eprintid: 2429 rev_number: 12 eprint_status: archive userid: 6 dir: disk0/00/00/24/29 datestamp: 2015-01-08 10:31:58 lastmod: 2015-01-12 13:16:01 status_changed: 2015-01-08 10:31:58 type: monograph metadata_visibility: show creators_name: Laurain, Vincent creators_name: Tóth, Roland creators_name: Piga, Dario creators_id: creators_id: creators_id: dario.piga@imtlucca.it title: An instrumental Least Squares Support Vector Machine for nonlinear system identification: enforcing zero-centering constraints ispublished: unpub subjects: QA75 divisions: CSA full_text_status: public monograph_type: technical_report note: TUE-CS-2013-001 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. date: 2013-04 date_type: published number: 001 publisher: University of Technology, Eindhoven place_of_pub: The Netherlands pages: 4 institution: University of Technology, Eindhoven department: Control Systems Group, Department of Electrical Engineering citation: 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 (Unpublished) document_url: http://eprints.imtlucca.it/2429/1/Tr012013.pdf