Prescribed-Time Fuzzy Tracking Control for Constrained Euler–Lagrange Systems via Reinforcement Learning: Theory and Experiment

This article presents a prescribed-time tracking control scheme for Euler–Lagrange (EL) systems with state constraints using the fuzzy reinforcement learning (RL) framework. Specifically, the prescribed function is constructed by devising a settling time regulator, which transforms the original tracking objective into a generalized control problem involving time-varying constraints. This formulation overcomes the limitation of traditional finite-time control methods whose convergence time depends on initial conditions, providing a distinct advantage in practical applications where the settling time and tracking error can be explicitly specified. To simultaneously achieve both control optimality and constraint satisfaction, a novel performance index is established by seamlessly integrating a barrier Lyapunov function. Within the backstepping control framework, a fuzzy RL algorithm with an identifier-actor-critic architecture is employed to approximate unknown dynamics, evaluate the performance index, and synthesize the optimal control policy. The designed method offers a unified solution that combines guaranteed prescribed performance, strict constraint satisfaction, and optimal control characteristics for EL systems. Moreover, the prescribed-time convergence and stability of the closed-loop system are rigorously derived via Lyapunov analysis. Simulation and experimental studies on robotic manipulators are conducted to validate the efficacy and practicality of the proposed strategy.