Automatica J. IFAC 45 (2009) 14621467; doi:10.1016/j.automatica.2009.02.002.Google Scholar
Zhang, L. and Boukas, E. K., “$H_{\infty }$ control for discrete-time Markovian jump linear systems with partly unknown transition probabilities”, Int. J. Robust Nonlinear Control 19 (2009) 868883; doi:10.1002/rnc.1355.CrossRefGoogle Scholar