Geodesic
Identification of Linear Dynamical Systems and Machine Learning
Journal of convex analysis, Tome 28 (2021) no. 2, pp. 311-328
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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.
Classification : 37N35, 93B30
Mots-clés : Control theory, machine learning, gradient descent, system identification 
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     author = {A. Bensoussan and F. Gelir and V. Ramakrishna and M.-B. Tran},
     title = {Identification of {Linear} {Dynamical} {Systems} and {Machine} {Learning}},
     journal = {Journal of convex analysis},
     pages = {311--328},
     year = {2021},
     volume = {28},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2021_28_2_JCA_2021_28_2_a2/}
}
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A. Bensoussan; F. Gelir; V. Ramakrishna; M.-B. Tran. Identification of Linear Dynamical Systems and Machine Learning. Journal of convex analysis, Tome 28 (2021) no. 2, pp. 311-328. http://geodesic.mathdoc.fr/item/JCA_2021_28_2_JCA_2021_28_2_a2/