Dynamic Event-Triggered Optimal Control for Nonlinear Switched Systems by Using Adaptive Dynamic Programming

This paper proposes an adaptive dynamic programming (ADP) algorithm based on a dynamic event-triggered mechanism (ETM) for the optimal control problem of a class of continuous-time nonlinear switched systems. First, a performance index function that incorporates switching signals is introduced, followed by the derivation of a hybrid control strategy that includes both optimal control law and optimal switching law. To save computational resources, a dynamic ETM is introduced. Unlike time-triggered and static ETMs, dynamic event triggering provides more flexible triggering conditions. The single-layer critic neural network (NN) is constructed to solve the event-triggered HJB equation for the switched system. The weights of the critic NN are then trained using the gradient descent algorithm, and the stability of the closed-loop system is proven using the Lyapunov theorem. The effectiveness of the proposed algorithm is verified through a single-link robot arm plant.