Stabilization of ODE with hyperbolic equation actuator subject to boundary control matched disturbance

In this paper, we consider stabilisation for a cascade of ODE and first-order hyperbolic equation with external disturbance flowing to the control end. The active disturbance rejection control (ADRC) and sliding mode control (SMC) approaches are adopted in investigation. By ADRC approach, the distur...

Full description

Saved in:
Bibliographic Details
Published inInternational journal of control Vol. 92; no. 1; pp. 12 - 26
Main Authors Zhou, Hua-Cheng, Guo, Bao-Zhu
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 02.01.2019
Taylor & Francis Ltd
Subjects
Active control
Active disturbance rejection control
Actuators
Boundary control
boundary feedback control
Closed loop systems
Closed loops
Control theory
Feedback control
Feedback loops
High gain
Sliding mode control
stabilisation
Online AccessGet full text

Cover

Abstract In this paper, we consider stabilisation for a cascade of ODE and first-order hyperbolic equation with external disturbance flowing to the control end. The active disturbance rejection control (ADRC) and sliding mode control (SMC) approaches are adopted in investigation. By ADRC approach, the disturbance is estimated through a disturbance estimator with both time-varying high gain and constant high gain, and the disturbance is canceled online in the feedback loop. It is shown that the resulting closed-loop system with time-varying high gain is asymptotically stable and is practically stable with constant high gain. By SMC approach, the existence and uniqueness of the solution for the closed loop via SMC are proved, and the monotonicity of the 'reaching condition' is presented. The resulting closed-loop system is shown to be exponentially stable. The numerical experiments are carried out to illustrate effectiveness of the proposed control law.
AbstractList In this paper, we consider stabilisation for a cascade of ODE and first-order hyperbolic equation with external disturbance flowing to the control end. The active disturbance rejection control (ADRC) and sliding mode control (SMC) approaches are adopted in investigation. By ADRC approach, the disturbance is estimated through a disturbance estimator with both time-varying high gain and constant high gain, and the disturbance is canceled online in the feedback loop. It is shown that the resulting closed-loop system with time-varying high gain is asymptotically stable and is practically stable with constant high gain. By SMC approach, the existence and uniqueness of the solution for the closed loop via SMC are proved, and the monotonicity of the 'reaching condition' is presented. The resulting closed-loop system is shown to be exponentially stable. The numerical experiments are carried out to illustrate effectiveness of the proposed control law.
