Choice of free parameters in expansions of discrete-time Volterra models using Kautz functions

da Rosa, Alex, Campello, Ricardo J.G.B., and Amaral, Wagner C. (2007) Choice of free parameters in expansions of discrete-time Volterra models using Kautz functions. Automatica, 43 (6). pp. 1084-1091.

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Abstract

This work tackles the problem of modeling nonlinear systems using Volterra models based on Kautz functions. The drawback of requiring a large number of parameters in the representation of these models can be circumvented by describing every kernel using an orthonormal basis of functions, such as the Kautz basis. The resulting model, so-called Wiener/Volterra model, can be truncated into a few terms if the Kautz functions are properly designed. The underlying problem is how to select the free-design complex poles that fully parameterize these functions. A solution to this problem has been provided in the literature for linear systems, which can be represented by first-order Volterra models. A generalization of such strategy focusing on Volterra models of any order is presented in this paper. This problem is solved by minimizing an upper bound for the error resulting from the truncation of the kernel expansion into a finite number of functions. The aim is to minimize the number of two-parameter Kautz functions associated with a given series truncation error, thus reducing the complexity of the resulting finite-dimensional representation. The main result is the derivation of an analytical solution for a sub-optimal expansion of the Volterra kernels using a set of Kautz functions.

Item ID: 47656
Item Type: Article (Research - C1)
ISSN: 1873-2836
Keywords: nonlinear systems, optimization, system identification, two-parameter Kautz functions, Volterra series
Additional Information:

This paper was also presented at the 6th IFAC World Congress, Prague, Czech Republic, July 2005.

Funders: CNPq, Brazil, FAPESP
Date Deposited: 02 May 2017 02:46
FoR Codes: 01 MATHEMATICAL SCIENCES > 0102 Applied Mathematics > 010299 Applied Mathematics not elsewhere classified @ 100%
SEO Codes: 97 EXPANDING KNOWLEDGE > 970101 Expanding Knowledge in the Mathematical Sciences @ 100%
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