Journal Home Page

Cumulative Index

List of all Volumes

Complete Contents
of this Volume

Previous Article

Next Article

Journal of Convex Analysis 28 (2021), No. 2, 311--328
Copyright Heldermann Verlag 2021

Identification of Linear Dynamical Systems and Machine Learning

Alain Bensoussan
International Center for Decision and Risk Analysis, Jindal School of Management, University of Texas, Dallas, U.S.A.
and: School of Data Science, City University, Hong Kong

Fatih Gelir
Department of Mathematics, University of Texas, Dallas, U.S.A.

Viswanath Ramakrishna
Department of Mathematics, University of Texas, Dallas, U.S.A.

Minh-Binh Tran
Department of Mathematics, Southern Methodist University, University Park, U.S.A.

The identification of dynamical systems is core to control theory. Driven by the advances in machine learning, data driven approaches are becoming important. In this paper, we study such an approach to the identification of a linear dynamical system under observation. The problem is formulated as an optimization problem to which gradient descent is applied. Surprisingly the fact that the state is available only through observations renders this a non-convex optimization problem. We study this problem in detail, including performing an asymptotic analysis and showing that the cost function is guaranteed to decrease along successive iterates.

Keywords: Control theory, machine learning, gradient descent, system identification.

MSC: 37N35, 93B30.

[ Fulltext-pdf  (132  KB)] for subscribers only.