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Fuzzy-based asynchronous controller design on reachable set synthesis of nonlinear hidden Markovian jump systems

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  • Feng, Zhiguang
  • Feng, Bo
  • Zhang, Naifu

Abstract

This article investigates the reachable set synthesis problem for delay nonlinear hidden Markovian jump systems (NHMJSs) subject to asynchronous control strategy. The purpose is to find a suitable fuzzy controller to ensure that all the states of the generated closed-loop NHMJSs are bounded in the predetermined ellipsoidal region. First of all, Takagi–Sugeno (T–S) fuzzy model is used to approximate the nonlinear dynamics systems (NDS). On this basis, the hidden Markov model (HMM) is introduced to represent the asynchronous phenomenon among the controller modes and subsystem modes. Under taking time-varying delays into account, two descriptions of the reachable set ellipsoidal bound are provided. In addition, the relevant parameters of the fuzzy asynchronous controller are obtained by selecting the Lyapunov functionals with two different mode-dependent matrices, respectively. Finally, some numerical examples are given to verify the feasibility of the method proposed in this paper.

Suggested Citation

  • Feng, Zhiguang & Feng, Bo & Zhang, Naifu, 2023. "Fuzzy-based asynchronous controller design on reachable set synthesis of nonlinear hidden Markovian jump systems," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    • Handle: RePEc:eee:chsofr:v:170:y:2023:i:c:s0960077923002412
    DOI: 10.1016/j.chaos.2023.113340
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    References listed on IDEAS

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    1. Xin, Xilin & Tu, Yidong & Stojanovic, Vladimir & Wang, Hai & Shi, Kaibo & He, Shuping & Pan, Tianhong, 2022. "Online reinforcement learning multiplayer non-zero sum games of continuous-time Markov jump linear systems," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    2. Karthick, S.A. & Sakthivel, R. & Ma, Y.K. & Leelamani, A., 2020. "Observer based guaranteed cost control for Markovian jump stochastic neutral-type neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    3. Peng Cheng & Hai Wang & Vladimir Stojanovic & Fei Liu & Shuping He & Kaibo Shi, 2022. "Dissipativity-based finite-time asynchronous output feedback control for wind turbine system via a hidden Markov model," International Journal of Systems Science, Taylor & Francis Journals, vol. 53(15), pages 3177-3189, November.
    4. Yang, Te & Wang, Zhen & Huang, Xia & Xia, Jianwei, 2022. "Sampled-data exponential synchronization of Markovian jump chaotic Lur'e systems with multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    5. Hyun Kim, Sung, 2019. "Generalized relaxation techniques for robust H∞ filtering of nonhomogeneous Markovian jump systems," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 542-556.
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    Cited by:

    1. Shen, Zhihao & Zhang, Liang & Niu, Ben & Zhao, Ning, 2023. "Event-based reachable set synthesis for delayed nonlinear semi-Markov systems," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).

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