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Sliding-mode surface-based fixed-time adaptive critic tracking control for zero-sum game of switched nonlinear systems

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  • Liu, Minggang
  • Xu, Ning
  • Niu, Ben
  • Alotaibi, Naif D.

Abstract

In this paper, the issue of sliding-mode surface (SMS)-based fixed-time adaptive tracking control under the framework of critic network is considered for the zero-sum game of switched nonlinear systems. Firstly, the tracking error and reference trajectory are combined to construct an augmented system, which transforms the optimal tracking control issue into a basic optimal regulation issue. Meanwhile, sliding mode control technology is introduced to improve the robustness and response speed of the system. Subsequently, a special cost function associated with SMS is developed to find a series of optimal control strategies. Besides, the numerical solution of a Hamilton-Jacobi-Isaacs equation is acquired based on a single-critic network architecture. Then, convergence of the tracking error in fixed time and boundedness of the closed-loop signals are strictly proved via the fixed-time stability theory. Finally, the feasibility and optimality of the developed control scheme are verified by two simulation examples.

Suggested Citation

  • Liu, Minggang & Xu, Ning & Niu, Ben & Alotaibi, Naif D., 2025. "Sliding-mode surface-based fixed-time adaptive critic tracking control for zero-sum game of switched nonlinear systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 229(C), pages 78-95.
    • Handle: RePEc:eee:matcom:v:229:y:2025:i:c:p:78-95
    DOI: 10.1016/j.matcom.2024.09.025
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    References listed on IDEAS

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    1. Yulin Li & Ben Niu & Guangdeng Zong & Jinfeng Zhao & Xudong Zhao, 2022. "Command filter-based adaptive neural finite-time control for stochastic nonlinear systems with time-varying full-state constraints and asymmetric input saturation," International Journal of Systems Science, Taylor & Francis Journals, vol. 53(1), pages 199-221, January.
    2. Liu, Shanlin & Niu, Ben & Zong, Guangdeng & Zhao, Xudong & Xu, Ning, 2022. "Adaptive fixed-time hierarchical sliding mode control for switched under-actuated systems with dead-zone constraints via event-triggered strategy," Applied Mathematics and Computation, Elsevier, vol. 435(C).
    3. Zeghlache, Samir & Ghellab, Mohammed Zinelaabidine & Djerioui, Ali & Bouderah, Brahim & Benkhoris, Mohamed Fouad, 2023. "Adaptive fuzzy fast terminal sliding mode control for inverted pendulum-cart system with actuator faults," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 210(C), pages 207-234.
    4. Minggang Liu & Ning Xu, 2024. "Adaptive neural predefined-time hierarchical sliding mode control of switched under-actuated nonlinear systems subject to bouc-wen hysteresis," International Journal of Systems Science, Taylor & Francis Journals, vol. 55(13), pages 2659-2676, October.
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