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

Author

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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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