Adjustable Nonsingular Prescribed-Time Performance Control for Nonlinear Systems Via Tuning Functions

Abstract This paper investigates a robust adaptive control framework for nonlinear systems. Firstly,a novel class of nonsingular prescribed-time performance functions is constructed, which possess n-th order continuous differentiability and piecewise tunability, thereby thoroughlyeliminating prescribed-time singularity and settling-time boundary divergence. On this basis, by utilizing a bounded nonlinear mapping function and an indirect constraint function, the tracking error is guaranteed to enter the prescribed performance region within the prescribed time, independently of the initial tracking error. In addition, a tuning-function-based adaptive scheme directly handles the linearly parameterized uncertainties without introducing approximation residuals. Finally, the effectiveness and superiority of the proposed control scheme are verified via comparative analysis of two simulation examples.