ON CONVERGENCE OF VOLTERRA SERIES EXPANSION OF A CLASS OF NONLINEAR SYSTEMS

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)1089-1102
Number of pages14
Journal / PublicationAsian Journal of Control
Volume19
Issue number3
Online published8 Mar 2017
Publication statusPublished - May 2017
Externally publishedYes

Abstract

A fundamental issue in conducting the analysis and design of a nonlinear system via Volterra series theory is how to ensure the excitation magnitude and/or model parameters will be in the appropriate range such that the nonlinear system has a convergent Volterra series expansion. To this aim, parametric convergence bounds of Volterra series expansion of nonlinear systems described by a NARX model, which can reveal under what excitation magnitude or within what parameter range a given NARX system is able to have a convergent Volterra series expansion subject to any given input signal, are investigated systematically in this paper. The existing bound results often are given as a function of the maximum input magnitude, which could be suitable for single-tone harmonic inputs but very conservative for complicated inputs (e.g. multi-tone or arbitrary inputs). In this study, the output response of nonlinear systems is expressed in a closed form, which is not only determined by the input magnitude but also related to the input energy or waveform. These new techniques result in more accurate bound criteria, which are not only functions of model parameters and the maximum input magnitude but also consider a factor reflecting the overall input energy or wave form. This is significant to practical applications, since the same nonlinear system could exhibit chaotic behavior subject to a simple single-tone input but might not with respect to other different input signals (e.g. multi-tone inputs) of the same input magnitude. The results provide useful guidance for the application of Volterra series-based theory and methods from an engineering point of view. The Duffing equation is used as a benchmark example to show the effectiveness of the results.

Research Area(s)

  • Volterra series, nonlinear systems, convergence bound, FREQUENCY-RESPONSE FUNCTIONS, NON-LINEAR SYSTEMS, CROSS-PRODUCTS, NARX MODEL, IDENTIFICATION, APPROXIMATION, DOMAIN, BOUNDS