Author Zhou, Hua-Cheng
Guo, Bao-Zhu
Author_xml – sequence: 1
  givenname: Hua-Cheng
  orcidid: 0000-0001-6856-2358
  surname: Zhou
  fullname: Zhou, Hua-Cheng
  organization: The Key Laboratory of System and Control, Academy of Mathematics and Systems Science, Academia Sinica
– sequence: 2
  givenname: Bao-Zhu
  orcidid: 0000-0001-9078-0001
  surname: Guo
  fullname: Guo, Bao-Zhu
  email: bzguo@iss.ac.cn
  organization: School of Computational and Applied Mathematics, University of the Witwatersrand
BookMark eNqFkE9LAzEQxYMo2FY_ghDwvHWSmGwWL4rWP1DwoJ5DNpvQlO2mJllK_fRurV486GVmYN57w_zG6LALnUXojMCUgIQLAAolKaspBSKmhDJOpThAI8KEKLikcIhGO02xEx2jcUpLAMK4JCPkXrKufes_dPahw8Hh57sZ3vi8wIvt2sY6tN5g-97v99rkYQoRp75eWpNxDrgOfdfouMUmdDmGFq90Ngvb4Man3Mdad8aeoCOn22RPv_sEvd3PXm8fi_nzw9PtzbwwjMlcaLC11txxWhEnGtEw0EyUwG1DjSVMl0D5JTjGq6EKa5ry0gpZcaGlpBTYBJ3vc9cxvPc2ZbUMfeyGk4qSqqScSGCD6mqvMjGkFK1TxuevB3PUvlUE1A6s-gGrdmDVN9jBzX-519GvBgD_-q73Pt-5EFd6E2LbqKy3bYguDpR8UuzviE-HkpIa
CitedBy_id crossref_primary_10_1002_rnc_5705
crossref_primary_10_1016_j_amc_2019_124698
crossref_primary_10_1002_asjc_3241
crossref_primary_10_1016_j_automatica_2024_111844
crossref_primary_10_1016_j_chaos_2023_113316
crossref_primary_10_1002_rnc_4632
crossref_primary_10_1016_j_jfranklin_2021_11_028
crossref_primary_10_1177_0142331217752040
crossref_primary_10_1080_00207179_2019_1622788
crossref_primary_10_1016_j_jfranklin_2020_10_027
crossref_primary_10_1080_00207179_2024_2397479
crossref_primary_10_1007_s11071_020_05845_7
crossref_primary_10_1007_s11424_020_9159_z
crossref_primary_10_1007_s10883_019_09461_6
Cites_doi 10.1016/j.sysconle.2011.03.008
10.1093/imamci/dnt034
10.1007/978-1-4612-5561-1
10.1137/0325029
10.1016/j.automatica.2013.06.018
10.1007/s10883-014-9262-3
10.1007/978-0-8176-4877-0
10.1002/rnc.2977
10.1109/TAC.2013.2239003
10.1016/j.automatica.2014.10.117
10.1080/00207179.2011.584197
10.1137/090781140
10.1109/TAC.2014.2335511
10.1137/1.9780898718607
10.1109/TAC.2005.858646
10.1137/0327028
10.1137/130940918
10.1007/978-1-4471-0419-3
10.1007/s10883-014-9241-8
10.1080/00207179.2015.1010179
10.1109/TAC.2012.2218669
10.1016/j.automatica.2010.10.045
10.1016/j.automatica.2007.09.022
10.1007/978-3-7643-8994-9
ContentType Journal Article
Copyright 2016 Informa UK Limited, trading as Taylor & Francis Group 2016
2016 Informa UK Limited, trading as Taylor & Francis Group
Copyright_xml – notice: 2016 Informa UK Limited, trading as Taylor & Francis Group 2016
– notice: 2016 Informa UK Limited, trading as Taylor & Francis Group
DBID AAYXX
CITATION
7SC
7SP
7TB
8FD
FR3
JQ2
L7M
L~C
L~D
DOI 10.1080/00207179.2016.1235286
DatabaseName CrossRef
Computer and Information Systems Abstracts
Electronics & Communications Abstracts
Mechanical & Transportation Engineering Abstracts
