# Efficient Learning of a Linear Dynamical System with Stability Guarantees

arXiv: https://arxiv.org/abs/2102.03664 · HTML: https://mlsanity.com/paper/2102.03664/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Feb 2021.

## Built on by (most cited first, 3 of 3)

- [Learning and Decision-Making with Data: Optimal Formulations and Phase Transitions](https://mlsanity.com/paper/2109.06911/) (2021)
- [Stable Linear Subspace Identification: A Machine Learning Approach](https://mlsanity.com/paper/2311.03197/) (2023)
- [An active learning method for solving competitive multi-agent decision-making and control problems](https://mlsanity.com/paper/2212.12561/) (2022)

## Abstract (arXiv)

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.