Linear System Identification via Atomic Norm Regularization

This paper proposes a new algorithm for linear system identification from noisy measurements. The proposed algorithm balances a data fidelity term with a norm induced by the set of single pole filters. We pose a convex optimization problem that approximately solves the atomic norm minimization probl...

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Bibliographic Details
Published inarXiv.org
Main Authors Shah, Parikshit, Badri Narayan Bhaskar, Tang, Gongguo, Recht, Benjamin
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 03.04.2012
Subjects
Algorithms
Asymptotic methods
Computational geometry
Computer Science - Information Theory
Convexity
Linear systems
Mathematics - Information Theory
Mathematics - Optimization and Control
Optimization
Regularization
System identification
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Summary:This paper proposes a new algorithm for linear system identification from noisy measurements. The proposed algorithm balances a data fidelity term with a norm induced by the set of single pole filters. We pose a convex optimization problem that approximately solves the atomic norm minimization problem and identifies the unknown system from noisy linear measurements. This problem can be solved efficiently with standard, freely available software. We provide rigorous statistical guarantees that explicitly bound the estimation error (in the H_2-norm) in terms of the stability radius, the Hankel singular values of the true system and the number of measurements. These results in turn yield complexity bounds and asymptotic consistency. We provide numerical experiments demonstrating the efficacy of our method for estimating linear systems from a variety of linear measurements.
ISSN:2331-8422
DOI:10.48550/arxiv.1204.0590