LPV model order selection in an LS-SVM setting

D. Piga, R. Toth

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

11 Citations (Scopus)
115 Downloads (Pure)

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.
Original languageEnglish
Title of host publicationProceedings of the 52nd Conference on Decision and Control, 10-13 December 2013, Florence, Italy
Pages4128-4133
DOIs
Publication statusPublished - 2013
Event52nd IEEE Conference on Decision and Control (CDC 2013) - Florence, Italy
Duration: 10 Dec 201313 Dec 2013
Conference number: 52

Conference

Conference52nd IEEE Conference on Decision and Control (CDC 2013)
Abbreviated titleCDC 2013
Country/TerritoryItaly
CityFlorence
Period10/12/1313/12/13

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