TY  - CHAP
TI  - LPV model order selection in an LS-SVM setting
AV  - public
Y1  - 2013/12//
KW  - Delays; Estimation; Kernel; Monte Carlo methods; Scheduling; Standards; Vectors
UR  - http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6760522&isnumber=6759837
A1  - Piga, Dario
A1  - Tóth, Roland
SN  - 978-1-4673-5714-2 
PB  - IEEE
SP  - 4128
N2  - 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.
ID  - eprints2460
T2  - Proceedings of the 52nd Annual Conference on Decision and Control (CDC), 2013
EP  - 4133
ER  -