Multiperson zero‐sum differential games for a class of uncertain nonlinear systems

Abstract

SUMMARYIn this paper, multiperson zero‐sum differential games for a class of continuous‐time uncertain nonlinear systems are solved using a new iterative adaptive dynamic programming (ADP) algorithm. The idea is to use ADP technique to obtain the optimal control pair iteratively that makes the performance index function reach the optimal solution of the zero‐sum differential games without the system model. It proves that the iterative performance index functions are convergent to the optimal solution of the game. Stability properties of the system under the iterative control pairs are also presented. Neural networks are used to build the system model, approximate the performance index function, and compute the optimal control policy, respectively, for facilitating the implementation of the iterative ADP method. Finally, two simulation examples are given to demonstrate the performance of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.