Nash Equilibrium Seeking for Nonzero-Sum Games of Switched Nonlinear Systems

Abstract

This article investigates Nash equilibrium seeking for nonzero-sum games of switched nonlinear systems. A novel cost function is presented that measures the system state cost and control cost while considering the dynamics under different switching modes. Then, a new coupled switching Hamilton-Jacobi (HJ) equation is derived. To address the challenge of directly solving the HJ equation, an event-triggered two-stage reinforcement learning strategy is proposed. Upon event triggering, each player’s switching law determines the optimal subsystem to switch to by minimizing the HJ equation. Subsequently, the corresponding learning law for each player updates its respective input via the determined optimal subsystem. The proposed algorithm achieves Nash equilibrium while ensuring system stability. Furthermore, Zeno behavior is avoided, and the computational and communication loads are reduced. Finally, the proposed algorithm’s efficacy is substantiated through two simulation examples.