This paper develops a model-free approach to solve the event-triggered optimal consensus of multiple Euler-Lagrange systems (MELSs) via reinforcement learning (RL). Firstly, an augmented system is constructed by defining a pre-compensator to circumvent the dependence on system dynamics. Secondly, the Hamilton-Jacobi-Bellman (HJB) equations are applied to the deduction of the model-free event-triggered optimal controller. Thirdly, we present a policy iteration (PI) algorithm derived from RL, which converges to the optimal policy. Then, the value function of each agent is represented through a neural network to realize the PI algorithm. Moreover, the gradient descent method is used to update the neural network only at a series of discrete event-triggered instants. The specific form of the event-triggered condition is then proposed, and it is guaranteed that the closed-loop augmented system under the event-triggered mechanism is uniformly ultimately bounded (UUB). Meanwhile, the Zeno behavior is also eliminated. Finally, the validity of this approach is verified by a simulation example.

中文翻译：

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通过强化学习对多个Euler-Lagrange系统进行无模型触发的最优共识控制

本文开发了一种无模型方法，通过强化学习（RL）解决了多个Euler-Lagrange系统（MELS）的事件触发的最优共识。首先，通过定义预补偿器来构建增强系统，以规避对系统动力学的依赖。其次，将Hamilton-Jacobi-Bellman（HJB）方程应用于无模型事件触发的最优控制器的推论。第三，我们提出了一种基于RL的策略迭代（PI）算法，该算法收敛于最优策略。然后，通过神经网络表示每个主体的值函数，以实现PI算法。此外，梯度下降法仅在一系列离散的事件触发时刻用于更新神经网络。然后提出事件触发条件的特定形式，并保证了事件触发机制下的闭环扩充系统是统一的最终有界（UUB）。同时，也消除了芝诺行为。最后，通过仿真实例验证了该方法的有效性。