Efficient Learning of a Linear Dynamical System With Stability Guarantees

• 成果类型: Article
• 署名作者: Jongeneel, Wouter; Sutter, Tobias; Kuhn, Daniel
• 署名单位: Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; University of Konstanz
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3213770
• 发表日期: 2023
• 页码: 2790-2804
• 关键词: Stability analysis; Covariance matrices; Eigenvalues and eigenfunctions; dynamical systems; Linear systems; asymptotic stability; trajectory; identification; stability of linear systems

摘要

We propose a principled method for projecting an arbitrary square matrix to the nonconvex 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.