Global prescribed-time control of a class of uncertain nonholonomic systems by smooth time-varying feedback

TL;DR

This paper develops a smooth, time-varying control approach for uncertain nonholonomic systems, enabling states to reach zero precisely at a predetermined time, with proven convergence and improved control performance.

Contribution

It introduces a novel smooth time-varying state transformation and high-gain feedback controllers for prescribed-time stabilization of uncertain nonholonomic systems.

Findings

States and controllers converge to zero at the prescribed time

The method enhances control performance with smooth time-varying functions

Numerical example verifies effectiveness of the proposed approach

Abstract

This paper investigates the prescribed-time smooth control problem for a class of uncertain nonholonomic systems. With a novel smooth time-varying state transformation, the uncertain chained nonholonomic system is reformulated as an uncertain linear time-varying system. By fully utilizing the properties of a class of parametric Lyapunov equations and constructing time-varying Lyapunov-like functions, smooth time-varying high-gain state and output feedback controllers are designed. The states and controllers are proven to converge to zero at any prescribed time. The proposed smooth time-varying method combines the advantage of a time-varying high-gain function, which enhances control performance, and a smooth time-varying function that can drive the states to zero at the prescribed time. The effectiveness of the proposed methods is verified by a numerical example.