Abstract and Applied Analysis

A Simplified Predictive Control of Constrained Markov Jump System with Mixed Uncertainties

Yanyan Yin, Yanqing Liu, and Hamid R. Karimi

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Abstract

A simplified model predictive control algorithm is designed for discrete-time Markov jump systems with mixed uncertainties. The mixed uncertainties include model polytope uncertainty and partly unknown transition probability. The simplified algorithm involves finite steps. Firstly, in the previous steps, a simplified mode-dependent predictive controller is presented to drive the state to the neighbor area around the origin. Then the trajectory of states is driven as expected to the origin by the final-step mode-independent predictive controller. The computational burden is dramatically cut down and thus it costs less time but has the acceptable dynamic performance. Furthermore, the polyhedron invariant set is utilized to enlarge the initial feasible area. The numerical example is provided to illustrate the efficiency of the developed results.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 475808, 7 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412605763

Digital Object Identifier
doi:10.1155/2014/475808

Mathematical Reviews number (MathSciNet)
MR3191044

Zentralblatt MATH identifier
07022449

Citation

Yin, Yanyan; Liu, Yanqing; Karimi, Hamid R. A Simplified Predictive Control of Constrained Markov Jump System with Mixed Uncertainties. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 475808, 7 pages. doi:10.1155/2014/475808. https://projecteuclid.org/euclid.aaa/1412605763


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References

  • Z. Xiang, R. Wang, and Q. Chen, “Robust reliable stabilization of stochastic switched nonlinear systems under asynchronous switching,” Applied Mathematics and Computation, vol. 217, no. 19, pp. 7725–7736, 2011.
  • Z. Xiang, C. Qiao, and M. S. Mahmoud, “Finite-time analysis and ${H}_{\infty }$ control for switched stochastic systems,” Journal of the Franklin Institute, vol. 349, no. 3, pp. 915–927, 2012.
  • Z. Xiang, R. Wang, and Q. Chen, “Robust stabilization of uncertain stochastic switched nonlinear systems under asynchronous switching,” Proceedings of the IMechE, Part I: Journal of Systems and Control Engineering, vol. 225, no. 1, pp. 8–20, 2011.
  • E. K. Boukas, “Static output feedback control for stochastic hybrid systems: LMI approach,” Automatica, vol. 42, no. 1, pp. 183–188, 2006.
  • H. Gao, J. Lam, S. Xu, and C. Wang, “Stabilization and ${H}_{\infty }$ control of two-dimensional Markovian jump systems,” IMA Journal of Mathematical Control and Information, vol. 21, no. 4, pp. 377–392, 2004.
  • S. He and F. Liu, “Robust peak-to-peak filtering for Markov jump systems,” Signal Processing, vol. 90, no. 2, pp. 513–522, 2010.
  • S. He and F. Liu, “Finite-time ${H}_{\infty }$ control of nonlinear jump systems with time-delays via dynamic observer-based state feedback,” IEEE Transactions on Fuzzy Systems, vol. 20, no. 4, pp. 605–614, 2012.
  • S. He and F. Liu, “Finite-time boundedness of uncertain time-delayed neural network with Markovian jumping parameters,” Neurocomputing, vol. 103, no. 1, pp. 87–92, 2013.
  • Internet traffic report, 2008, http://www.internettracreport.com.
  • L. Zhang and E.-K. Boukas, “${H}_{\infty }$ control for discrete-time Markovian jump linear systems with partly unknown transition probabilities,” International Journal of Robust and Nonlinear Control, vol. 19, no. 8, pp. 868–883, 2009.
  • J. Xiong, J. Lam, H. Gao, and D. W. C. Ho, “On robust stabilization of Markovian jump systems with uncertain switching probabilities,” Automatica, vol. 41, no. 5, pp. 897–903, 2005.
  • Y. Yin, P. Shi, and F. Liu, “Gain-scheduled robust fault detection on time-delay stochastic nonlinear systems,” IEEE Transactions on Industrial Electronics, vol. 58, no. 10, pp. 4908–4916, 2011.
  • J. B. R. do Val and T. Basar, “Receding horizon control of Markov jump linear systems,” in Proceedings of the American Control Conference, pp. 3195–3199, Albuquerque, NM, USA, June 1997.
  • B.-G. Park, J.-W. Lee, and W. H. Kwon, “Receding horizon control for linear discrete systems with jump parameters,” in Proceedings of the 36th IEEE Conference on Decision and Control, pp. 3956–3957, San Diego, Calif, USA, December 1997.
  • D. Q. Mayne, J. B. Rawlings, C. V. Rao, and P. O. M. Scokaert, “Constrained model predictive control: stability and optimality,” Automatica, vol. 36, no. 6, pp. 789–814, 2000.
  • L. Liu, Z. Liu, and J. Zhang, “Nonlinear model predictive control with terminal invariant manifolds for stabilization of underactuated surface vessel,” Abstract and Applied Analysis, vol. 47, no. 4, pp. 861–864, 2011.
  • J. A. De Doná, M. M. Seron, D. Q. Mayne, and G. C. Goodwin, “Enlarged terminal sets guaranteeing stability of receding horizon control,” Systems & Control Letters, vol. 47, no. 1, pp. 57–63, 2002.
  • R. S. C. Lambert, P. Rivotti, and E. N. Pistikopoulos, “A novel approximation technique for online and multi-parametric model predictive control,” Computer Aided Chemical Engineering, vol. 29, pp. 739–742, 2011.
  • M. V. Kothare, V. Balakrishnan, and M. Morari, “Robust constrained model predictive control using linear matrix inequalities,” Automatica, vol. 32, no. 10, pp. 1361–1379, 1996.
  • B. Pluymers, J. A. Rossiter, J. A. K. Suykens, and B. De Moor, “The efficient computation of polyhedral invariant sets for linear systems with polytopic uncertainty,” in Proceedings of the American Control Conference (ACC '05), pp. 804–809, June 2005. \endinput