Finite-Time Stability of Adaptive Parameter Estimation and Control

Abstract

This paper presents extensions of finite-time stability results to some prototypical adaptive control and estimation frameworks. First, we present a novel scheme of online parameter estimation that guarantees convergence of the estimation error in a fixed time under a relaxed persistence of excitation condition. Subsequently, we design a novel Model Reference Adaptive Control (MRAC) for a scalar system with finite-time convergence guarantees for both the state- and the parameter-error. Lastly, for a general class of strict-feedback systems with unknown parameters, we propose a finite-time stabilizing control based on adaptive backstepping techniques. We also present some numerical examples demonstrating the efficacy of our scheme.

The authors have found a mistake in the proof of the main results which doesn't seem to be (easily) fixable. So we are retracting this paper from arxiv. This paper hasn't been published yet