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Adaptive practical finite-time \(H_\infty \) tracking control for nonlinear stochastic Markov jump systems

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Abstract

This paper intends to address an adaptive practical finite-time \(H_\infty \) tracking control problem for nonlinear stochastic Markov jump systems (NSMJSs) with uncertain parameters and external interferences. Firstly, the concepts of practical finite-time stochastic stability (PFSS) in p-th moment sense and weak \(H_\infty \) performance are presented, and a Lyapunov-type criterion is suggested which guarantees that NSMJSs satisfy both of the above concepts. Secondly, a semi-globally adaptive practical finite-time \(H_\infty \) tracking control algorithm is developed by utilizing the adaptive backstepping technique and a fuzzy logic system (FLS) used for estimating uncertain functions. Finally, to verify the efficacy of the proposed control approach, a simulation comparison is conducted.

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Funding

This work was supported by the National Natural Science Foundation of China (Grant Nos. 62203220, 62373229, 62073144), the National Science Foundation of Jiangsu Province under Grant BK2022094, the Taishan Scholar Program Special Fund.

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Authors and Affiliations

  1. School of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, 266590, China

    Qingkang Zhang & Weihai Zhang

  2. School of Information and Control Engineering, Qingdao University of Technology, Qingdao, 266520, China

    Tianliang Zhang

  3. School of Automation, Nanjing University of Science and Technology, Nanjing, 210094, China

    Tianliang Zhang

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  1. Qingkang Zhang
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Correspondence to Tianliang Zhang or Weihai Zhang.

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Zhang, Q., Zhang, T. & Zhang, W. Adaptive practical finite-time \(H_\infty \) tracking control for nonlinear stochastic Markov jump systems. Nonlinear Dyn 111, 21765–21778 (2023). https://doi.org/10.1007/s11071-023-08991-w

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  • DOI: https://doi.org/10.1007/s11071-023-08991-w

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