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...

Full description

Saved in:
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
Online AccessGet full text

Cover

Abstract 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.
AbstractList 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.
Author Takata, Hitoshi
Komatsu, Kazuo
Author_xml – sequence: 1
  fullname: Komatsu, Kazuo
  organization: National Institute of Technology, Kumamoto College
– sequence: 2
  fullname: Takata, Hitoshi
  organization: Kagoshima University
BookMark eNo9kEtP6zAQhS0EEs8Nv8ASuyul-FE7yeIuoFBAKg8JWEcTe0JTpXawUwSIH4-hwGoe-s6Z0dklm847JOSQs5EQZXm8iP1IqBFXaoPs8KJgGWdcbqZejkWmhWTbZDfGBWNa50rukI-JX_arAQM96Z58aIf5MtLGB3oXcWV9NvVhCR2dtQ4htO8wtN7Raxzm3tJTiGhpms_aaAIOSKd-FdrkdY-pRHr-2oOLXwpwlt54133b0Ns6YnjBsE-2GugiHvzUPfI4PX-YXGaz24urycksMyLXKuPamlyMrSibvKlZjba2ec5KraVGpZoxExJMA2NeSJPXJeOWFXUNkoMAA7XcI0dr3z745xXGoVqkR106WQmlC8mUKkSi_q0pE3yMAZuqD-0SwlvFWfWVbpXSTYIqpZvg_2t4EQd4wj8UwtCaDn9R9cP_7c0cQoVOfgKOwoeX
Cites_doi 10.1109/TPEL.2017.2662062
10.2299/jsp.21.291
10.1109/CDC.1996.574256
10.1016/S0167-6911(82)80042-X
10.2299/jsp.22.9
10.1016/S0167-6911(84)80100-0
10.2299/jsp.25.25
10.1109/TPAS.1970.292668
10.1115/1.3426360
10.1016/S1474-6670(17)66062-2
10.1109/TAC.1969.1099191
ContentType Journal Article
Copyright 2021 Research Institute of Signal Processing, Japan
Copyright Japan Science and Technology Agency 2021
Copyright_xml – notice: 2021 Research Institute of Signal Processing, Japan
– notice: Copyright Japan Science and Technology Agency 2021
DBID AAYXX
CITATION
DOI 10.2299/jsp.25.155
DatabaseName CrossRef
DatabaseTitle CrossRef
DatabaseTitleList

