On dynamic regressor extension and mixing parameter estimators: Two Luenberger observers interpretations

Dynamic regressor extension and mixing is a new technique for parameter estimation with guaranteed performance improvement – with respect to classical gradient or least-squares estimators – that has proven instrumental in the solution of several open problems in system identification and adaptive control. In this brief note we give two interpretations of this parameter estimator in terms of the recent extensions, to the cases of nonlinear systems and observation of linear functionals for time-varying systems, of the classical Luenberger’s state observers.