Exponential Finite-Time Consensus of Fractional-Order Multiagent Systems

The application of the fast sliding-mode control technique on solving consensus problems of fractional-order multiagent systems is investigated. The design and analysis are based on a combination of the distributed coordination theory and the knowledge of fractional-order dynamics. First, a sliding-...

Full description

Saved in:
Bibliographic Details
Published inIEEE transactions on systems, man, and cybernetics. Systems Vol. 50; no. 4; pp. 1549 - 1558
Main Authors Liu, Huiyang, Cheng, Long, Tan, Min, Hou, Zeng-Guang
Format Journal Article
LanguageEnglish
Published New York IEEE 01.04.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Algorithms
Convergence
Directed network topology
exponential finite-time consensus
fast sliding-mode algorithms
fractional-order dynamics
Graph theory
Heuristic algorithms
Liapunov functions
Lyapunov methods
Manifolds
Multi-agent systems
Multiagent systems
Protocols
Sliding mode control
Online AccessGet full text

Cover

Abstract The application of the fast sliding-mode control technique on solving consensus problems of fractional-order multiagent systems is investigated. The design and analysis are based on a combination of the distributed coordination theory and the knowledge of fractional-order dynamics. First, a sliding-mode manifold (surface) vector is defined, and then the fractional-order multiagent system is transformed into an integer-order (namely, first-order) multiagent system. Second, based on the fast sliding-mode control technique, a protocol is proposed for the obtained first-order multiagent system. Third, a new Lyapunov function is presented. By suitably estimating the derivative of the Lyapunov function, the reachability of the sliding-mode manifold is derived. It is proved that the exponential finite-time consensus can be achieved if the communication network has a directed spanning tree. Finally, the effectiveness of the proposed algorithms is demonstrated by some examples.
AbstractList The application of the fast sliding-mode control technique on solving consensus problems of fractional-order multiagent systems is investigated. The design and analysis are based on a combination of the distributed coordination theory and the knowledge of fractional-order dynamics. First, a sliding-mode manifold (surface) vector is defined, and then the fractional-order multiagent system is transformed into an integer-order (namely, first-order) multiagent system. Second, based on the fast sliding-mode control technique, a protocol is proposed for the obtained first-order multiagent system. Third, a new Lyapunov function is presented. By suitably estimating the derivative of the Lyapunov function, the reachability of the sliding-mode manifold is derived. It is proved that the exponential finite-time consensus can be achieved if the communication network has a directed spanning tree. Finally, the effectiveness of the proposed algorithms is demonstrated by some examples.
Author Cheng, Long
Liu, Huiyang
Hou, Zeng-Guang
Tan, Min
Author_xml – sequence: 1
  givenname: Huiyang
  orcidid: 0000-0003-1827-7684
  surname: Liu
  fullname: Liu, Huiyang
  organization: School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, China
– sequence: 2
  givenname: Long
  orcidid: 0000-0001-7565-8788
  surname: Cheng
  fullname: Cheng, Long
  email: long.cheng@ia.ac.cn
  organization: State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China
– sequence: 3
  givenname: Min
  surname: Tan
  fullname: Tan, Min
  organization: State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China
– sequence: 4
  givenname: Zeng-Guang
  orcidid: 0000-0002-1534-5840
  surname: Hou
  fullname: Hou, Zeng-Guang
  organization: State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China
BookMark eNp9kE9rAjEQxUOxUGv9AKWXhZ7X5s8ak2NZtBYUD9pzyMbZElmzNslC_fbNovTQQ08zMO_3Zubdo4FrHSD0SPCEECxfdtt1OaGYiAkVhGOOb9CQEi5yShkd_PaE36FxCAeMMaGCM8yHaDn_PiUzF61usoV1NkK-s0fIytYFcKELWVtnC69NtK3TTb7xe_DZumsS8Zm4bHsOEY7hAd3WugkwvtYR-ljMd-UyX23e3svXVW6oZDEXAMaItFrsi4pLPjOUFYaTSjAghNVmX2vQQDUzQmPNJYNpleZSV1RTU7MRer74nnz71UGI6tB2Pl0WFGUzyaaEFTKpZheV8W0IHmplbNT9C9Fr2yiCVZ-c6pNTfXLqmlwiyR_y5O1R-_O_zNOFsQDwqxdsymnB2Q_tQ3vj
