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Gain-Scheduled Worst-Case Control on Nonlinear Stochastic Systems Subject to Actuator Saturation and Unknown Information

Author

Listed:
  • Peng Shi

    (Victoria University
    The University of Adelaide
    University of Glamorgan
    Jiangnan University)

  • Yanyan Yin

    (Jiangnan University)

  • Fei Liu

    (Jiangnan University)

Abstract

In this paper, we propose a method for designing continuous gain-scheduled worst-case controller for a class of stochastic nonlinear systems under actuator saturation and unknown information. The stochastic nonlinear system under study is governed by a finite-state Markov process, but with partially known jump rate from one mode to another. Initially, a gradient linearization procedure is applied to describe such nonlinear systems by several model-based linear systems. Next, by investigating a convex hull set, the actuator saturation is transferred into several linear controllers. Moreover, worst-case controllers are established for each linear model in terms of linear matrix inequalities. Finally, a continuous gain-scheduled approach is employed to design continuous nonlinear controllers for the whole nonlinear jump system. A numerical example is given to illustrate the effectiveness of the developed techniques.

Suggested Citation

  • Peng Shi & Yanyan Yin & Fei Liu, 2013. "Gain-Scheduled Worst-Case Control on Nonlinear Stochastic Systems Subject to Actuator Saturation and Unknown Information," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 844-858, March.
    • Handle: RePEc:spr:joptap:v:156:y:2013:i:3:d:10.1007_s10957-012-0142-2
    DOI: 10.1007/s10957-012-0142-2
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    References listed on IDEAS

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    1. M. S. Mahmoud & P. Shi & A. W. A. Saif, 2009. "Stabilization of Linear Switched Delay Systems: ℋ2 and ℋ∞ Methods," Journal of Optimization Theory and Applications, Springer, vol. 142(3), pages 583-601, September.
    2. T. Senthilkumar & P. Balasubramaniam, 2011. "Delay-dependent robust control for uncertain stochastic T–S fuzzy systems with time-varying state and input delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(5), pages 877-887.
    3. S. Xu & J. Lam & P. Shi & E. K. Boukas & Y. Zou, 2009. "Guaranteed Cost Control for Uncertain Neutral Stochastic Systems via Dynamic Output Feedback Controllers," Journal of Optimization Theory and Applications, Springer, vol. 143(1), pages 207-223, October.
    4. K. Benjelloun & E. K. Boukas & O. L. V. Costa, 2000. "H∞-Control for Linear Time-Delay Systems with Markovian Jumping Parameters," Journal of Optimization Theory and Applications, Springer, vol. 105(1), pages 73-95, April.
    5. Mao, Xuerong, 1999. "Stability of stochastic differential equations with Markovian switching," Stochastic Processes and their Applications, Elsevier, vol. 79(1), pages 45-67, January.
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    Cited by:

    1. Guoliang Wei & Zidong Wang & Wangyan Li & Lifeng Ma, 2014. "A Survey on Gain-Scheduled Control and Filtering for Parameter-Varying Systems," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-10, April.

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