Yang Xiong, Wei Qinglai
IEEE Trans Neural Netw Learn Syst. 2021 Jan;32(1):91-104. doi: 10.1109/TNNLS.2020.2976787. Epub 2021 Jan 4.
This article studies an optimal event-triggered control (ETC) problem of nonlinear continuous-time systems subject to asymmetric control constraints. The present nonlinear plant differs from many studied systems in that its equilibrium point is nonzero. First, we introduce a discounted cost for such a system in order to obtain the optimal ETC without making coordinate transformations. Then, we present an event-triggered Hamilton-Jacobi-Bellman equation (ET-HJBE) arising in the discounted-cost constrained optimal ETC problem. After that, we propose an event-triggering condition guaranteeing a positive lower bound for the minimal intersample time. To solve the ET-HJBE, we construct a critic network under the framework of adaptive critic learning. The critic network weight vector is tuned through a modified gradient descent method, which simultaneously uses historical and instantaneous state data. By employing the Lyapunov method, we prove that the uniform ultimate boundedness of all signals in the closed-loop system is guaranteed. Finally, we provide simulations of a pendulum system and an oscillator system to validate the obtained optimal ETC strategy.
本文研究了受非对称控制约束的非线性连续时间系统的最优事件触发控制（ETC）问题。当前的非线性装置与许多已研究的系统不同，其平衡点非零。首先，我们为这样一个系统引入一个折扣成本，以便在不进行坐标变换的情况下获得最优ETC。然后，我们给出了在折扣成本约束最优ETC问题中出现的事件触发哈密顿 - 雅可比 - 贝尔曼方程（ET - HJBE）。之后，我们提出了一个事件触发条件，保证最小采样间隔时间有一个正的下界。为了解决ET - HJBE，我们在自适应批评家学习框架下构建了一个批评家网络。批评家网络权重向量通过一种改进的梯度下降方法进行调整，该方法同时使用历史和瞬时状态数据。通过使用李雅普诺夫方法，我们证明了闭环系统中所有信号的一致最终有界性得到保证。最后，我们提供了一个摆系统和一个振荡器系统的仿真，以验证所获得的最优ETC策略。
