Normalization of regressor excitation as a part of dynamic regressor extension and mixing procedure

TL;DR

This paper introduces a novel excitation normalization method within the dynamic regressor extension and mixing framework, enabling consistent parameter estimation error bounds across regressors with varying excitation levels, improving practical robustness.

Contribution

It proposes a new excitation normalization technique based on the DREM procedure, offering uniform error bounds with a constant adaptation rate, unlike classical amplitude normalization methods.

Findings

The proposed method achieves consistent error bounds regardless of excitation level.

Mathematical modeling confirms the method's effectiveness over classical approaches.

The approach simplifies parameter estimation in practical applications.

Abstract

The method of excitation normalization of the regressor, which is used in the estimation loop to solve the plant identification problem, is proposed. It is based on the dynamic regressor extension and mixing procedure. Its application allows to obtain the same upper bound of the parameter identification error for the scalar regressors with different excitation level, using a constant value of the adaptation rate for all of them. This fact is a significant advantage from the practical point of view. Comparison of the developed method with the known one of the regressor amplitude normalization is conducted. It is shown that the classical approach does not have the above-stated property. To validate the theoretical conclusions made, the results of the comparative mathematical modeling of three loops are presented: 1) the classical gradient one, 2) the one with the normalization of the regressor amplitude, 3) the proposed one with the normalization of the regressor excitation.