Large-Scale System Identification Using a Randomized SVD

TL;DR

This paper introduces a randomized SVD approach for large-scale system identification, enabling efficient and reliable modeling of high-dimensional dynamical systems where traditional SVD computations are infeasible.

Contribution

It proposes replacing the standard SVD with a randomized method in system realization algorithms, maintaining performance guarantees for large models.

Findings

Randomized SVD can effectively replace classical SVD in system identification.

The method scales to high-dimensional models where traditional SVD is intractable.

Numerical examples demonstrate the approach's ability to produce models for large systems.

Abstract

Learning a dynamical system from input/output data is a fundamental task in the control design pipeline. In the partially observed setting there are two components to identification: parameter estimation to learn the Markov parameters, and system realization to obtain a state space model. In both sub-problems it is implicitly assumed that standard numerical algorithms such as the singular value decomposition (SVD) can be easily and reliably computed. When trying to fit a high-dimensional model to data, for example in the cyber-physical system setting, even computing an SVD is intractable. In this work we show that an approximate matrix factorization obtained using randomized methods can replace the standard SVD in the realization algorithm while maintaining the non-asymptotic (in data-set size) performance and robustness guarantees of classical methods. Numerical examples illustrate that for large system models, this is the only method capable of producing a model.