School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China.
School of Automation, Beijing Institute of Technology, Beijing 100081, China.
Neural Netw. 2020 Dec;132:30-42. doi: 10.1016/j.neunet.2020.08.004. Epub 2020 Aug 20.
In this paper, we study an event-driven H control problem of continuous-time nonlinear systems. Initially, with the introduction of a discounted cost function, we convert the nonlinear H control problem into an event-driven nonlinear two-player zero-sum game. Then, we develop an event-driven Hamilton-Jacobi-Isaacs equation (HJIE) related to the two-player zero-sum game. After that, we propose a novel event-triggering condition guaranteeing Zeno behavior not to happen. The triggering threshold in the newly proposed event-triggering condition can be kept positive without requiring to properly choose the prescribed level of disturbance attenuation. To solve the event-driven HJIE, we employ an adaptive critic architecture which contains a unique critic neural network (NN). The weight parameters used in the critic NN are tuned via the gradient descent method. After that, we carry out stability analysis of the hybrid closed-loop system based on Lyapunov's direct approach. Finally, we provide two nonlinear plants, including the pendulum system, to validate the proposed event-driven H control scheme.
在本文中，我们研究了连续时间非线性系统的事件驱动 H 控制问题。首先，通过引入折扣代价函数，我们将非线性 H 控制问题转化为事件驱动的非线性二人零和博弈。然后，我们提出了一个与二人零和博弈相关的事件驱动的 Hamilton-Jacobi-Isaacs 方程（HJIE）。之后，我们提出了一种新的事件触发条件，保证不会发生零和行为。在新提出的事件触发条件中，触发阈值可以保持正值，而无需正确选择规定的干扰衰减水平。为了解决事件驱动的 HJIE，我们采用了一种自适应评论家架构，其中包含一个独特的评论家神经网络（NN）。评论家 NN 中的权值参数通过梯度下降法进行调整。之后，我们基于 Lyapunov 直接方法对混合闭环系统进行了稳定性分析。最后，我们提供了两个非线性被控对象，包括摆锤系统，以验证所提出的事件驱动 H 控制方案。
