Optimal expansions of discrete-time Volterra models using Laguerre functions

被引:72
作者
Campello, RJGB
Favier, G
do Amaral, WC
机构
[1] CNRS, UNSA, I3S, F-06903 Sophia Antipolis, France
[2] Univ Santos, COPOP, BR-11070906 Santos, SP, Brazil
[3] Univ Estadual Campinas, FEEC, DCA, BR-13083970 Campinas, SP, Brazil
关键词
nonlinear systems; volterra series; Laguerre functions; optimization; model reduction;
D O I
10.1016/j.automatica.2003.11.016
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
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. (C) 2003 Elsevier Ltd. All rights reserved.
引用
收藏
页码:815 / 822
页数:8
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