title: Reduced-size kernel models for nonlinear hybrid system identification.
abstract: This brief paper focuses on the identification of nonlinear hybrid dynamical systems, i.e., systems switching between multiple nonlinear dynamical behaviors. Thus the aim is to learn an ensemble of submodels from a single set of input-output data in a regression setting with no prior knowledge on the grouping of the data points into similar behaviors. To be able to approximate arbitrary nonlinearities, kernel submodels are considered. However, in order to maintain efficiency when applying the method to large data sets, a preprocessing step is required in order to fix the submodel sizes and limit the number of optimization variables. This brief paper proposes four approaches, respectively inspired by the fixed-size least-squares support vector machines, the feature vector selection method, the kernel principal component regression and a modification of the latter, in order to deal with this issue and build sparse kernel submodels. These are compared in numerical experiments, which show that the proposed approach achieves the simultaneous classification of data points and approximation of the nonlinear behaviors in an efficient and accurate manner.
authors: Centre de Recherche en Automatique de Nancy (CRAN), Université de Lorraine, Centre National de la Recherche Scientifique, Vandoeuvre-lès-Nancy F-54500, France. Luong.Le-Van@ensem.inpl-nancy.fr
authors: Van Luong
authors: VL
authors: Le
authors: Grard
authors: G
authors: Bloch
authors: Fabien
authors: F
authors: Lauer
mesh_terms: D001185:Artificial Intelligence; D057225:Data Mining / Q000379:methods*; D016208:Databases, Factual; D005246:Feedback; D017711:Nonlinear Dynamics; D010363:Pattern Recognition, Automated / Q000379:methods*