Publikation:

Efficient Learning of a Linear Dynamical System with Stability Guarantees

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Datum

2023

Autor:innen

Jongeneel, Wouter
Kuhn, Daniel

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IEEE Transactions on Automatic Control. IEEE. 2023, 68(5), S. 2790-2804. ISSN 0018-9286. eISSN 1558-2523. Verfügbar unter: doi: 10.1109/tac.2022.3213770

Zusammenfassung

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.

Zusammenfassung in einer weiteren Sprache

Fachgebiet (DDC)
004 Informatik

Schlagwörter

Stability analysis, Covariance matrices, Eigenvalues and eigenfunctions, Dynamical systems, Linear systems, Asymptotic stability, Trajectory

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ISO 690JONGENEEL, 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.2022.3213770
BibTex
@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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