Neural network-based near-optimal control for nonlinear discrete-time zero-sum differential games associated with the H<inf>∞</inf> control problem

Abstract

In this paper, we will present a new method to solve online the Hamilton-Jacobi-Isaacs (HJI) equation appearing in the two-player zero-sum differential game of the nonlinear system. First, an online parametric structure is designed by using a neural network to approximate the value function associating with the two-player zero-sum differential game. Second, online approximator-based controller designs are presented by using two neural networks to find (saddle point) equilibria. Third, Novel weight update laws for the critic, action and disturbance networks are given, and all parameters are tuned online. Fourth, it is shown that the system state, all neural networks weight estimation errors are uniformly ultimately bounded by using Lyapunov techniques. Further, it is shown that the output of the action network approaches the optimal control input with small bounded error and the output of the disturbance network approaches the worst disturbance with small bounded error and. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.