Nonlinear Hybrid System Identification with Kernel Models
Identifieur interne : 003612 ( Hal/Curation ); précédent : 003611; suivant : 003613Nonlinear Hybrid System Identification with Kernel Models
Auteurs : Fabien Lauer [France] ; Gérard Bloch [France] ; René Vidal [États-Unis]Source :
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Abstract
This paper focuses on the identification of nonlinear hybrid systems involving unknown nonlinear dynamics. The proposed method extends the framework of [1] by introducing nonparametric models based on kernel functions in order to estimate arbitrary nonlinearities without prior knowledge. In comparison to the previous work of [2], which also dealt with unknown nonlinearities, the new algorithm assumes the form of an unconstrained nonlinear continuous optimization problem, which can be efficiently solved for moderate numbers of parameters in the model, as is typically the case for linear hybrid systems. However, to maintain the efficiency of the method on large data sets with nonlinear kernel models, a preprocessing step is required in order to fix the model size and limit the number of optimization variables. A support vector selection procedure, based on a maximum entropy criterion, is proposed to perform this step. The efficiency of the resulting algorithm is demonstrated on large-scale experiments involving the identification of nonlinear switched dynamical systems.
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<front><div type="abstract" xml:lang="en">This paper focuses on the identification of nonlinear hybrid systems involving unknown nonlinear dynamics. The proposed method extends the framework of [1] by introducing nonparametric models based on kernel functions in order to estimate arbitrary nonlinearities without prior knowledge. In comparison to the previous work of [2], which also dealt with unknown nonlinearities, the new algorithm assumes the form of an unconstrained nonlinear continuous optimization problem, which can be efficiently solved for moderate numbers of parameters in the model, as is typically the case for linear hybrid systems. However, to maintain the efficiency of the method on large data sets with nonlinear kernel models, a preprocessing step is required in order to fix the model size and limit the number of optimization variables. A support vector selection procedure, based on a maximum entropy criterion, is proposed to perform this step. The efficiency of the resulting algorithm is demonstrated on large-scale experiments involving the identification of nonlinear switched dynamical systems.</div>
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<author role="aut"><persName><forename type="first">Fabien</forename>
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</persName>
<email>fabien.lauer@loria.fr</email>
<idno type="idHal">fabien-lauer</idno>
<idno type="halAuthorId">522979</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>
<author role="aut"><persName><forename type="first">René</forename>
<surname>Vidal</surname>
</persName>
<idno type="halAuthorId">355764</idno>
<affiliation ref="#struct-58645"></affiliation>
</author>
</analytic>
<monogr><title level="m">49th IEEE Conference on Decision and Control, CDC 2010</title>
<meeting><title>49th IEEE Conference on Decision and Control, CDC 2010</title>
<date type="start">2010-12-15</date>
<date type="end">2010-12-17</date>
<settlement>Atlanta, GA</settlement>
<country key="US">United States</country>
</meeting>
<editor>IEEE</editor>
<imprint><publisher>IEEE</publisher>
<biblScope unit="pp">696-701</biblScope>
<date type="datePub">2010-12-15</date>
</imprint>
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<profileDesc><langUsage><language ident="en">English</language>
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<textClass><keywords scheme="author"><term xml:lang="en">Nonlinear Hybrid System Identification</term>
<term xml:lang="en">Kernel Models</term>
<term xml:lang="en">continuous optimization</term>
<term xml:lang="en">large data sets</term>
<term xml:lang="en">support vector selection</term>
<term xml:lang="en">fixed-size Least Squares SVM (LS-SVM)</term>
</keywords>
<classCode scheme="halDomain" n="spi.auto">Engineering Sciences [physics]/Automatic</classCode>
<classCode scheme="halDomain" n="info.info-au">Computer Science [cs]/Automatic Control Engineering</classCode>
<classCode scheme="halDomain" n="info.info-lg">Computer Science [cs]/Machine Learning [cs.LG]</classCode>
<classCode scheme="halDomain" n="info.info-mo">Computer Science [cs]/Modeling and Simulation</classCode>
<classCode scheme="halDomain" n="info.info-ne">Computer Science [cs]/Neural and Evolutionary Computing [cs.NE]</classCode>
<classCode scheme="halDomain" n="stat.ot">Statistics [stat]/Other Statistics [stat.ML]</classCode>
<classCode scheme="halTypology" n="COMM">Conference papers</classCode>
</textClass>
<abstract xml:lang="en">This paper focuses on the identification of nonlinear hybrid systems involving unknown nonlinear dynamics. The proposed method extends the framework of [1] by introducing nonparametric models based on kernel functions in order to estimate arbitrary nonlinearities without prior knowledge. In comparison to the previous work of [2], which also dealt with unknown nonlinearities, the new algorithm assumes the form of an unconstrained nonlinear continuous optimization problem, which can be efficiently solved for moderate numbers of parameters in the model, as is typically the case for linear hybrid systems. However, to maintain the efficiency of the method on large data sets with nonlinear kernel models, a preprocessing step is required in order to fix the model size and limit the number of optimization variables. A support vector selection procedure, based on a maximum entropy criterion, is proposed to perform this step. The efficiency of the resulting algorithm is demonstrated on large-scale experiments involving the identification of nonlinear switched dynamical systems.</abstract>
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