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

Journal article (2022)

Authors

S. Shi Team Bart De Schutter - Mechanical, Maritime and Materials Engineering
Othmane Mazhar KTH Royal Institute of Technology
B.H.K. De Schutter Team Bart De Schutter - Mechanical, Maritime and Materials Engineering
Research Group
Team Bart De Schutter (Mechanical, Maritime and Materials Engineering) (TU Delft)
Copyright: © 2022 S. Shi, Othmane Mazhar, B.H.K. De Schutter
DOI
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https://doi.org/10.1109/LCSYS.2022.3187511
Identification Switched systems Measurement uncertainty Control systems Linear systems Switches Upper bound Estimation error
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Published Date

2022

Language

English

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Faculty

Mechanical, Maritime and Materials Engineering

Department

Delft Center for Systems and Control

Research Group

Team Bart De Schutter

Abstract

For the identification of switched systems with measured states and a measured switching signal, this work aims to analyze the effect of switching strategies on the estimation error. The data 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.