Efficient Learning of a Linear Dynamical System with Stability Guarantees¶
Authors: Wouter Jongeneel, Tobias Sutter, Daniel Kuhn
Published: 2021 ()
arXiv: 2102.03664
Summary¶
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.