An Approximate Control Algorithm for Zero-Sum Differential Games Using Adaptive Critic Technique

Abstract

This paper investigates the optimal control for a class of continuous-time systems in the framework of zero-sum differential game. A novel adaptive dynamic programming (ADP) algorithm is proposed to approximate the optimal value function through a critic neural network (NN). First, a class of control systems with external disturbances are formulated as two-player zero-sum differential game. Then, the proposed approximate structure is implemented to obtain the approximate optimal control policy and the worst-base disturbance policy. Moreover, Lyapunov theory is utilized to demonstrate the uniform ultimate bounded stability of the closed-loop system. Finally, two simulation examples are given to demonstrate the effectiveness of the developed control scheme.