Synchronous Fault-Tolerant Near-Optimal Control for Discrete-Time Nonlinear PE Game

In this article, the synchronous fault-tolerant near-optimal control strategy design problem is studied for a class of discrete-time nonlinear pursuit-evasion (PE) games. In the studied PE game, the input saturation phenomenon and possible actuator fault are simultaneously taken into consideration. To accelerate the estimation speed, a novel nonlinear fault estimator is designed by introducing a nonlinear function. Then, for the purpose of obtaining the synchronous control strategy for the discrete-time PE games, an approximate Hamilton-Jacobi-Isaacs (HJI) equation is established, which is seldom utilized for the discrete-time approximate dynamic programming in most existing results. It should be noticed that the synchronous control strategy designed based on the approximate HJI equation can be convergent very fast because of its quasi-Newton's iteration form. Furthermore, the sufficient condition is established to guarantee that the studied system is uniformly ultimately bounded. Finally, a numerical simulation of the hypersonic vehicle system is carried out to validate the proposed methodology.