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LPV model order selection in an LS-SVM setting

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)

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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.

Item Type: Book Section
Identification Number: 10.1109/CDC.2013.6760522
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).
Uncontrolled Keywords: Delays; Estimation; Kernel; Monte Carlo methods; Scheduling; Standards; Vectors
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Research Area: Computer Science and Applications
Depositing User: Ms T. Iannizzi
Date Deposited: 12 Jan 2015 12:49
Last Modified: 12 Jan 2015 12:49
URI: http://eprints.imtlucca.it/id/eprint/2460

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