Event-Triggered Optimal Control for a Class of Continuous-Time Switched Nonlinear Systems

Abstract

This paper studies the optimal switching and control co-design for a class of continuous-time switched nonlinear systems. An event-triggered adaptive dynamic programming (ADP) algorithm is developed to obtain the optimal hybrid control policy. At the event-triggered instant, the switching controller determines which subsystem to activate and the input controller updates the system input. Compared with the time-triggered methods, the computation and communication are reduced. A critic neural network (NN) is applied to approximate the solution of the switched Hamilton-Jacobi-Bellman (HJB) equation. The proposed critic NN is tuned according to the HJB error in real time. A stability analysis of the closed-loop system is given by Lyapunov method. Moreover, the design of the event-triggered mechanism can also exclude Zeno behavior of the switching signal without fixing a minimum dwell time. Finally, the effectiveness of the developed algorithm is evaluated by a numerical simulation. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper is motivated by the great potential switched nonlinear systems have demonstrated in improving system dynamic performances. However, the existing results mainly focus on optimal control for discrete-time switched nonlinear systems. Moreover, fairly few researchers have investigated the optimal switching and control co-design for switched nonlinear systems. Therefore, this paper develops a novel event-triggered adaptive dynamic programming algorithm that can learn the optimal hybrid control policy online. The design of the event triggering mechanism can exclude Zeno behavior of the switching signal. It is noteworthy that the proposed control method is of great significance for many practical systems, such as automotive engine systems and single-link robot arm systems.