Adaptive Event Triggered Optimal Control for Constrained Continuous-time Nonlinear Systems

This paper considers the event-triggered optimal control (ETOC) strategy for constrained continuous-time nonlinear systems via adaptive dynamic programming (ADP). First, a novel event-triggering condition is proposed, which can guarantee the stability of the closed-loop system. Meanwhile, the existence of a lower bound for the execution time is proved, which can guarantee that the designed event-trigger scheme avoids Zeno behavior. Then, to solve the partial differential Hamilton-Jacobi-Bellman (HJB) equation, the critic Neural Network (NN) is designed to approximate the cost function. So that the ADP-based ETOC scheme is designed. Moreover, through Lyapunov stability analysis, the stability of the closed-loop system can be ensured. Also, the uniform ultimate boundedness of the states and the weight estimation error can also be guaranteed. Last, a numerical example is given to illustrate the effectiveness and advantages of the proposed control scheme.