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A clustering technique for the identification of piecewise affine systems

Authors
  • Ferrari-Trecate, Giancarlo
  • Muselli, Marco
  • Liberati, Diego
  • Morari, Manfred
Type
Published Article
Journal
Automatica
Publisher
Elsevier
Publication Date
Jan 01, 2002
Accepted Date
Sep 03, 2002
Volume
39
Issue
2
Pages
205–217
Identifiers
DOI: 10.1016/S0005-1098(02)00224-8
Source
Elsevier
Keywords
License
Unknown

Abstract

We propose a new technique for the identification of discrete-time hybrid systems in the piecewise affine (PWA) form. This problem can be formulated as the reconstruction of a possibly discontinuous PWA map with a multi-dimensional domain. In order to achieve our goal, we provide an algorithm that exploits the combined use of clustering, linear identification, and pattern recognition techniques. This allows to identify both the affine submodels and the polyhedral partition of the domain on which each submodel is valid avoiding gridding procedures. Moreover, the clustering step (used for classifying the datapoints) is performed in a suitably defined feature space which allows also to reconstruct different submodels that share the same coefficients but are defined on different regions. Measures of confidence on the samples are introduced and exploited in order to improve the performance of both the clustering and the final linear regression procedure.

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