In this article, a method that applies event-triggered (ET) mechanism control to continuous-time (C-T) nonlinear systems with asymmetric constraints based on dual heuristic dynamic programing (DHP) structure is proposed. At first, we derive ET mechanism from traditional time-triggered and give the Hamilton–Jacobi–Isaacs (HJI) equation. Second, we give the triggering condition and prove the stability of system under ET mechanism. Then, two neural networks (NNs) are introduced, one of which is the critic network, which is designed to approximate the partial derivatives of value function with respect to inputs, and approximate disturbance policy. The other is the action network, which is used to acquire the estimation optimal control policy. Furthermore, we choose a suitable Lyapunov candidate function to prove that the system and NNs weight estimation errors are uniformly ultimately bounded (UUB). Besides, it is important that we prove that Zeno phenomenon can be avoided. Finally, simulation results are shown that the proposed method is feasible.

中文翻译：

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基于双重启发式动态规划结构的非对称约束CT系统事件触发最优控制

在本文中，一种应用事件触发（ET）机制的方法提出了基于对偶启发式动态规划 (DHP) 结构的具有非对称约束的连续时间 (CT) 非线性系统的控制。首先，我们从传统的时间触发中导出ET机制，并给出Hamilton-Jacobi-Isaacs（HJI）方程。其次，给出了触发条件，证明了ET机制下系统的稳定性。然后，引入了两种神经网络（NN），其中一种是批评网络，其设计用于近似值函数关于输入的偏导数，以及近似扰动策略。另一个是动作网络，用于获取估计最优控制策略。此外，我们选择合适的 Lyapunov 候选函数来证明系统和神经网络的权重估计误差最终一致有界 (UUB)。除了，重要的是我们要证明芝诺现象是可以避免的。最后仿真结果表明所提方法是可行的。