Publikation: Efficient Learning of a Linear Dynamical System with Stability Guarantees
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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 statistical bounds on the estimation error.
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JONGENEEL, Wouter, Tobias SUTTER, Daniel KUHN, 2023. Efficient Learning of a Linear Dynamical System with Stability Guarantees. In: IEEE Transactions on Automatic Control. IEEE. 2023, 68(5), S. 2790-2804. ISSN 0018-9286. eISSN 1558-2523. Verfügbar unter: doi: 10.1109/tac.2022.3213770BibTex
@article{Jongeneel2023Effic-66616, year={2023}, doi={10.1109/tac.2022.3213770}, title={Efficient Learning of a Linear Dynamical System with Stability Guarantees}, number={5}, volume={68}, issn={0018-9286}, journal={IEEE Transactions on Automatic Control}, pages={2790--2804}, author={Jongeneel, Wouter and Sutter, Tobias and Kuhn, Daniel} }
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