Technology Research Database
Engineering Research Database
ProQuest Computer Science Collection
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts – Academic
Computer and Information Systems Abstracts Professional
DatabaseTitle CrossRef
Technology Research Database
Computer and Information Systems Abstracts – Academic
Mechanical & Transportation Engineering Abstracts
Electronics & Communications Abstracts
ProQuest Computer Science Collection
Computer and Information Systems Abstracts
Engineering Research Database
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts Professional
DatabaseTitleList
Technology Research Database
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
EISSN 1366-5820
EndPage 26
ExternalDocumentID 10_1080_00207179_2016_1235286
1235286
Genre Article
GrantInformation_xml – fundername: National Natural Science Foundation of China
  grantid: 61273129
  funderid: 10.13039/501100001809
GroupedDBID -~X
.7F
.QJ
0BK
0R~
29J
2DF
30N
4.4
5GY
5VS
AAENE
AAJMT
AALDU
AAMIU
AAPUL
AAQRR
ABCCY
ABFIM
ABHAV
ABJNI
ABLIJ
ABPAQ
ABPEM
ABTAI
ABXUL
ABXYU
ACBEA
ACGEJ
ACGFO
ACGFS
ACIWK
ACTIO
ADCVX
ADGTB
ADIYS
ADXPE
AEISY
AENEX
AEOZL
AEPSL
AEYOC
AFKVX
AGDLA
AGMYJ
AHDZW
AIJEM
AJWEG
AKBVH
AKOOK
ALMA_UNASSIGNED_HOLDINGS
ALQZU
AQRUH
AVBZW
AWYRJ
BLEHA
CCCUG
CE4
CS3
DGEBU
DKSSO
DU5
EBS
EJD
E~A
E~B
F5P
GTTXZ
H13
HF~
HZ~
H~P
IPNFZ
J.P
KYCEM
LJTGL
M4Z
NA5
NX~
O9-
P2P
RIG
RNANH
ROSJB
RTWRZ
S-T
SNACF
TBQAZ
TDBHL
TEN
TFL
TFT
TFW
TN5
TNC
TTHFI
TUROJ
TWF
UT5
UU3
ZGOLN
~S~
AAGDL
AAHIA
AAYXX
ADYSH
AFRVT
AIYEW
AMPGV
AMVHM
CITATION
7SC
7SP
7TB
8FD
FR3
JQ2
L7M
L~C
L~D
TASJS
ID FETCH-LOGICAL-c338t-a0ebaa5f5291f6d6d30a36705ed2ce13a702540f35940f6ecd74e68956a882203
ISSN 0020-7179
IngestDate Fri Jul 25 06:34:15 EDT 2025
Tue Jul 01 03:39:08 EDT 2025
Thu Apr 24 22:56:59 EDT 2025
Wed Dec 25 09:09:15 EST 2024
IsPeerReviewed true
IsScholarly true
Issue 1
Language English
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-c338t-a0ebaa5f5291f6d6d30a36705ed2ce13a702540f35940f6ecd74e68956a882203
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ORCID 0000-0001-6856-2358
0000-0001-9078-0001
PQID 2197251803
PQPubID 176145
PageCount 15
ParticipantIDs crossref_citationtrail_10_1080_00207179_2016_1235286
crossref_primary_10_1080_00207179_2016_1235286
proquest_journals_2197251803
informaworld_taylorfrancis_310_1080_00207179_2016_1235286
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate 2019-01-02
PublicationDateYYYYMMDD 2019-01-02
PublicationDate_xml – month: 01
  year: 2019
  text: 2019-01-02
  day: 02
PublicationDecade 2010
PublicationPlace Abingdon
PublicationPlace_xml – name: Abingdon
PublicationTitle International journal of control
PublicationYear 2019
Publisher Taylor & Francis
Taylor & Francis Ltd
Publisher_xml – name: Taylor & Francis
– name: Taylor & Francis Ltd
