A Backstepping-Free Framework for Adaptive Prescribed-Time Stabilization of Uncertain Nonlinear Systems

Abstract

This article investigates the problem of global adaptive prescribed-time (PT) stabilization for a class of nonlinear systems subject to parametric uncertainties. Unlike prevalent adaptive control strategies that rely on recursive backstepping procedures, this work proposes a novel backstepping-free control framework. By leveraging the solution to a time-varying parametric Lyapunov equation (TV-PLE), we construct an adaptive time-varying gain feedback controller. A distinguishing feature of this approach is the utilization of a logarithmic Lyapunov function instead of the conventional quadratic form, which not only simplifies the stability analysis but also effectively characterizes the nonlinear coupling between the singular control gain and the adaptation dynamics. Rigorous theoretical analysis establishes that the proposed controller guarantees global PT stability, ensuring that all closed-loop signals—particularly the control input—remain bounded despite the singularity of the time-varying gain at the terminal time. Furthermore, the proposed method accommodates unknown linear growth conditions, offering a less restrictive design compared to existing linear time-varying feedback schemes. Comparative simulation results are presented to validate the effectiveness and superiority of the developed approach. Note to Practitioners—This paper is motivated by the practical challenges in controlling strict-feedback uncertain nonlinear systems, such as robotic manipulators and electromechanical devices, where precise task completion within a strict deadline is critical. Traditional adaptive control methods often rely on the “backstepping” technique. While theoretically sound, backstepping requires complex recursive calculations and repeated differentiations, leading to the “explosion of complexity” and making real-time implementation on embedded processors difficult. To address these issues, this paper presents a backstepping-free adaptive control framework. The primary contribution is a simplified controller design that guarantees the system stabilizes globally within a user-defined preset time, regardless of the initial conditions or unknown physical parameters.