Prescribed‐Time Tracking Control for Non‐Affine Nonlinear Systems Subject to Input Delay and Unmatched Disturbances via Singular Perturbation Theory

Abstract

This paper proposes a prescribed‐time tracking control method for non‐affine nonlinear systems with input delay and unmatched disturbances, addressing the challenge that existing research often struggles to coordinate the handling of non‐affine characteristics, input delay, and disturbance suppression simultaneously. An integrated framework is developed by combining singular perturbation theory (SPT) with prescribed‐time control. First, an auxiliary subsystem and a singular perturbation parameter are introduced to construct a fast subsystem that compensates for the input delay, converting the original system into a standard singular perturbation form. Using SPT, the system is then reduced to a reduced‐order slow subsystem (ROSS) in cascaded integral form, thereby eliminating the non‐affine structure. Subsequently, a prescribed‐time disturbance observer (PTDO) with a time‐varying gain function is designed to accurately reconstruct disturbances while guaranteeing convergence within a user‐defined time. Furthermore, a prescribed‐time controller is synthesized by integrating the ROSS and the PTDO, and the dynamic surface control technique is employed to effectively avoid the “computational explosion” problem. Closed‐loop stability within the prescribed‐time is rigorously proven via singular perturbation analysis and Lyapunov theory. Simulations in two cases confirm the method's excellent performance and robustness. The study extends the applicability of prescribed‐time control and offers a new solution for high‐precision fast control under multi‐source disturbances.