Laurain, Vincent and Tóth, Roland and Piga, Dario
An instrumental Least Squares Support Vector Machine for nonlinear system identification: enforcing zero-centering constraints.
Technical Report
#001/2013
University of Technology, Eindhoven
, The Netherlands.
(Unpublished)
Abstract
Least-Squares Support Vector Machines (LS-SVM's), originating from Stochastic Learning
theory, represent a promising approach to identify nonlinear systems via nonparametric es-
timation of nonlinearities in a computationally and stochastically attractive way. However,
application of LS-SVM's in the identification context is formulated as a linear regression aim-
ing at the minimization of the ℓ2 loss in terms of the prediction error. This formulation
corresponds to a prejudice of an auto-regressive noise structure, which, especially in the non-
linear context, is often found to be too restrictive in practical applications. In [1], a novel
Instrumental Variable (IV) based estimation is integrated into the LS-SVM approach provid-
ing, under minor conditions, a consistent identification of nonlinear systems in case of a noise
modeling error. It is shown how the cost function of the LS-SVM is modified to achieve an IV-based solution.
In this technical report, a detailed derivation of the results presented in Section 5.2 of [1]
is given as a supplement material for interested readers.
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