Adaptive prescribed-time tracking control with guaranteed performance for uncertain nonlinear systems with arbitrary initial errors.

This paper addresses the challenging problem of adaptive prescribed-time tracking control with guaranteed performance for uncertain strict-feedback nonlinear systems subject to arbitrary initial errors. Unlike existing methods that require restrictive initial conditions or are limited to stabilization problems, this work develops a unified control framework that simultaneously achieves three key objectives: handling arbitrary initial errors without performance violation, ensuring exact prescribed-time convergence, and maintaining guaranteed transient performance throughout the operation. The main contributions include a novel generalized tanh-based error transformation technique that decouples control performance from initial error magnitudes, automatically confining arbitrary initial errors within asymmetric prescribed performance bounds. Furthermore, an enhanced adaptive backstepping framework incorporating fractional-order terms is proposed to guarantee that the tracking error enters the prescribed performance region before a user-specified entry time and converges to zero exactly at a prescribed settling time. Rigorous theoretical analysis demonstrates the uniform ultimate boundedness of all closed-loop signals while achieving both prescribed-time convergence and guaranteed transient performance under system uncertainties. Simulation results confirm the effectiveness of the proposed method.