Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

alain.bensoussan@utdallas.edu

Viswanath Ramakrishna

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

vish@utdallas.edu

Minh-Binh Tran

Department of Mathematics, Southern Methodist University, University Park, U.S.A.

minhbinht@mail.smu.edu

Keywords

  • Control theory
  • machine learning
  • gradient descent
  • system identification

Mathematics Subject Classification

37N35, 93B30

References

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Suggested citation

A. Bensoussan, F. Gelir, V. Ramakrishna, M.-B. Tran. “Identification of Linear Dynamical Systems and Machine Learning.” Journal of Convex Analysis 28 (2021), No. 2, 311–328. https://doi.org/10.68381/jca28020a

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Published by Heldermann Verlag, 2021. Rights now held by Banach Press.