Nash Equilibrium Solutions for Switched Nonlinear Systems: A Fuzzy-Based Dynamic Game Method

Abstract

This article seeks the Nash equilibrium solutions for mixed zero-sum (MZS) games in unknown switched nonlinear systems. A new paradigm is presented, which offers a framework for analyzing strategic interactions of MZS games. To solve the coupled switching Hamilton–Jacobi equations, an event-triggered fuzzy reinforcement learning strategy is proposed. An identifier is designed to approximate the system's unknown nonlinear dynamics, and a critic is proposed to guide policy optimization. The proposed algorithm achieves Nash equilibrium while ensuring system stability. In addition, Zeno behavior is avoided, and the computational and communication loads are reduced. Finally, two simulation examples are provided to verify the effectiveness of the proposed method.