Efficient Learning of a Linear Dynamical System with Stability Guarantees

We propose a principled method for projecting an arbitrary square matrix to the non-convex set of asymptotically stable matrices. Leveraging ideas from large deviations theory, we show that this projection is optimal in an information-theoretic sense and that it simply amounts to shifting the initia...

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Bibliographic Details
Published in:arXiv.org 2022-06
Main Authors: Jongeneel, Wouter, Sutter, Tobias, Kuhn, Daniel
Format: Article
Language:English
Subjects:
Dynamic stability
Dynamical systems
Information theory
Linear quadratic regulator
Mathematical analysis
Matrix methods
Online Access:Get full text
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Summary:We propose a principled method for projecting an arbitrary square matrix to the non-convex set of asymptotically stable matrices. Leveraging ideas from large deviations theory, we show that this projection is optimal in an information-theoretic sense and that it simply amounts to shifting the initial matrix by an optimal linear quadratic feedback gain, which can be computed exactly and highly efficiently by solving a standard linear quadratic regulator problem. The proposed approach allows us to learn the system matrix of a stable linear dynamical system from a single trajectory of correlated state observations. The resulting estimator is guaranteed to be stable and offers explicit statistical bounds on the estimation error.
ISSN:2331-8422
DOI:10.48550/arxiv.2102.03664