Reinforcement Learning-Based Prescribed-Time Optimal Tracking Control for Uncertain Nonlinear Strict-Feedback Systems

This paper investigates the reinforcement learning (RL)-based prescribed-time optimal tracking control problem for a class of uncertain nonlinear strict-feedback systems. To circumvent the 'explosion of complexity' inherent in recursive backstepping, the High-Order Fully Actuated (HOFA) system approach is employed to reformulate the dynamics. Based on the actor-critic framework, this work integrates the prescribed-time adjustment function into the neural network (NN) update laws, which synchronizes the prescribed-time convergence of both the tracking error and the network weights under a unified Lyapunov framework, thus ensuring the stability of the entire system within a prescribed time. A complete and rigorous proof is presented via Lyapunov theory. Finally, a numerical example is given to show the effectiveness of the proposed results.