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arXiv · 2102.03664

Efficient Learning of a Linear Dynamical System with Stability Guarantees

Wouter Jongeneel·Tobias Sutter·Daniel Kuhn
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Abstract

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.

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Wouter Jongeneel, Tobias Sutter, Daniel Kuhn. 2021-02-06. Efficient Learning of a Linear Dynamical System with Stability Guarantees. https://doi.org/10.1109/tac.2022.3213770

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