Fixed-time optimized control for nonlinear strict-feedback systems based on reinforcement learning and disturbance observer

The present study focuses on the fixed-time optimal control problem for a class of nonlinear strict-feedback systems subject to unknown external disturbances. First, a fuzzy state and disturbance observer is developed to estimate both unmeasurable states and external disturbances. To further improve estimation accuracy of external disturbances, a novel intermediate variable estimator incorporating a time-varying gain parameter is introduced. Subsequently, based on the disturbance-observer-critic-actor (DOCA) reinforcement learning architecture, a fixed-time optimal control strategy is proposed by integrating fuzzy approximation and backstepping techniques. This approach ensures optimality in both virtual and actual control of the controlled system while guaranteeing its fixed-time stability. Finally, the effectiveness of the proposed strategy is validated through theoretical and simulation studies.