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Identification of linear hybrid systems: a geometric approach

Identifieur interne : 002920 ( Hal/Corpus ); précédent : 002919; suivant : 002921

Identification of linear hybrid systems: a geometric approach

Auteurs : Van Luong Le ; Fabien Lauer ; Gérard Bloch

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RBID : Hal:hal-00799147

English descriptors

Abstract

This paper deals with the identification of linear hybrid systems switching between multiple linear subsystems. We propose a new approach based on the geometric properties of hybrid systems in parameter space. More precisely, the data are mapped in that space such that each submodel is represented by a hypersphere. Then, we show how these hyperspheres can be easily separated by Principal Component Analysis (PCA) and derive a condition under which this separation is optimal for systems with two modes. Finally, classical (robust) regression is applied to estimate the system parameters from the classified data set. A simple procedure is also proposed to extend the method to the identification of switched systems with multiple modes. Experiments show that the final algorithm can accurately estimate both the parameters and the number of modes while being simple to apply and far more robust to noise than other methods.

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<idno type="halRefHtml">American Control Conference, ACC 2013, Jun 2013, Washington, United States. pp.CD-ROM, 2013</idno>
<idno type="halRef">American Control Conference, ACC 2013, Jun 2013, Washington, United States. pp.CD-ROM, 2013</idno>
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<idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
<idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
<idno type="stamp" n="LORIA">LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications</idno>
<idno type="stamp" n="CRAN-CID" p="CRAN">CRAN-CID</idno>
<idno type="stamp" n="CRAN">Centre de Recherche en Automatique de Nancy</idno>
<idno type="stamp" n="UNIV-LORRAINE">Université de Lorraine</idno>
<idno type="stamp" n="INPL">Institut National Polytechnique de Lorraine</idno>
<idno type="stamp" n="LORIA2">Publications du LORIA</idno>
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<title xml:lang="en">Identification of linear hybrid systems: a geometric approach</title>
<author role="aut">
<persName>
<forename type="first">Van Luong</forename>
<surname>Le</surname>
</persName>
<idno type="halAuthorId">826068</idno>
<affiliation ref="#struct-1001"></affiliation>
</author>
<author role="aut">
<persName>
<forename type="first">Fabien</forename>
<surname>Lauer</surname>
</persName>
<email>fabien.lauer@loria.fr</email>
<ptr type="url" target="http://www.loria.fr/~lauer/"></ptr>
<idno type="idHal">fabien-lauer</idno>
<idno type="halAuthorId">1091620</idno>
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</author>
<author role="aut">
<persName>
<forename type="first">Gérard</forename>
<surname>Bloch</surname>
</persName>
<email>gerard.bloch@esstin.uhp-nancy.fr</email>
<idno type="halAuthorId">81023</idno>
<affiliation ref="#struct-1001"></affiliation>
</author>
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<monogr>
<idno type="localRef">CID</idno>
<title level="m">American Control Conference, ACC 2013</title>
<meeting>
<title>American Control Conference, ACC 2013</title>
<date type="start">2013-06-17</date>
<date type="end">2013-06-19</date>
<settlement>Washington</settlement>
<country key="US">United States</country>
</meeting>
<imprint>
<biblScope unit="pp">CD-ROM</biblScope>
<date type="datePub">2013-06-17</date>
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<langUsage>
<language ident="en">English</language>
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<textClass>
<keywords scheme="author">
<term xml:lang="en">system identification</term>
<term xml:lang="en">switched systems</term>
<term xml:lang="en">hybrid systems</term>
<term xml:lang="en">switched regression</term>
</keywords>
<classCode scheme="halDomain" n="spi.auto">Engineering Sciences [physics]/Automatic</classCode>
<classCode scheme="halTypology" n="COMM">Conference papers</classCode>
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<abstract xml:lang="en">This paper deals with the identification of linear hybrid systems switching between multiple linear subsystems. We propose a new approach based on the geometric properties of hybrid systems in parameter space. More precisely, the data are mapped in that space such that each submodel is represented by a hypersphere. Then, we show how these hyperspheres can be easily separated by Principal Component Analysis (PCA) and derive a condition under which this separation is optimal for systems with two modes. Finally, classical (robust) regression is applied to estimate the system parameters from the classified data set. A simple procedure is also proposed to extend the method to the identification of switched systems with multiple modes. Experiments show that the final algorithm can accurately estimate both the parameters and the number of modes while being simple to apply and far more robust to noise than other methods.</abstract>
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