An ℓ0−ℓ1 norm based optimization procedure for the identification of switched nonlinear systems

We consider the problem of identifying a switched nonlinear system from a finite collection of input-output data. The constituent subsystems of such a switched system are all nonlinear systems. We model each individual subsystem as a sparse expansion over a dictionary of elementary nonlinear smooth...

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Bibliographic Details
Published in49th IEEE Conference on Decision and Control (CDC) pp. 4467 - 4472
Main Authors Bako, Laurent, Boukharouba, Khaled, Lecoeuche, Stéphane
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.12.2010
Subjects
Convex functions
Data models
Mathematical model
Nickel
Noise
Nonlinear systems
Switches
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ISBN142447745X
9781424477456
ISSN0191-2216
DOI10.1109/CDC.2010.5717199

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Summary:We consider the problem of identifying a switched nonlinear system from a finite collection of input-output data. The constituent subsystems of such a switched system are all nonlinear systems. We model each individual subsystem as a sparse expansion over a dictionary of elementary nonlinear smooth functions shaped by the whole available dataset. Estimating the switched model from data is a doubly challenging problem. First one needs, without any knowledge of the parameters, to decide which subsystem is active at which time instant. Second, the representation of each nonlinear subsystem over the considered basis shall be performed in a high dimensional space. We tackle both tasks simultaneously by sparse optimization. More specifically, we view the switched nonlinear system identification problem as the problem of minimizing the ℓ 0 norm of an error vector. We subsequently relax it into an ℓ 1 convex minimization problem for which powerful numerical tools exist.
ISBN:142447745X
9781424477456
ISSN:0191-2216
DOI:10.1109/CDC.2010.5717199