References cit0011
Komornik V. (cit0016) 1990; 69
cit0012
cit0010
cit0019
cit0017
cit0018
cit0015
Müller V. (cit0023) 2007
cit0013
cit0014
cit0022
cit0020
cit0021
cit0008
Engel K.J. (cit0005) 2000
cit0009
Adams R.A. (cit0001) 2003
cit0006
cit0028
cit0007
cit0004
cit0026
cit0027
cit0002
cit0024
cit0003
cit0025
References_xml – ident: cit0011
  doi: 10.1016/j.sysconle.2011.03.008
– ident: cit0021
  doi: 10.1093/imamci/dnt034
– volume-title: Spectral theory of linear operators and spectral systems in Banach algebras
  year: 2007
  ident: cit0023
– ident: cit0024
  doi: 10.1007/978-1-4612-5561-1
– ident: cit0002
  doi: 10.1137/0325029
– ident: cit0007
  doi: 10.1016/j.automatica.2013.06.018
– ident: cit0020
  doi: 10.1007/s10883-014-9262-3
– ident: cit0017
  doi: 10.1007/978-0-8176-4877-0
– ident: cit0009
  doi: 10.1002/rnc.2977
– ident: cit0015
  doi: 10.1109/TAC.2013.2239003
– ident: cit0027
  doi: 10.1016/j.automatica.2014.10.117
– ident: cit0006
  doi: 10.1080/00207179.2011.584197
– ident: cit0025
  doi: 10.1137/090781140
– ident: cit0013
  doi: 10.1109/TAC.2014.2335511
– volume: 69
  start-page: 33
  year: 1990
  ident: cit0016
  publication-title: Journal de Mathématiques Pures et Appliqués,
– ident: cit0018
  doi: 10.1137/1.9780898718607
– ident: cit0019
  doi: 10.1109/TAC.2005.858646
– ident: cit0028
  doi: 10.1137/0327028
– volume-title: One-parameter semigroups for linear evolution equations
  year: 2000
  ident: cit0005
– ident: cit0012
  doi: 10.1137/130940918
– ident: cit0022
  doi: 10.1007/978-1-4471-0419-3
– ident: cit0014
  doi: 10.1007/s10883-014-9241-8
– volume-title: Sobolev spaces
  year: 2003
  ident: cit0001
– ident: cit0010
  doi: 10.1080/00207179.2015.1010179
– ident: cit0008
  doi: 10.1109/TAC.2012.2218669
– ident: cit0003
  doi: 10.1016/j.automatica.2010.10.045
– ident: cit0004
  doi: 10.1016/j.automatica.2007.09.022
– ident: cit0026
  doi: 10.1007/978-3-7643-8994-9
SSID ssj0013581
Score 2.3428283
Snippet In this paper, we consider stabilisation for a cascade of ODE and first-order hyperbolic equation with external disturbance flowing to the control end. The...
SourceID proquest
crossref
informaworld
SourceType Aggregation Database
Enrichment Source
Index Database
Publisher
StartPage 12
SubjectTerms Active control
Active disturbance rejection control
Actuators
Boundary control
boundary feedback control
Closed loop systems
Closed loops
Control theory
Feedback control
Feedback loops
High gain
Sliding mode control
stabilisation
Title Stabilization of ODE with hyperbolic equation actuator subject to boundary control matched disturbance
URI https://www.tandfonline.com/doi/abs/10.1080/00207179.2016.1235286
https://www.proquest.com/docview/2197251803
Volume 92
