In this article, the neural network (NN)-based adaptive dynamic programming (ADP) event-triggered control method is presented to obtain the near-optimal control policy for the model-free finite-horizon $H_\infty $ optimal tracking control problem with constrained control input. First, using available input–output data, a data-driven model is established by a recurrent NN (RNN) to reconstruct the unknown system. Then, an augmented system with event-triggered mechanism is obtained by a tracking error system and a command generator. We present a novel event-triggering condition without Zeno behavior. On this basis, the relationship between event-triggered Hamilton–Jacobi–Isaacs (HJI) equation and time-triggered HJI equation is given in Theorem 3 . Since the solution of the HJI equation is time-dependent for the augmented system, the time-dependent activation functions of NNs are considered. Moreover, an extra error is incorporated to satisfy the terminal constraints of cost function. This adaptive control pattern finds, in real time, approximations of the optimal value while also ensuring the uniform ultimate boundedness of the closed-loop system. Finally, the effectiveness of the proposed near-optimal control pattern is verified by two simulation examples.

中文翻译：

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具有事件触发机制的连续时间非线性系统的数据驱动有限视野H-跟踪控制


本文提出了基于神经网络（NN）的自适应动态规划（ADP）事件触发控制方法，以获得无模型有限范围 $H_\infty $ 最优跟踪控制问题的近最优控制策略具有受约束的控制输入。首先，利用可用的输入输出数据，通过循环神经网络（RNN）建立数据驱动模型来重建未知系统。然后，通过跟踪误差系统和命令生成器获得具有事件触发机制的增强系统。我们提出了一种新颖的没有芝诺行为的事件触发条件。在此基础上，定理3给出了事件触发的Hamilton-Jacobi-Isaacs (HJI)方程与时间触发的HJI方程之间的关系。由于增强系统的 HJI 方程的解与时间相关，因此需要考虑神经网络的时间相关激活函数。此外，还引入了额外的误差来满足成本函数的终端约束。这种自适应控制模式实时找到最佳值的近似值，同时确保闭环系统的统一最终有界性。最后，通过两个仿真例子验证了所提出的近最优控制模式的有效性。