Adaptive Dynamic Programming for Robust Event-Driven Tracking Control of Nonlinear Systems With Asymmetric Input Constraints

This article considers the robust dynamic event-driven tracking control problem of nonlinear systems having mismatched disturbances and asymmetric input constraints. Initially, to tackle the asymmetric constraints, a novel nonquadratic value function is constructed for the original system. This makes the asymmetrically constrained tracking control problem transformed into an unconstrained optimal regulation problem. Then, a dynamic event-driven mechanism is proposed. Meanwhile, the event-driven Hamilton-Jacobi-Bellman equation (ED-HJBE) is developed for the optimal regulation problem in order to acquire the optimal control with distinctly decreased computational burden. To solve the ED-HJBE, a single critic neural network (CNN) is designed in the adaptive dynamic programming framework. Meanwhile, the gradient descent method is employed to update the CNN's weights. After that, both the weight estimation error and the tracking error are proved to be uniformly ultimately bounded via Lyapunov's direct method. Finally, simulations of the spring-mass-damper system and the pendulum plant are separately utilized to validate the established theoretical claims.