Optimal expansions of discrete-time Volterra models using Laguerre functions

Campello, Ricardo J.G.B., Favier, Gérard, and Amaral, Wagner C. (2004) Optimal expansions of discrete-time Volterra models using Laguerre functions. Automatica, 40 (5). pp. 815-822.

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Abstract

This work is concerned with the optimization of Laguerre bases for the orthonormal series expansion of discrete-time Volterra models. The aim is to minimize the number of Laguerre functions associated with a given series truncation error, thus reducing the complexity of the resulting finite-dimensional representation. Fu and Dumont (IEEE Trans. Automatic Control 38(6) (1993) 934) indirectly approached this problem in the context of linear systems by minimizing an upper bound for the error resulting from the truncated Laguerre expansion of impulse response models, which are equivalent to first-order Volterra models. A generalization of the work mentioned above focusing on Volterra models of any order is presented in this paper. The main result is the derivation of analytic strict global solutions for the optimal expansion of the Volterra kernels either using an independent Laguerre basis for each kernel or using a common basis for all the kernels.

Item ID: 47658
Item Type: Article (Research - C1)
ISSN: 1873-2836
Keywords: Laguerre functions, model reduction, nonlinear systems, optimization, Volterra series
Funders: CAPES, CNPq, Brazil
Projects and Grants: CAPES BEX0467/02-2, CNPq 301345184
Date Deposited: 02 May 2017 23:59
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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