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A kernel method for non-linear systems indentification - infinite degree volerra series estimation

Wan, Y., Dodd, T.J. and Harrison, R.F. (2003) A kernel method for non-linear systems indentification - infinite degree volerra series estimation. Research Report. ACSE Research Report no. 842 . Automatic Control and Systems Engineering, University of Sheffield.


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Volterra series expansions are widely used in analyzing and solving the problems of non-linear dynamical systems. However, the problem that the number of terms to be determined increases exponentially with the order of the expansion restricts its practical application. In practice, Volterra series expansions are truncated severely so that they may not give accurate representations of the original system. To address this problem, kernel methods are shown to be deserving of exploration. In this report, we make use of an existing result from the theory of approximation in reproducing kernel Hilbert space (RKHS) that has not yet been exploited in the systems identification field. An exponential kernel method, based on an RKHS called a generalized Fock space, is introduced, to model non-linear dynamical systems and to specify the corresponding Volterra series expansion. In this way a non-linear dynamical system can be modelled using a finite memory length, infinite degree Volterra series expansion, thus reducing the source of approximation error solely to truncation in time. We can also, in principle, recover any coefficient in the Volterra series.

Item Type: Monograph (Research Report)
Copyright, Publisher and Additional Information: The Department of Automatic Control and Systems Engineering research reports offer a forum for the research output of the academic staff and research students of the Department at the University of Sheffield. Papers are reviewed for quality and presentation by a departmental editor. However, the contents and opinions expressed remain the responsibility of the authors. Some papers in the series may have been subsequently published elsewhere and you are advised to cite the later published version in these instances.
Institution: The University of Sheffield
Academic Units: The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Automatic Control and Systems Engineering (Sheffield) > ACSE Research Reports
Depositing User: Miss Anthea Tucker
Date Deposited: 11 Sep 2012 10:34
Last Modified: 09 Jun 2014 08:14
Status: Published
URI: http://eprints.whiterose.ac.uk/id/eprint/74489

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