Robust tracking control with reinforcement learning for nonlinear‐constrained systems

Abstract

Abstract This article considers the robust tracking control problem of uncertain nonlinear systems with asymmetric input constraints. Initially, the tracking error dynamics and the desired trajectory dynamics are constructed as an augmented system. Then, with a discounted value function being introduced for the nominal augmented system, the original tracking control problem is transformed into a constrained optimal control problem. To solve the constrained optimal control problem, its related Hamilton–Jacobi–Bellman equation (HJBE) is developed. After that, a critic approximator is constructed to solve the HJBE in the reinforcement learning framework. To tune the parameters used in the critic approximator, a novel concurrent learning technique is introduced, which could remove the persistence of excitation condition. Moreover, the uniform ultimate boundedness of the tracking error and the parameters' estimation error of the critic approximator is assured via the Lyapunov's approach. Finally, a spring‐mass‐damper mechanical system and a robot manipulator system are given to validate the theoretical claims.