IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v360y2019icp122-130.html
   My bibliography  Save this article

A necessary and sufficient RHC stabilizability condition for stochastic control with delayed input

Author

Listed:
  • Gao, Rong
  • Xu, Juanjuan
  • Li, Wuquan
  • Liu, Xiaohua

Abstract

We study the mean-square stabilizability of Itô stochastic systems with delayed input. In contrast to most previous results, where only sufficient condition was derived, this paper proposes a necessary and sufficient stabilization condition by exploring the receding horizon control (RHC) and the coupled Riccati equations. It is shown that the system controlled by RHC is stabilizable if and only if the two coupled Lyapunov type inequalities are satisfied. The key is to design a novel cost function based on the optimal cost of finite horizon optimization problem.

Suggested Citation

  • Gao, Rong & Xu, Juanjuan & Li, Wuquan & Liu, Xiaohua, 2019. "A necessary and sufficient RHC stabilizability condition for stochastic control with delayed input," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 122-130.
    • Handle: RePEc:eee:apmaco:v:360:y:2019:i:c:p:122-130
    DOI: 10.1016/j.amc.2019.04.072
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319303741
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.04.072?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. Chen, Guoliang & Xia, Jianwei & Zhuang, Guangming & Zhao, Junsheng, 2018. "Improved delay-dependent stabilization for a class of networked control systems with nonlinear perturbations and two delay components," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 1-17.
    Full references (including those not matched with items on IDEAS)

    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. Jiao, Shiyu & Shen, Hao & Wei, Yunliang & Huang, Xia & Wang, Zhen, 2018. "Further results on dissipativity and stability analysis of Markov jump generalized neural networks with time-varying interval delays," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 338-350.
    2. Wang, Jing & Hu, Xiaohui & Wei, Yunliang & Wang, Zhen, 2019. "Sampled-data synchronization of semi-Markov jump complex dynamical networks subject to generalized dissipativity property," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 853-864.
    3. Cui, Beibei & Song, Xinmin & Liu, Xiyu, 2019. "Unbiased steady minimum-variance estimation for systems with measurement-delay and unknown inputs," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 379-391.
    4. Wu, Kai-Ning & Sun, Han-Xiao & Yang, Baoqing & Lim, Cheng-Chew, 2018. "Finite-time boundary control for delay reaction–diffusion systems," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 52-63.
    5. Yang, Te & Chen, Guoliang & Xia, Jianwei & Wang, Zhen & Sun, Qun, 2019. "Robust H∞ filtering for polytopic uncertain stochastic systems under quantized sampled outputs," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 688-701.
    6. Ma, Zheng & Song, Jiasheng & Zhou, Jianping, 2022. "Reliable event-based dissipative filter design for discrete-time system with dynamic quantization and sensor fault," Applied Mathematics and Computation, Elsevier, vol. 418(C).
    7. Tan, Guoqiang & Wang, Zhanshan & Li, Cong, 2020. "H∞ performance state estimation of delayed static neural networks based on an improved proportional-integral estimator," Applied Mathematics and Computation, Elsevier, vol. 370(C).
    8. Haghighi, Payam & Tavassoli, Babak & Farhadi, Alireza, 2020. "A practical approach to networked control design for robust H∞ performance in the presence of uncertainties in both communication and system," Applied Mathematics and Computation, Elsevier, vol. 381(C).
    9. Hejun Yao & Fangzheng Gao, 2022. "Design of Observer and Dynamic Output Feedback Control for Fuzzy Networked Systems," Mathematics, MDPI, vol. 11(1), pages 1-13, December.
    10. Feng, Hongyan & Xu, Huiling & Xu, Shengyuan & Chen, Weimin, 2019. "Model reference tracking control for spatially interconnected discrete-time systems with interconnected chains," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 50-62.
    11. Liang, Xingyue & Xia, Jianwei & Chen, Guoliang & Zhang, Huasheng & Wang, Zhen, 2019. "Dissipativity-based sampled-data control for fuzzy Markovian jump systems," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 552-564.
    12. Wang, Zhichuang & Chen, Guoliang & Ba, Hezhen, 2019. "Stability analysis of nonlinear switched systems with sampled-data controllers," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 297-309.
    13. Sohaira Ahmad & Muhammad Rehan & Anas Ibrar & Muhammad Umair Ali & Amad Zafar & Seong Han Kim, 2024. "Novel Robust Estimation-Based Control of One-Sided Lipschitz Nonlinear Systems Subject to Output and Input Delays," Mathematics, MDPI, vol. 12(9), pages 1-35, April.
    14. Hongqian Lu & Yue Hu & Chaoqun Guo & Wuneng Zhou, 2019. "New Stability Criteria for Event-Triggered Nonlinear Networked Control System with Time Delay," Complexity, Hindawi, vol. 2019, pages 1-13, June.
    15. Zhang, Jing & Xia, Jianwei & Sun, Wei & Zhuang, Guangming & Wang, Zhen, 2018. "Finite-time tracking control for stochastic nonlinear systems with full state constraints," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 207-220.

    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:eee:apmaco:v:360:y:2019:i:c:p:122-130. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.