Identification of Sparse Continuous-Time Linear Systems with Low Sampling Rate: Optimization Approaches

TL;DR

This paper introduces an optimization-based method for identifying sparse continuous-time linear systems from low-rate sampled data, crucial for applications with expensive or infrequent sampling, outperforming traditional least squares in noisy scenarios.

Contribution

It presents a novel iterative optimization approach with $l_1$-regularization tailored for low-sampling-rate data, addressing a gap in system identification under limited sampling conditions.

Findings

Method outperforms least squares in high-noise environments.

Effective in identifying sparse systems from low-rate samples.

Applicable to biomedical and other applications with sampling constraints.

Abstract

This paper addresses identification of sparse linear and noise-driven continuous-time state-space systems, i.e., the right-hand sides in the dynamical equations depend only on a subset of the states. The key assumption in this study, is that the sample rate is not high enough to directly infer the continuous time system from the data. This assumption is relevant in applications where sampling is expensive or requires human intervention (e.g., biomedicine applications). We propose an iterative optimization scheme with $l_1$-regularization, where the search directions are restricted those that decrease prediction error in each iteration. We provide numerical examples illustrating the proposed method; the method outperforms the least squares estimation for large noise.