Robust Optimal Control for Disturbed Nonlinear Zero-Sum Differential Games Based on Single NN and Least Squares

This paper establishes an approximate optimal critic learning algorithm based on single neural network (NN) policy iteration (PI) aiming at solving for continuous-time (CT) 2-player zero-sum games (ZSGs). In fact, we have to face the problem that the errors will disturb the dynamics and in turn identifying dynamics will generate errors. In order to prevent the effect of errors, in this paper, a single NN-based online PI algorithm is developed for the CT system, which is disturbed nonlinear ZSG. With plenty of online data, the Hamilton-Jacobi-Isaacs equation can be solved without complete dynamics. Then by the least-squares method, we can obtain the NN weights. Moreover, in the process of dealing with the undisturbed system, we find the way that obtains NN weights in this paper is equal to the way that obtains the optimal solution by the Gauss-Newton method. Based on the convergence of the Gauss-Newton method, we can efficiently obtain the optimal controller for the undisturbed system by utilizing online data. After getting the controller of the undisturbed system, it is time to take disturbance into consideration, so that we design a robust control pair to overcome the disturbance. In order to demonstrate the effectiveness of this algorithm, we design a set of simulations. The results verify that we can solve the disturbed nonlinear ZSG by this algorithm.