GPI-Based design for partially unknown nonlinear two-player zero-sum games

Abstract

This article focuses on obtaining the solution of two-player zero-sum games (ZSGs) where the saddle point may not exist. From the standpoints of the upper performance index function (PIF) and lower PIF separately, we seek the solution of two-player differential ZSGs without assuming the strict existence of saddle point. To achieve the objective, we apply the generalized policy iteration (GPI) technique to design the controller. With neural network approximators, the system trajectory data are used to update the approximation of the PIFs. It is established that the upper (lower) PIF sequence is convergent along the iteration axis under the GPI scheme. When the two function sequences converge to equal values, the saddle point is attained, and vice versa. Numerical simulation results conformed to the suitability of the designed algorithm.