Convergence and consistency of recursive least squares with variable-rate forgetting. (September 2020)

• Record Type: Journal Article
• Authors: Bruce, Adam L.; Goel, Ankit; Bernstein, Dennis S.
• Is Part Of: Automatica. Volume 119(2020)
• Publication Date: 2020-09
• Subjects: System identification -- Identification methods -- Tracking and adaptation -- Adaptive systems -- Adaptive control; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2020.109052
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: A recursive least squares algorithm with variable rate forgetting (VRF) is derived by minimizing a quadratic cost function. Under persistent excitation, the minimizer given by VRF is shown to converge to the true parameters. In addition, under persistent excitation and with noisy measurements, where the noise is uncorrelated with the regressor, conditions are given under which the minimizer given by VRF is a consistent estimator of the true parameters. The results are illustrated by a numerical example involving abruptly changing parameters.