eprintid: 2460
rev_number: 8
eprint_status: archive
userid: 6
dir: disk0/00/00/24/60
datestamp: 2015-01-12 12:49:00
lastmod: 2015-01-12 12:49:00
status_changed: 2015-01-12 12:49:00
type: book_section
metadata_visibility: show
creators_name: Piga, Dario
creators_name: Tóth, Roland
creators_id: dario.piga@imtlucca.it
creators_id: 
title: LPV model order selection in an LS-SVM setting
ispublished: pub
subjects: QA75
divisions: CSA
full_text_status: public
keywords: Delays; Estimation; Kernel; Monte Carlo methods; Scheduling; Standards; Vectors
abstract: In parametric identification of Linear Parameter-Varying (LPV) systems, the scheduling dependencies of the model coefficients are commonly parameterized in terms of linear combinations of a-priori selected basis functions. Such functions need to be adequately chosen, e.g., on the basis of some first-principles or expert's knowledge of the system, in order to capture the unknown dependencies of the model coefficient functions on the scheduling variable and, at the same time, to achieve a low-variance of the model estimate by limiting the number of parameters to be identified. This problem together with the well-known model order selection problem (in terms of number of input lags, output lags and input delay of the model structure) in system identification can be interpreted as a trade-off between bias and variance of the resulting model estimate. The problem of basis function selection can be avoided by using a non-parametric estimator of the coefficient functions in terms of a recently proposed Least-Square Support-Vector-Machine (LS-SVM) approach. However, the selection of the model order still appears to be an open problem in the identification of LPV systems via the LS-SVM method. In this paper, we propose a novel reformulation of the LPV LS-SVM approach, which, besides of the non-parametric estimation of the coefficient functions, achieves data-driven model order selection via convex optimization. The properties of the introduced approach are illustrated via a simulation example.
date: 2013-12
publisher: IEEE
pagerange: 4128-4133
event_title: Decision and Control (CDC), 2013 IEEE 52nd Annual Conference on
id_number: 10.1109/CDC.2013.6760522
refereed: TRUE
isbn: 978-1-4673-5714-2 
book_title: Proceedings of the 52nd Annual Conference on Decision and Control (CDC), 2013
official_url: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6760522&isnumber=6759837
funders: This work was supported by the Netherlands Organization for Scientific Research (NWO, grant. no.: 639.021.127) and by the French ministries of Foreign Affairs, Education and Research and the French-Dutch Academy (PHC Van Gogh project, n. 29342QL).
citation:   Piga, Dario and Tóth, Roland  LPV model order selection in an LS-SVM setting.   In:  Proceedings of the 52nd Annual Conference on Decision and Control (CDC), 2013.   IEEE, pp. 4128-4133.  ISBN 978-1-4673-5714-2       (2013)  
document_url: http://eprints.imtlucca.it/2460/1/CDC2013Preprint_Piga.pdf