IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v156y2013i3d10.1007_s10957-012-0142-2.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-012-0142-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-012-0142-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. Mao, Xuerong, 1999. "Stability of stochastic differential equations with Markovian switching," Stochastic Processes and their Applications, Elsevier, vol. 79(1), pages 45-67, January.
    5. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. T. Senthilkumar & P. Balasubramaniam, 2011. "Delay-Dependent Robust Stabilization and H ∞ Control for Nonlinear Stochastic Systems with Markovian Jump Parameters and Interval Time-Varying Delays," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 100-120, October.
    2. E. K. Boukas, 2004. "Nonfragile Controller Design for Linear Markovian Jumping Parameters Systems," Journal of Optimization Theory and Applications, Springer, vol. 122(2), pages 241-255, August.
    3. Li, Yuyuan & Lu, Jianqiu & Kou, Chunhai & Mao, Xuerong & Pan, Jiafeng, 2018. "Robust discrete-state-feedback stabilization of hybrid stochastic systems with time-varying delay based on Razumikhin technique," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 152-161.
    4. Song, Gongfei & Zhang, Zimeng & Zhu, Yanan & Li, Tao, 2022. "Discrete-time control for highly nonlinear neutral stochastic delay systems," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    5. Mao, Xuerong & Shen, Yi & Yuan, Chenggui, 2008. "Almost surely asymptotic stability of neutral stochastic differential delay equations with Markovian switching," Stochastic Processes and their Applications, Elsevier, vol. 118(8), pages 1385-1406, August.
    6. Rathinasamy, Anandaraman & Nair, Priya, 2018. "Asymptotic mean-square stability of weak second-order balanced stochastic Runge–Kutta methods for multi-dimensional Itô stochastic differential systems," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 276-303.
    7. Chen, Wenbin & Gao, Fang & She, Jinhua & Xia, Weifeng, 2020. "Further results on delay-dependent stability for neutral singular systems via state decomposition method," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    8. Xi, Fubao, 2004. "Stability of a random diffusion with nonlinear drift," Statistics & Probability Letters, Elsevier, vol. 68(3), pages 273-286, July.
    9. Li, Bing, 2017. "A note on stability of hybrid stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 299(C), pages 45-57.
    10. Guo, Beibei & Xiao, Yu, 2024. "Synchronization of multi-link and multi-delayed inertial neural networks with Markov jump via aperiodically intermittent adaptive control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 435-453.
    11. Liang, Tiantian & Shi, Shengli & Ma, Yuechao, 2023. "Asynchronous sliding mode control of continuous-time singular markov jump systems with time-varying delay under event-triggered strategy," Applied Mathematics and Computation, Elsevier, vol. 448(C).
    12. Ruan, Dehao & Xu, Liping & Luo, Jiaowan, 2019. "Stability of hybrid stochastic functional differential equations," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 832-841.
    13. Zhou, Jianping & Sang, Chengyan & Li, Xiao & Fang, Muyun & Wang, Zhen, 2018. "H∞ consensus for nonlinear stochastic multi-agent systems with time delay," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 41-58.
    14. Yuan, Chenggui & Mao, Xuerong, 2004. "Convergence of the Euler–Maruyama method for stochastic differential equations with Markovian switching," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(2), pages 223-235.
    15. Xu, Jiang & Chen, Tao & Wen, Xiangdan, 2021. "Analysis of a Bailey–Dietz model for vector-borne disease under regime switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 580(C).
    16. Zhou, Qi & Yao, Deyin & Wang, Jiahui & Wu, Chengwei, 2016. "Robust control of uncertain semi-Markovian jump systems using sliding mode control method," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 72-87.
    17. Ye, Zhiyong & Zhang, He & Zhang, Hongyu & Zhang, Hua & Lu, Guichen, 2015. "Mean square stabilization and mean square exponential stabilization of stochastic BAM neural networks with Markovian jumping parameters," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 156-165.
    18. Li, Jin & Guo, Ying & Liu, Xiaotong & Zhang, Yifan, 2024. "Stabilization of highly nonlinear stochastic coupled systems with Markovian switching under discrete-time state observations control," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    19. Quanxin Zhu & Fubao Xi & Xiaodi Li, 2012. "Robust Exponential Stability of Stochastically Nonlinear Jump Systems with Mixed Time Delays," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 154-174, July.
    20. Bei Wu & Mou Chen & Xiaoming Chen, 2015. "Observer-Based Bounded Control for Discrete Time-Delay Uncertain Nonlinear Systems," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-16, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:156:y:2013:i:3:d:10.1007_s10957-012-0142-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.