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<p>In this paper, the zero-sum game issue for constrained multi-agent systems is investigated by utilizing the adaptive critic control approach. First, an innovative non-quadratic function is constructed to solve the asymmetric constraint problem in the multi-agent framework. Subsequently, the optimal control, the worst disturbance, and coupled Hamilton-Jacobi-Isaacs equation are rigorously derived for each follower. An adaptive critic control scheme is then developed to approximate the optimal cost function, thereby obtaining the near-optimal control and the near-worst disturbance of each agent. Notably, the Lyapunov method is employed to demonstrate the stability of the local neighborhood synchronization error and weight estimation error for each agent. It is worth mentioning that the stability analysis addresses the challenge induced by the non-quadratic function. Finally, an example is offered to verify the efficiency of the innovative learning algorithm proposed in this paper.</p>

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Adaptive critic designs for asymmetric constrained zero-sum games of nonlinear multi-agent systems

  • 期刊论文

  • 发表日期：

    2026年5月8日

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  • Wenting Yan,
  • Ding Wang,
  • Menghua Li,
  • Junfei Qiao

摘要

In this paper, the zero-sum game issue for constrained multi-agent systems is investigated by utilizing the adaptive critic control approach. First, an innovative non-quadratic function is constructed to solve the asymmetric constraint problem in the multi-agent framework. Subsequently, the optimal control, the worst disturbance, and coupled Hamilton-Jacobi-Isaacs equation are rigorously derived for each follower. An adaptive critic control scheme is then developed to approximate the optimal cost function, thereby obtaining the near-optimal control and the near-worst disturbance of each agent. Notably, the Lyapunov method is employed to demonstrate the stability of the local neighborhood synchronization error and weight estimation error for each agent. It is worth mentioning that the stability analysis addresses the challenge induced by the non-quadratic function. Finally, an example is offered to verify the efficiency of the innovative learning algorithm proposed in this paper.