A clustering technique for the identification of piecewise affine systems |
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Authors: | Giancarlo Ferrari-Trecate [Author Vitae] Marco Muselli [Author Vitae] |
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Affiliation: | a Institut für Automatik, ETH, Swiss Federal Institute of Technology, ETHZ - ETL, CH 8092 Zurich, Switzerland b INRIA, Domaine de Voluceau, 78153 Le Chesnay Cedex, France c Istituto per i Circuiti Elettronici, Consiglio Nazionale delle Ricerche, Via De Marini, 6 16149 Genova, Italy d Centro di studio sulle Tecnologie dell'Informatica e dell'Automazione, Consiglio Nazionale delle Ricerche, Dipartimento di Elettronica e Informazione, Politecnico di Milano, Piazza Leonardo da Vinci 32 I-20133 Milano, Italy |
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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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Keywords: | Nonlinear identification Hybrid systems Clustering Linear regression Classification |
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