On parameter tuning and convergence properties of the DREM procedure

Abstract

The recently proposed Dynamic Regressor Extension and Mixing (DREM) procedure has been proven to enhance transient performance in online parameter estimation and it has been successfully applied to a variety of adaptive control problems and applications. However, to use this procedure, a linear operator has to be chosen to perform the dynamic extension. A poor choice of the operator can reduce excitation of signals and hence it can compromise convergence properties. This paper presents a systematic selection of operators such that the excitation is always preserved. The paper also studies convergence conditions when the DREM procedure is combined with a least-squares estimator.

New Results on Parameter Estimation via Dynamic Regressor Extension and Mixing: Continuous and Discrete-Time Cases

“…Remark 2. As pointed out in [10] applying Cramer's law we have that Y i = det{Φ Yi } where Φ Yi is the matrix obtained replacing the i-column of Φ with Y .…”

“…Proposition 6. Consider the scalar CT LREs (7) and the gradient-descent estimator (10). Fix a constant ν i ∈ (0, 1) and assume there exists a time t c ∈ R >0 such that…”

“…We consider the simplest case of a scalar system y(t) = ∆(t)θ and simulate the gradient estimator (10), that is,…”

DREM procedure application for piecewise constant parameters identification

“…Для простоты дальнейшего анализа и изложения, не теряя общности результатов, рассмотрим случай n = 2. В соответствии с [1][2][3], введем оператор задержки:…”

“…Процедура динамического расширения и смешивания DREM (Dynamic Regressor Extension and Mixing) [1][2][3] получила широкое распространение при решении задачи оценки постоянных параметров линейных регрессионных уравнений. Благодаря применению данной процедуры удалось получить решение ряда ранее открытых проблем теории управления [4][5][6][7][8][9].…”