In this paper, an event-triggered control (ETC) method is investigated to solve zero-sum game (ZSG) problems of unknown multi-player continuous-time nonlinear systems with input constraints by using adaptive dynamic programming (ADP). To relax the requirement of system dynamics, a neural network (NN) observer is constructed to identify the dynamics of multi-player system via the input and output data. Then, the event-triggered Hamilton–Jacobi–Isaacs (HJI) equation of the ZSG can be solved by constructing a critic NN, and the approximated optimal control law and the worst disturbance law can be obtained directly. A triggering scheme which determines the updating time instants of the control law and the disturbance law is developed. Thus, the proposed ADP-based ETC method cannot only reduce the computational burden, but also save communication resource and bandwidths. Furthermore, we prove that the signals of the closed-loop system and the approximate errors of the critic NN weights are uniformly ultimately bounded by using Lyapunov’s direct method, and the Zeno behavior is excluded. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed ETC scheme.

在本文中，研究了一种事件触发控制（ETC）方法，以通过使用自适应动态规划（ADP）来解决具有输入约束的未知多人连续时间非线性系统的零和博弈（ZSG）问题。为了放宽对系统动力学的要求，构建了一个神经网络 (NN) 观察器，通过输入和输出数据来识别多人系统的动力学。然后，可以通过构造critic NN来求解ZSG的事件触发Hamilton-Jacobi-Isaacs(HJI)方程，直接得到近似最优控制律和最坏扰动律。开发了一种确定控制律和扰动律更新时刻的触发方案。因此，所提出的基于 ADP 的 ETC 方法不仅可以减少计算负担，同时也节省了通信资源和带宽。此外，我们证明了闭环系统的信号和critic NN 权重的近似误差最终一致地通过使用Lyapunov 直接方法有界，并且排除了Zeno 行为。最后，提供了两个仿真例子来证明所提出的 ETC 方案的有效性。