Practical prescribed-time prescribed performance control with asymptotic convergence -- A vanishing sigma-modification approach

TL;DR

This paper introduces a control method for nonlinear systems that guarantees prescribed performance within a set time, handling uncertainties and unmodeled dynamics through a novel sigma-modification approach.

Contribution

It proposes a practical prescribed-time control strategy with asymptotic convergence using a performance-rate function and sigma-modification, addressing uncertainties effectively.

Findings

Ensures prescribed-time control with guaranteed performance.

Handles uncertainties and unmodeled dynamics effectively.

Validated through numerical simulations.

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.