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

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.(c) 2023 The Franklin Institute. Published by Elsevier Inc. All rights reserved.

Automated summary

This article focuses on solving two-player zero-sum games without assuming the strict existence of saddle point. The upper and lower performance index functions are used to seek the solution of the games. The generalized policy iteration technique is applied to design the controller, and neural network approximators are used to update the approximation of the performance index functions. The convergence of the upper and lower performance index function sequences indicates the attainment of the saddle point.