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Resilient controller synthesis for Markovian jump systems with probabilistic faults and gain fluctuations under stochastic sampling operational mechanism

Author

Listed:
  • Li, Xiaoqing
  • Nguang, Sing Kiong
  • She, Kun
  • Cheng, Jun
  • Zhong, Shouming

Abstract

In this article, by exploiting the sampling communication mechanism (SCM) with probabilistically switching signals, the dissipativity-based resilient reliable control design problem is addressed for Markovian jump systems (MJSs), which simultaneous against the multiplicate stochastic intermittent actuator faults (MSIAFs) and randomly occurring controller gain fluctuations (ROCGFs). The primary objective of this work is to synthesis a resilient controller such that the underlying MJSs is stochastically stable while meeting an expected (Q,S,R)−ϑ dissipative performance index in the presence of ROCGFs. First and foremost, the randomly occurring actuator faults (ROAFs) and their failures rates are characterized by a series of mutually independent stochastic variables that satisfy prescribed probabilistic distributions for each actuator. The distortion degree and failure rate of each actuator can be quantized and calculated with the help of mathematical variance and expectation respectively. Secondly, the sampling controller with stochastically variable operation periods is considered and just assumed to switch between two different values in stochastic circumstances with certain probability. Thirdly, the nonfragile controller gain fluctuations also happens in a random framework which are obedient to Bernoulli distribution sequence (BDS). Fourthly, by resorting to an appropriately Lyapunov–Krasovskii functional (LKF) and adopting matrix inequality decoupling technique, several sufficient conditions for the solvability of the addressed problem are eventually formulated in the shape of linear matrix inequalities (LMIs). Ultimately, three real-life numerical examples are exploited to illustrate the effectiveness and applicability of the presented theoretical findings.

Suggested Citation

  • Li, Xiaoqing & Nguang, Sing Kiong & She, Kun & Cheng, Jun & Zhong, Shouming, 2021. "Resilient controller synthesis for Markovian jump systems with probabilistic faults and gain fluctuations under stochastic sampling operational mechanism," Applied Mathematics and Computation, Elsevier, vol. 392(C).
  • Handle: RePEc:eee:apmaco:v:392:y:2021:i:c:s0096300320305774
    DOI: 10.1016/j.amc.2020.125623
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    References listed on IDEAS

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    1. Li, Xiaoqing & She, Kun & Zhong, Shouming & Shi, Kaibo & Kang, Wei & Cheng, Jun & Yu, Yongbin, 2018. "Extended robust global exponential stability for uncertain switched memristor-based neural networks with time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 271-290.
    2. Cheng, Jun & Zhan, Yang, 2020. "Nonstationary l2−l∞ filtering for Markov switching repeated scalar nonlinear systems with randomly occurring nonlinearities," Applied Mathematics and Computation, Elsevier, vol. 365(C).
    3. Peng, Zhinan & Hu, Jiangping & Shi, Kaibo & Luo, Rui & Huang, Rui & Ghosh, Bijoy Kumar & Huang, Jiuke, 2020. "A novel optimal bipartite consensus control scheme for unknown multi-agent systems via model-free reinforcement learning," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    4. Wang, Xuelian & Xia, Jianwei & Wang, Jing & Wang, Zhen & Wang, Jian, 2020. "Reachable set estimation for Markov jump LPV systems with time delays," Applied Mathematics and Computation, Elsevier, vol. 376(C).
    5. Wang, Yudong & Xia, Jianwei & Wang, Zhen & Shen, Hao, 2020. "Design of a fault-tolerant output-feedback controller for thickness control in cold rolling mills," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    6. Shi, Kaibo & Wang, Jun & Zhong, Shouming & Zhang, Xiaojun & Liu, Yajuan & Cheng, Jun, 2019. "New reliable nonuniform sampling control for uncertain chaotic neural networks under Markov switching topologies," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 169-193.
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