Fixed-time learning-based optimal tracking control for robotic systems with prescribed performance constraints

This paper presents a fixed-time learning-based dynamic event-triggered control framework to address the optimal tracking control problem in robotic systems with the prescribed performance constraints. In many practical scenarios, the states of robotic systems are often subject to performance constraints imposed by structural characteristics and task requirements. To address this issue, prescribed performance control (PPC) theory is employed to ensure performance state constraints and construct an unconstrained tracking error system. Subsequently, a critic-only adaptive dynamic programming (ADP) control framework is designed to approximate the optimal control law for the transformed unconstrained system. Furthermore, in the design of critic neural network (NN), a novel fixed-time convergence (FTC) weight update law based on concurrent learning (CL) techniques is proposed, which guarantees the fixed-time convergence of weight estimation error under relaxed persistent excitation (PE) condition. Throughout the controller design, a dynamic event-triggered mechanism is adopted to reduce the number of sampling instances and computational resources. Meanwhile, the stability of the closed-loop system under this mechanism is rigorously proven. Finally, the effectiveness of the proposed method is demonstrated through simulation results and comparative analysis.