No CrossRef data available.
Article contents
FEEDBACK PREDICTIVE CONTROL OF NONHOMOGENEOUS MARKOV JUMP SYSTEMS WITH NONSYMMETRIC CONSTRAINTS
Published online by Cambridge University Press: 18 December 2014
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.
Keywords
- Type
- Research Article
- Information
- 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)
3–20; 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)
6799–6814; 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)
861–864; 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
Kothare, M. V., Balakrishnan, V. and Morari, M., “Robust constrained model predictive
control using linear matrix inequalities”,
Automatica J. IFAC 32 (1996)
1361–1379; 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)
1299–1310; 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)
789–814; 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)
193–199; 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)
804–809; 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)
1592–1597; 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)
2139–2144; 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)
97–103; 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)
1006–1017; 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)
5801–5812; 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)
837–846; 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)
1172–1177; 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)
1361–1379; 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)
1462–1467; doi:10.1016/j.automatica.2009.02.002.Google Scholar
$H_{\infty }$ filtering for discrete-time Markovian jump linear systems with
partly unknown transition probabilities”,
Automatica J. IFAC 45 (2009)
1462–1467; doi:10.1016/j.automatica.2009.02.002.Google ScholarZhang, 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)
868–883; doi:10.1002/rnc.1355.CrossRefGoogle Scholar
$H_{\infty }$ control for discrete-time Markovian jump linear systems with
partly unknown transition probabilities”, Int.
J. Robust Nonlinear Control 19 (2009)
868–883; doi:10.1002/rnc.1355.CrossRefGoogle Scholar
You have
Access