Nonlinear multi-person zero-sum differential games using iterative adaptive dynamic programming

In this paper, a class of continuous-time nonlinear multi-person zero-sum differential game problems is solved using an iterative adaptive dynamic programming (ADP) method. The idea is to use ADP technique to obtain the optimal control pair iteratively which makes the performance index function reach the saddle point of the zero-sum differential games, which does not require to check the existence of saddle point in advance. It can be proved that the optimal control pair can make the performance index function reach the optimum. Stability analysis of the nonlinear systems is presented and the convergence property of the performance index function is also proved. A simulation example is given to illustrate the performance of the present method.