Finite-sample analysis of identification of switched linear systems with arbitrary or restricted switching

TL;DR

This paper provides finite-sample error bounds for identifying switched linear systems, revealing how switching strategies and stability modes influence estimation accuracy, with implications for designing effective switching strategies.

Contribution

It introduces finite-sample error bounds for LS estimation of switched systems under various switching strategies and stability conditions, highlighting the impact of unstable modes.

Findings

Estimation error grows logarithmically with switching parameters for stable modes.

Error bounds increase linearly with switching parameters when unstable modes are present.

Proper switching strategy design is crucial to control estimation error in unstable systems.

Abstract

For the identification of switched systems with a measured switching signal, this work aims to analyze the effect of switching strategies on the estimation error. The data for identification is assumed to be collected from globally asymptotically or marginally stable switched systems under switches that are arbitrary or subject to an average dwell time constraint. Then the switched system is estimated by the least-squares (LS) estimator. To capture the effect of the parameters of the switching strategies on the LS estimation error, finite-sample error bounds are developed in this work. The obtained error bounds show that the estimation error is logarithmic of the switching parameters when there are only stable modes; however, when there are unstable modes, the estimation error bound can increase linearly as the switching parameter changes. This suggests that in the presence of unstable modes, the switching strategy should be properly designed to avoid the significant increase of the estimation error.