Adaptive critic learning for approximate optimal event-triggered tracking control of nonlinear systems with prescribed performances

This paper studies the approximate optimal event-triggered tracking control problem for a class of second-order nonlinear systems with prescribed performances. By employing a prescribed performances function, restrictions on tracking errors are removed for prescribed performances including convergence rate, maximum overshoot, and steady-state error. On this basis, a complex optimal tracking control problem can be transformed into an optimal stabilising control problem by constructing an augmented system. Subsequently, an event-triggered mechanism is introduced to reduce communication resources. Then, an adaptive critic learning algorithm is used to solve the Hamilton-Jacobi-Bellman equation, where the weights in the critic networks are tuned through the gradient descent approach and experience replay technology. Through the developed learning method, the persistence of excitation condition is released, and the data efficiency is improved. The Lyapunov stability theory is introduced to verify the stability of the close-loop system and the tracking errors are uniformly ultimately bounded. Finally, simulation results are presented to show the effectiveness of the proposed approach.