Global optimal strategies of a class of finite-horizon continuous-time nonaffine nonlinear zero-sum game using a new iteration algorithm

In this paper we aim to solve the global optimal strategies of a class of finite-horizon continuous-time nonaffine nonlinear zero-sum game. The idea is to use a iterative algorithm to obtain the saddle point. The iterative algorithm is between two sequences which are a sequence of linear quadratic zero-sum game and a sequence of Riccati differential equation. The necessary conditions of global optimal strategies are established. A simulation example is given to illustrate the performance of the proposed approach.