Practical prescribed-time prescribed performance control with asymptotic convergence -- A vanishing sigma-modification approach
Abstract
In this paper, we present a method capable of ensuring practical prescribed-time control with guaranteed performance for a class of nonlinear systems in the presence of time-varying parametric and dynamic uncertainties, and uncertain control coefficients. Our design consists of two key steps. First, we construct a performance-rate function that freezes at and after a user-specified time T, playing a crucial role in achieving desired precision within prescribed time T and dealing with unmodeled dynamics. Next, based on this function and a sigma-modification strategy in which the leakage term starts to vanish at t > T, we develop an adaptive dynamic surface control framework to reduce control complexity, deal with uncertainties, ensure prescribed performance, practical prescribed-time convergence to a specific region, and ultimately achieve asymptotic convergence. The effectiveness of the proposed control method is validated through numerical simulations.
Cite
@article{arxiv.2601.14882,
title = {Practical prescribed-time prescribed performance control with asymptotic convergence -- A vanishing sigma-modification approach},
author = {Mehdi Golestani and Yongduan Song and Weizhen Liu and Guangren Duan and He Kong},
journal= {arXiv preprint arXiv:2601.14882},
year = {2026}
}