Adaptive Prescribed-Performance Variable-Gain Sliding Mode Control for Flexible-Joint Robots via Composite Learning

This paper investigates the prescribed-performance tracking control problem for uncertain flexible-joint robots subject to slow-fast dynamics and model uncertainties. By employing singular perturbation theory, the original system is decomposed into slow and fast subsystems. Composite-learning neural networks are constructed to approximate the unknown lumped uncertainties in both subsystems. Based on this decomposition, an adaptive prescribed-performance variable-gain sliding mode control scheme is developed, in which the slow subsystem achieves constrained trajectory tracking and the fast subsystem is stabilized. Lyapunov analysis shows that all closed-loop signals are semi-globally uniformly ultimately bounded and that the tracking errors remain within the prescribed bounds. Simulation results verify the effectiveness of the proposed method.