Nonlinear Hybrid System Identification with Kernel Models

Fabien Lauer (1) , Gérard Bloch (2) , René Vidal (3)

1 ABC - Machine Learning and Computational Biology
2 CRAN - Centre de Recherche en Automatique de Nancy
3 CIS - Center for Imaging Science

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.

Mots clés: Kernel Models; continuous optimization; large data sets; support vector selection; fixed-size Least Squares SVM (LS-SVM); Nonlinear Hybrid System Identification

Domaines: Automatique / Robotique; Automatique; Apprentissage [cs.LG]; Modélisation et simulation; Réseau de neurones [cs.NE]; Autres [stat.ML]

Fabien Lauer, Gérard Bloch, René Vidal. Nonlinear Hybrid System Identification with Kernel Models. 49th IEEE Conference on Decision and Control, CDC 2010, Dec 2010, Atlanta, GA, United States. pp.696-701. ⟨hal-00514429v2⟩