DeliveryMethod fulltext_linktorsrc
Discipline Engineering
EISSN 1880-1013
EndPage 162
ExternalDocumentID 10_2299_jsp_25_155
article_jsp_25_5_25_155_article_char_en
GroupedDBID 2WC
5GY
ALMA_UNASSIGNED_HOLDINGS
CS3
JSF
JSH
KQ8
OK1
RJT
RZJ
AAYXX
CITATION
ID FETCH-LOGICAL-c2765-16dc724d29f7fb0bedbd77096636e55f4023acfa4183c7b901d08bba31a2acab3
ISSN 1342-6230
IngestDate Thu Oct 10 20:37:46 EDT 2024
Wed Sep 11 13:57:32 EDT 2024
Wed Apr 05 06:57:53 EDT 2023
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 5
Language English
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-c2765-16dc724d29f7fb0bedbd77096636e55f4023acfa4183c7b901d08bba31a2acab3
OpenAccessLink https://www.jstage.jst.go.jp/article/jsp/25/5/25_155/_article/-char/en
PQID 2568305582
PQPubID 2028978
PageCount 8
ParticipantIDs proquest_journals_2568305582
crossref_primary_10_2299_jsp_25_155
jstage_primary_article_jsp_25_5_25_155_article_char_en
PublicationCentury 2000
PublicationDate 2021/09/01
2021-9-1
20210901
PublicationDateYYYYMMDD 2021-09-01
PublicationDate_xml – month: 09
  year: 2021
  text: 2021/09/01
  day: 01
PublicationDecade 2020
PublicationPlace Tokyo
PublicationPlace_xml – name: Tokyo
PublicationTitle Journal of Signal Processing
PublicationTitleAlternate Journal of Signal Processing
PublicationYear 2021
Publisher Research Institute of Signal Processing, Japan
Japan Science and Technology Agency
Publisher_xml – name: Research Institute of Signal Processing, Japan
– name: Japan Science and Technology Agency
References [1] Y. N. Yu, K. Vongsuriya and L. N. Wedman: Application of an optimal control theory to a power system, IEEE Trans. Power Appl. Syst., Vol. PAS-89, No. 1, pp. 55-62, 1970.
[8] K. Komatsu and H. Takata: A formal linearization by the Chebyshev interpolation and its applications, Proc. IEEE CDC, Vol. 1, pp. 70-75, 1996.
[2] M. Vidyasagar: Nonlinear Systems Analysis, Prentice-Hall, 1978.
[9] K. Komatsu and H. Takata: A nonlinear observer via pseudo-formal linearization for both state and measurement equations of nonlinear scalar-measurement systems J. Signal Process., Vol. 21, No. 6, pp. 291-296, 2017.
[10] H. Takata and K. Komatsu: A pseudo-formal linearization of polynomial type for nonlinear systems and its applications, J. Signal Process., Vol. 22, No. 1, pp. 9-16, 2018.
[3] R. W. Brockett: Feedback invariants for nonlinear systems, Proc. IFAC Congress, pp. 1115-1120, 1978.
[7] H. Takata and K. Komatsu: A formal linearization of nonlinear systems on the trigonometric Fourier expansion, Proc. '89 KACC, Vol. 2, pp. 939-942, 1989.
[12] H. Sunouchi: Introduction to Functional Analysis, Saiensu-sha Co.,Ltd, 1976 (in Japanese).
[4] R. Su: On the linear equivalents of nonlinear systems, Syst. Control Lett., Vol. 2, No. 1, pp. 48-52, 1982.
[5] A. J. Krener: Approximate linearization by state feedback and coordinate change, Syst. Control Lett., Vol. 5, pp. 181-185, 1984.
[6] S. Yang, P. Wang and Y. Tang: Feedback linearization-based current control strategy for modular multilevel converters, IEEE Trans. Power Electron., Vol. 33, No. 1, pp. 161-174, 2018.
[11] K. Komatsu and H. Takata: On a pseudo-formal linearization method based on Fourier expansion, J. Signal Process., Vol. 25, No. 1, pp. 25-31, 2021.
[13] G. W. Johnson: A deterministic theory of estimation and control, IEEE Trans. Autom. Control, Vol. 14, pp. 380-384, 1974.
11
12
13
1
2
3
4
5
6
7
8
9
10
References_xml – ident: 6
  doi: 10.1109/TPEL.2017.2662062
– ident: 9
  doi: 10.2299/jsp.21.291
– ident: 8
  doi: 10.1109/CDC.1996.574256
– ident: 12
– ident: 4
  doi: 10.1016/S0167-6911(82)80042-X
– ident: 10
  doi: 10.2299/jsp.22.9
– ident: 5
  doi: 10.1016/S0167-6911(84)80100-0
– ident: 11
  doi: 10.2299/jsp.25.25
– ident: 1
  doi: 10.1109/TPAS.1970.292668
– ident: 2
  doi: 10.1115/1.3426360
– ident: 7
– ident: 3
  doi: 10.1016/S1474-6670(17)66062-2
– ident: 13
  doi: 10.1109/TAC.1969.1099191
SSID ssj0066753
Score 2.2112503
Snippet In this paper, we propose a computational algorithm of a pseudo-formal linearization method for nonlinear dynamic systems using the discrete Fourier series...
SourceID proquest
crossref
jstage
SourceType Aggregation Database
Publisher
StartPage 155
SubjectTerms 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
Title Computer Algorithms for Pseudo-Formal Linearization Method Based on Discrete Fourier Series Expansion and Nonlinear Observer
URI https://www.jstage.jst.go.jp/article/jsp/25/5/25_155/_article/-char/en
https://www.proquest.com/docview/2568305582
Volume 25
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
ispartofPNX Journal of Signal Processing, 2021/09/01, Vol.25(5), pp.155-162
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1bb9MwFLbK4AEeEFdRGMgSvFUujeNL8jguUwXaEGKT9hbZjtN1TG21NC8Tf4n_yHFspw3lYewlSi03af19Oeezc84xQu8A4sxIlRMmlCWMVobkXBpSZkKnaaqYqdyC_tGxmJ6yL2f8bDD4vRW11Kz12Fz_M6_kNqhCG-DqsmT_A9nuotAA54AvHAFhON4I47glw-jgcraEWf65r64AVs025ZIcOj166abdQOeQbzk6areMHn0A71W6NwWf5mA4QDm7DZba3evcepmtXQ1k8GIxWPnYV9RQV6Nv2q3jhpjeXVX7Yz5zZyH_IPrFNrcGtHHd-AiO62a5WTL4qbyCnYJxqc_n2-sQNOkCrUIAUwgU7Ac57NzUx_-uAvO9zU0ZJaDC_OsZ69vArICH8Gmq0VD7DOlASL5ldRNf6Tc48MSb9799AwXH63xDvRpTPu6-0qu1HZAsoFNBecHdAXoWsd1lwgHx7qC7VObcRZB-_d69tBLCFz3t_o-vhuvu-35z157-uXcBU4DZrg5oxc3JI_Qw4IcP_A94jAZ28QQ92KpV-RT9imTDG7JhIBvukQ33yIY92XBLNgyfI9lwIBv2ZMMd2TCQDXdkw5Fsz9Dp4eeTj1MStu4ghkrBSSJKIykraV7JSk-0LXUpJUyXRSos5xUDqahMpRh4FCM1iNJykmmt0kRRZZROn6O9xXJhXyAMEpqLSuZUqYoxXmXKWpklVvNsUgphh-htHNBi5Su0FDCzdcMecYRhHyLhx7rrc0Osh2g_YlOER7-GriJzpfIy-vK2132F7m-eon20t75q7GvQt2v9pmXVHy5TtCg
link.rule.ids 315,786,790,27955,27956
linkProvider Colorado Alliance of Research Libraries
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Computer+Algorithms+for+Pseudo-Formal+Linearization+Method+Based+on+Discrete+Fourier+Series+Expansion+and+Nonlinear+Observer&rft.jtitle=Journal+of+Signal+Processing&rft.au=Komatsu%2C+Kazuo&rft.au=Takata%2C+Hitoshi&rft.date=2021-09-01&rft.pub=Research+Institute+of+Signal+Processing%2C+Japan&rft.issn=1342-6230&rft.eissn=1880-1013&rft.volume=25&rft.issue=5&rft.spage=155&rft.epage=162&rft_id=info:doi/10.2299%2Fjsp.25.155&rft.externalDocID=article_jsp_25_5_25_155_article_char_en
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1342-6230&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1342-6230&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1342-6230&client=summon