Optimal and Stable Control for Two-Player Zero-Sum Game Using Adaptive Dynamic Programming

In this paper, an optimal and stable iteration learning scheme is developed for two-player zero-sum game (ZSG) in the discrete-time nonlinear systems. In the implementation of developed algorithm, the optimal and stable solution of Hamilton-Jacobi-Isaacs can be obtained based on adaptive dynamic programming (ADP). First, in order to obtain the optimal control policies, value iteration approach is employed with the proof of convergence given. Second, based on Lyapunov theory, an easy condition is proposed to get the stable control laws. Third, neural networks are used to implement the developed algorithm. Finally, a simulation example is included to verify the present method.