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1Lb9swDBa29LIdhj2xrt2gw26FAluyHftYtCmCoWsvDhb0Iki2hGAY4i61D-uvLxnJjyzBuu0iBA5oG-JnipTIj4R8hkUBoGA1K6yOGBLKMR0UlmVFYbCSEZwQLE7-epXM5tGXRbz4rbqk1uPifm9dyf9oFa6BXrFK9h80290ULsBv0C-MoGEY_0rH4Clibut95_Zdn0_dzuoSwsu1Rs7fE_PTsXkjbUaDIfbJXaNx9wXdTr3pqrT-1aWsgwMLaizx4AYWI91h4nuf8d5vIA5oJ7x8vw9dNZtVrVHsbGn88oh5Pk3ljjkqdrNshnsOWOYUsqCPUPOd9h-DHCRXIhAwiBOdLTTOsookYXHKg6HpzfgOxJwddanVO-a9zYfkGIVimVGYjLHYl--j0766lhfzy0uZTxf5U3LAIY7gI3JwOju_-dYfNMWpa6ro37gt8kL69X2P2XJftshtdxbzjYeSvyQvfGhBTx1OXpEnZvWaPB8QTr4hdgsxtLIUEEMRMbRHDG0RQ1vEUI8YWle0RQz1GqceMXSAmLdkfjHNz2bMd9pghRBpzVRgtFKxjXkW2qRMShEoZPaLTckLEwo1QdKEwIo4gzExRTmJTJJCbK0gQuOBeEdGq2pl3hOqYpWkpkzBlc0ixa2CyUsFCE2UNnwSHpKonUBZeBp67IbyQ4YdW62bd4nzLv28H5JxJ3breFgeE8iG2pH1BrPWwVWKR2SPW1VK_yXdSY4N-uIwDcSHP_99RJ7138wxGdXrxnwEz7XWnzz6HgDrPZYM
linkProvider Library Specific Holdings
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV07T8MwELagDMDAG1GeHlhT5WUnGREUlVdZQOpm2Y4tJFALbTrAr-cuTkoLQh26ZInOSi7n893lvu8IOYdDAUzBKk9bFXtIKOcpX1sv09ogkhGCEAQnP3R55zm-7bHeFBYG2yoxh7aOKKL01bi5sRhdt8QhhBvTEMSZBLyFaM8w5ctkhWU8wSkGkd_9-ZPAUjc1D9IklKlRPP8tM3M-zbCX_vHW5RF0vUl0_fCu8-S1NS5US3_94nVc7O22yEYVodILZ1LbZMn0d8j6FG_hLrEQomJTrYNw0oGlj1dtiiVd-gJ57VAh2TA1H45GnEoEqUBuT0djhWUfWgyoKsc5DT9p1StPIXIG-8lpDnY3Hio0xj3yfN1-uux41cAGT0OmW3jSN0pKZlmYBZbnPI98iQRxzOShNkEkE8Te-zZiGVy50XkSG55CiiYh0A_9aJ80-oO-OSBUMslTk6cQEWWxDK0EXaQRCCVSmTAJmiSuP5PQFZs5DtV4E8GE9NSpUaAaRaXGJmlNxN4dncc8gWzaBkRR1lGsG3oiojmyx7XBiMozjESIc95YkPrR4QJLn5HVztPDvbi_6d4dkTW4lZV1ofCYNIrh2JxApFSo03IrfANu7gP_
linkToPdf http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LT8MwDI5gSAgOvBGDATlw7dRn1h4R2zRegwOTuEVJmggJtI2tPcCvx27asYEQh116qRy1ruPYrr_PhFzAoQCmYKSjjAwdJJRzpKuMkyilEckIQQiCk-_7rDcIb56jqptwWrZVYg5tLFFE4atxc49TU3XEIYIbsxCEmXisiWBPP2arZI0heTiiONz-94-EKLZD8yBLQpkKxPPXMgvH0wJ56S9nXZxA3W0iq2e3jSevzTyTTfX5g9ZxqZfbIVtlfEovrUHtkhU93CObc6yF-8RAgIottRbASUeGPrQ7FAu69AWy2olEqmGq3y2JOBUIUYHMnk5ziUUfmo2oLIY5TT5o2SlPIW4G60lpClaXTySa4gEZdDtPVz2nHNfgKMhzM0e4WgoRmchPPMNSlgauQHq4SKe-0l4gWoi8d00QJXBlWqWtULMYEjQBYb7vBoekNhwN9RGhIhIs1mkM8VASCt8I0EUcgFBLSO23vDoJq6_EVclljiM13rg3ozy1auSoRl6qsU6aM7GxJfP4TyCZNwGeFVUUY0ee8OAf2UZlL7z0C1Pu45S3yIvd4HiJpc_J-mO7y--u-7cnZAPuJEVRyG-QWjbJ9SmESZk8KzbCFyxYAqM
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=Stabilization+of+ODE+with+hyperbolic+equation+actuator+subject+to+boundary+control+matched+disturbance&rft.jtitle=International+journal+of+control&rft.au=Zhou%2C+Hua-Cheng&rft.au=Guo%2C+Bao-Zhu&rft.date=2019-01-02&rft.pub=Taylor+%26+Francis+Ltd&rft.issn=0020-7179&rft.eissn=1366-5820&rft.volume=92&rft.issue=1&rft.spage=12&rft_id=info:doi/10.1080%2F00207179.2016.1235286&rft.externalDBID=NO_FULL_TEXT
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0020-7179&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0020-7179&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0020-7179&client=summon