Piga, Dario and Tóth, Roland
LPV model order selection in an LSSVM setting.
In:
Proceedings of the 52nd Annual Conference on Decision and Control (CDC), 2013.
IEEE, pp. 41284133.
ISBN 9781467357142
(2013)
Abstract
In parametric identification of Linear ParameterVarying (LPV) systems, the scheduling dependencies of the model coefficients are commonly parameterized in terms of linear combinations of apriori selected basis functions. Such functions need to be adequately chosen, e.g., on the basis of some firstprinciples 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 lowvariance of the model estimate by limiting the number of parameters to be identified. This problem together with the wellknown 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 tradeoff between bias and variance of the resulting model estimate. The problem of basis function selection can be avoided by using a nonparametric estimator of the coefficient functions in terms of a recently proposed LeastSquare SupportVectorMachine (LSSVM) approach. However, the selection of the model order still appears to be an open problem in the identification of LPV systems via the LSSVM method. In this paper, we propose a novel reformulation of the LPV LSSVM approach, which, besides of the nonparametric estimation of the coefficient functions, achieves datadriven model order selection via convex optimization. The properties of the introduced approach are illustrated via a simulation example.
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