Recursive Least Squares with Variable-Direction Forgetting -- Compensating for the loss of persistency

• Published in: arXiv.org
• Main Authors: Goel, Ankit, Bruce, Adam L, Bernstein, Dennis S
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 07.03.2020
• Subjects: Least squares; Mathematics - Optimization and Control; Upgrading
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2003.03523

Learning depends on the ability to acquire and assimilate new information. This ability depends---somewhat counterintuitively---on the ability to forget. In particular, effective forgetting requires the ability to recognize and utilize new information to order to update a system model. This article is a tutorial on forgetting within the context of recursive least squares (RLS). To do this, RLS is first presented in its classical form, which employs uniform-direction forgetting. Next, examples are given to motivate the need for variable-direction forgetting, especially in cases where the excitation is not persistent. Some of these results are well known, whereas others complement the prior literature. The goal is to provide a self-contained tutorial of the main ideas and techniques for students and researchers whose research may benefit from variable-direction forgetting.