Fixed‐Time ESO‐Based Reinforcement Learning for Manipulator Time‐Delay System

ABSTRACT This article investigates the fixed‐time optimal tracking control problem for the single‐link manipulator time‐delay system with unknown disturbance. An improved fixed‐time extended state observer is established, which not only estimates the disturbance existing in the system but also estimates the state information of the system. Subsequently, the reinforcement learning (RL) approach with a critic‐actor framework is utilized to construct the optimal fixed‐time controller. During the RL process, a modification term is introduced to prevent the occurrence of the training termination, in which critic and actor algorithms can converge within a fixed‐time interval. Finally, an appropriate Lyapunov‐Krasovskii function is designed to compensate for the state delay. With the proposed optimal control scheme, all signals achieve the fixed‐time convergence, which ensures that the system output effectively tracks the desired trajectory. The effectiveness of the proposed strategy is verified through the simulation example.