Adaptive-Critic-Based Robust Trajectory Tracking of Uncertain Dynamics and Its Application to a Spring–Mass–Damper System

In this paper, the robust trajectory tracking design of uncertain nonlinear systems is investigated by virtue of a self-learning optimal control formulation. The primary novelty lies in that an effective learning based robust tracking control strategy is developed for nonlinear systems under a general uncertain environment. The augmented system construction is performed by combining the tracking error with the reference trajectory. Then, an improved adaptive critic technique, which does not depend on the initial stabilizing controller, is employed to solve the Hamilton- Jacobi-Bellman (HJB) equation with respect to the nominal augmented system. Using the obtained control law, the closed-loop form of the augmented system is built with stability proof. Moreover, the robust trajectory tracking performance is guaranteed via Lyapunov approach in theory and then through simulation demonstration, where an application to a practical spring-mass-damper system is included.