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.

中文翻译：

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离散时间非线性 PE 博弈的同步容错近最优控制

在本文中，针对一类离散时间非线性追逃（PE）博弈研究了同步容错近最优控制策略设计问题。在研究的 PE 游戏中，同时考虑了输入饱和现象和可能的执行器故障。为了加快估计速度，通过引入非线性函数设计了一种新颖的非线性故障估计器。然后，为了获得离散时间 PE 游戏的同步控制策略，建立了一个近似 Hamilton-Jacobi-Isaacs (HJI) 方程，该方程在大多数现有结果中很少用于离散时间近似动态规划。需要注意的是，基于近似 HJI 方程设计的同步控制策略由于其拟牛顿迭代形式可以非常快地收敛。此外，建立了充分条件以保证所研究的系统是一致最终有界的。最后，对高超音速飞行器系统进行了数值模拟，以验证所提出的方法。