Computer Algorithms for Pseudo-Formal Linearization Method Based on Discrete Fourier Series Expansion and Nonlinear Observer

In this paper, we propose a computational algorithm of a pseudo-formal linearization method for nonlinear dynamic systems using the discrete Fourier series expansion in order to reduce computational burden. A nonlinear dynamic system is transformed into some augmented linear systems piecewisely with...

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Bibliographic Details
Published inJournal of Signal Processing Vol. 25; no. 5; pp. 155 - 162
Main Authors Komatsu, Kazuo, Takata, Hitoshi
Format Journal Article
LanguageEnglish
Published Tokyo Research Institute of Signal Processing, Japan 01.09.2021
Japan Science and Technology Agency
Subjects
Algorithms
discrete Fourier series expansion
Dynamical systems
Fourier series
lin-earization function
Linear systems
Linearization
Nonlinear dynamics
nonlinear observer
nonlinear system
Nonlinear systems
pseudo-formal linearization
Series expansion
trigonometric function
Trigonometric functions
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Summary:In this paper, we propose a computational algorithm of a pseudo-formal linearization method for nonlinear dynamic systems using the discrete Fourier series expansion in order to reduce computational burden. A nonlinear dynamic system is transformed into some augmented linear systems piecewisely with respect to a linearization function that consists of trigonometric functions by a pseudo-formal linearization method using the discrete Fourier series expansion. Then all of the linearized systems are smoothly united into a single linear system. As an application of this method, a computational algorithm for a nonlinear observer is also proposed. Numerical experiments are demonstrated to indicate the effectiveness of the proposed algorithms.
ISSN:1342-6230
1880-1013
DOI:10.2299/jsp.25.155