Relaxation of Conditions for Convergence of Dynamic Regressor Extension and Mixing Procedure

TL;DR

This paper generalizes the dynamic regressor extension and mixing procedure, ensuring faster convergence and exponential tracking error reduction under less restrictive excitation conditions.

Contribution

It introduces a generalized method that guarantees parameter error reduction and exponential convergence with relaxed excitation requirements.

Findings

Guarantees parameter error reduction with semi-finite excitation.

Ensures exponential convergence with semi-persistent excitation.

Applicable to regressors with rank one or higher.

Abstract

A generalization of the dynamic regressor extension and mixing procedure is proposed, which, unlike the original procedure, first, guarantees a reduction of the unknown parameter identification error if the requirement of regressor semi-finite excitation is met, and second, it ensures exponential convergence of the regression function (regressand) tracking error to zero when the regressor is semi-persistently exciting with a rank one or higher.