Reinforcement learning‐based optimized backstepping control for strict‐feedback nonlinear systems subject to external disturbances

Abstract

This article investigates a reinforcement learning‐based optimal backstepping control strategy for strict‐feedback nonlinear systems, which contain output constraints, external disturbances and uncertain unknown dynamics. The simplified reinforcement learning algorithm with the identifier‐critic‐actor architecture is constructed in the control design to build optimal virtual and actual controllers. To compensate for the disturbance, a lemma is adopted to transform external disturbances into an unknown “bounding functions‘’, which satisfy a triangular condition. Moreover, the unknown nonlinear functions, which composed of unknown dynamics and external disturbances, approximated by neural networks. Meanwhile, in order to avoid violating output constraints, a barrier‐type Lyapunov function approach is integrated into the optimal control strategy to satisfy output constraints requirements under the framework of backstepping technique. Furthermore, the presented optimal control strategy guarantees that all signals in the closed‐loop system are semi‐globally uniformly ultimately bounded. Finally, the effectiveness of the proposed optimal control approach is performed by a numerical example.