Large-Scale System Identification Using a Randomized SVD
This addresses a computational bottleneck for researchers and engineers in control systems dealing with high-dimensional data, though it is incremental as it adapts existing randomized techniques to a specific application.
The paper tackles the intractability of computing singular value decompositions (SVD) for large-scale system identification in high-dimensional models, such as cyber-physical systems, by showing that randomized methods can approximate the SVD while maintaining performance and robustness guarantees, enabling model production where classical methods fail.
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.