A Zero-Sum Game-Based Hybrid Iteration Reinforcement Learning Scheme to Optimal Control for Fuzzy Singularly Perturbed Systems

This paper proposes a model-free hybrid iteration algorithm to solve the zero-sum game for nonlinear singularly perturbed systems based on the Takagi-Sugeno fuzzy model. Firstly, the original nonlinear systems are approximated using fuzzy modeling, while the zero-sum game framework is employed to solve the optimal control problem of singularly perturbed systems. Therefore, the nonlinear optimal control problem is reduced to designing fuzzy control policies by solving game algebraic Riccati equations. Subsequently, a model-free hybrid iteration approach is developed that removes the requirement for system dynamics. Furthermore, the hybrid iteration method does not rely on initial stabilizing control policies and has a faster convergence rate than value iteration. Meanwhile, the convergence of the proposed algorithm is demonstrated through Lyapunov stability analysis. Finally, a numerical example is employed to illustrate the effectiveness of the designed algorithm.