Sparse RKHS estimation via globally convex optimization and its application in LPV-IO identification
| Autor: | Dario Piga, Mohamed Abdelmonim Hassan Darwish, Roland Tóth, Vincent Laurain |
|---|---|
| Přispěvatelé: | Control Systems, EAISI High Tech Systems, Centre de Recherche en Automatique de Nancy (CRAN), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Eindhoven University of Technology [Eindhoven] (TU/e), DALLE MOLLE INSTITUTE FOR ARTIFICIAL INTELLIGENCE IDSIA LUGANO CHE, Partenaires IRSTEA, Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA)-Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA), Assiut University |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Reproducing kernel
0209 industrial biotechnology Mathematical optimization Computer science Model order selection Gaussian processes 02 engineering and technology [SPI.AUTO]Engineering Sciences [physics]/Automatic symbols.namesake Linear parameter-varying systems 020901 industrial engineering & automation Convergence (routing) 0202 electrical engineering electronic engineering information engineering Quadratic programming Electrical and Electronic Engineering Gaussian process Reproducing kernel Hilbert spaces Hilbert spaces Support vector machines 020208 electrical & electronic engineering Elastic net Estimator Support vector machine Parameter identification problem Control and Systems Engineering Convex optimization symbols Non-parametric estimation Reproducing kernel Hilbert space |
| Zdroj: | Automatica, 115:108914. Elsevier Automatica Automatica, Elsevier, 2020, 115, pp.108914. ⟨10.1016/j.automatica.2020.108914⟩ |
| ISSN: | 0005-1098 |
| Popis: | International audience; Function estimation using the Reproducing Kernel Hilbert Space (RKHS) framework is a powerful tool for identification of a general class of nonlinear dynamical systems without requiring much a priori information on model orders and nonlinearities involved. However, the high degrees-of-freedom (DOFs) of RKHS estimators has its price, as in case of large scale function estimation problems, they often require a serious amount of data samples to explore the search space adequately for providing high-performance model estimates. In cases where nonlinear dynamic relations can be expressed as a sum of functions, the literature proposes solutions to this issue by enforcing sparsity for adequate restriction of the DOFs of the estimator, resulting in parsimonious model estimates. Unfortunately, all existing solutions are based on greedy approaches, leading to optimization schemes which cannot guarantee convergence to the global optimum. In this paper, we propose an $\ell_1$-regularized non-parametric RKHS estimator which is the solution of a quadratic optimization problem. Effectiveness of the scheme is demonstrated on the non-parametric identification problem of LPV-IO models where the method solves simultaneously (i) the model order selection problem (in terms of number of input–output lags and input delay in the model structure) and (ii) determining the unknown functional dependency of the model coefficients on the scheduling variable directly from data. The paper also provides an extensive simulation study to illustrate effectiveness of the proposed scheme. |
| Databáze: | OpenAIRE |
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