@incollection{eprints2460,
            year = {2013},
       booktitle = {Proceedings of the 52nd Annual Conference on Decision and Control (CDC), 2013},
           title = {LPV model order selection in an LS-SVM setting},
          author = {Dario Piga and Roland T{\'o}th},
           pages = {4128--4133},
       publisher = {IEEE},
           month = {December},
        keywords = {Delays; Estimation; Kernel; Monte Carlo methods; Scheduling; Standards; Vectors},
             url = {http://eprints.imtlucca.it/2460/},
        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.}
}