A Lyapunov approach to Robust and Adaptive finite time stabilization of integrator chains with bounded uncertainty

TL;DR

This paper develops Lyapunov-based robust and adaptive controllers for finite-time stabilization of integrator chains with bounded uncertainties, applicable to chains of any length, and capable of estimating convergence time.

Contribution

It introduces a unified Lyapunov-based framework for designing finite-time controllers for integrator chains with known or unknown uncertainties, extending to arbitrary chain lengths.

Findings

Controllers achieve finite-time stabilization.

Upper bounds on convergence time are computed.

Applicable to integrator chains of any length.

Abstract

In this paper, we present Lyapunov-based robust and adaptive controllers for the finite time stabilization of a perturbed chain of integrators with bounded uncertainties. The proposed controllers can be designed for integrator chains of any arbitrary length. The uncertainty bounds are known in the robust control problem whereas they are unknown in the adaptive control problem. Both controllers are developed from a class of finite time stabilization controllers for pure integrator chains. Lyapunov-based design permits to calculate upper bound on convergence time.