Optimal expansions of discrete-time Volterra models using Laguerre functions

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-dimensio...

Full description

Saved in:
Bibliographic Details
Published inAutomatica (Oxford) Vol. 40; no. 5; pp. 815 - 822
Main Authors Campello, Ricardo J.G.B., Favier, Gérard, do Amaral, Wagner C.
Format Journal Article
LanguageEnglish
Published Oxford Elsevier Ltd 01.05.2004
Elsevier
Subjects
Applied sciences
Automatic
Computer Science
Computer science; control theory; systems
Control theory. Systems
Engineering Sciences
Exact sciences and technology
Laguerre functions
Model reduction
Nonlinear systems
Optimization
Signal and Image Processing
Volterra series
Volterra series
Model reduction
Nonlinear systems
Laguerre functions
Optimization
Laguerre function
Time series
Non linear control
Laguerre polynomial
Non linear system
Modeling
Time response
Global solution
Truncation error
Kernels
Orthonormal basis
Minimum time
Upper bound
Pulse response
Focusing
Optimal solution
Discrete time
Automatic control
Series expansion
Reduced order systems
Volterra equation
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2003.11.016