Robust predefined-time sliding-mode tracking control for a class of nonlinear systems with preassigned convergence constraints

Abstract

This paper addresses high-precision tracking control for a class of uncertain nonlinear systems under the stringent requirement that the convergence time of the tracking error be explicitly preassigned by the user. To meet this requirement, a predefined-time sliding-mode control (PTSMC) scheme is developed. The controller is designed within an auxiliary-variable-based transformation framework, which facilitates the co-design of a nonlinear barrier function and a self-adjusting gain law. Rigorous analysis shows that the closed-loop system achieves practical predefinedtime stability: for arbitrary initial conditions, both the sliding variable and the tracking error are guaranteed to enter a user-specified compact set within the preassigned total convergence time TZ + TS, while maintaining robustness against external disturbances and parametric uncertainties. Numerical simulations validate the theoretical results and demonstrate the effectiveness and superior performance of the proposed approach.