CODEN ITSMFE
CitedBy_id crossref_primary_10_1002_asjc_3012
crossref_primary_10_1631_FITEE_2100565
crossref_primary_10_1016_j_amc_2025_129357
crossref_primary_10_1109_TSMC_2019_2933570
crossref_primary_10_1109_TCSI_2022_3177407
crossref_primary_10_1109_TSMC_2021_3129794
crossref_primary_10_1109_TSMC_2022_3205654
crossref_primary_10_1109_ACCESS_2020_3048178
crossref_primary_10_1109_TSMC_2022_3220650
crossref_primary_10_1038_s41598_022_12634_2
crossref_primary_10_1007_s12555_020_0685_1
crossref_primary_10_1109_TSMC_2020_3037030
crossref_primary_10_1007_s12555_020_0283_2
crossref_primary_10_1016_j_isatra_2021_07_022
crossref_primary_10_1007_s00034_023_02372_9
crossref_primary_10_1109_TNSE_2022_3217618
crossref_primary_10_1109_ACCESS_2019_2926526
crossref_primary_10_3390_e25020299
crossref_primary_10_1109_TSMC_2019_2896614
crossref_primary_10_1109_TSMC_2023_3282267
crossref_primary_10_1007_s12555_020_0760_7
crossref_primary_10_1016_j_isatra_2023_03_010
crossref_primary_10_1080_00207721_2020_1772404
crossref_primary_10_1109_TCYB_2022_3208124
crossref_primary_10_1109_TSMC_2018_2867900
crossref_primary_10_1016_j_ins_2023_119092
crossref_primary_10_1177_01423312241232354
crossref_primary_10_1109_ACCESS_2020_2971337
crossref_primary_10_1080_03081079_2022_2132488
crossref_primary_10_3390_act14010038
crossref_primary_10_1080_00207721_2019_1645913
crossref_primary_10_1016_j_chaos_2022_111943
crossref_primary_10_1109_TASE_2023_3261891
crossref_primary_10_3390_electronics11071117
crossref_primary_10_1109_TSMC_2020_2987335
crossref_primary_10_1109_TSMC_2019_2931411
crossref_primary_10_1007_s11071_024_10200_1
crossref_primary_10_1007_s12555_021_0009_0
crossref_primary_10_3390_electronics11050726
crossref_primary_10_1007_s10483_021_2789_6
crossref_primary_10_1016_j_fraope_2023_100028
crossref_primary_10_1109_TSMC_2022_3228798
crossref_primary_10_1109_TAC_2021_3079208
crossref_primary_10_3390_fractalfract6120698
crossref_primary_10_1109_TCSII_2021_3053624
crossref_primary_10_1109_TSMC_2024_3514697
crossref_primary_10_1109_TSMC_2021_3120432
crossref_primary_10_1109_TSMC_2023_3257186
crossref_primary_10_1177_01423312241291089
crossref_primary_10_1515_jncds_2023_0073
crossref_primary_10_1016_j_istruc_2023_06_117
crossref_primary_10_1177_09596518221118125
crossref_primary_10_1109_TSMC_2019_2938419
crossref_primary_10_1137_19M1282970
crossref_primary_10_1063_5_0032932
crossref_primary_10_1109_TSMC_2022_3195293
crossref_primary_10_1109_TSMC_2019_2895027
crossref_primary_10_1080_00207721_2020_1780515
crossref_primary_10_1109_TCSII_2019_2947353
crossref_primary_10_1109_TSMC_2022_3206874
crossref_primary_10_1016_j_neucom_2020_02_036
crossref_primary_10_1049_iet_cta_2019_1241
crossref_primary_10_1109_TSMC_2020_3010221
crossref_primary_10_3390_act12090364
crossref_primary_10_1109_ACCESS_2024_3392578
crossref_primary_10_3390_machines10050383
crossref_primary_10_1109_TSMC_2023_3253511
crossref_primary_10_1007_s10846_022_01698_x
crossref_primary_10_1109_TCYB_2021_3123697
Cites_doi 10.1016/j.automatica.2006.06.015
10.1109/TCYB.2015.2494738
10.1016/j.automatica.2013.02.024
10.1016/j.automatica.2011.06.020
10.1109/ACCESS.2017.2723462
10.1080/00207179.2014.944872
10.1016/j.automatica.2009.07.012
10.1080/00207170802123895
10.1177/1077546306070608
10.1080/00029890.1949.11990209
10.1051/proc:1998006
10.3390/app7070713
10.1109/TAC.2011.2146830
10.1016/j.automatica.2011.03.014
10.1109/TAC.2005.864190
10.1016/j.sysconle.2010.01.008
10.1109/81.983876
10.1002/rnc.1565
10.1109/TSMC.2016.2564929
10.1109/TNNLS.2015.2424225
10.1109/TSMC.2016.2577578
10.1109/TAC.2010.2041610
10.1016/j.automatica.2011.02.045
10.1017/CBO9780511608704
10.1007/978-0-85729-169-1
10.1155/2017/3465076
10.1109/TAC.2013.2270873
10.1080/00207721.2010.517857
10.1016/j.automatica.2011.05.013
10.1109/TAC.2012.2208295
10.1109/TSMC.2017.2660883
10.1109/TAC.2016.2522647
10.1109/TNN.2010.2050601
10.1016/j.sysconle.2012.01.012
10.1016/j.automatica.2015.11.005
10.1109/TMECH.2009.2014057
10.1109/TAC.2005.846556
10.1109/TAC.2016.2560145
10.1016/j.sysconle.2011.05.009
10.1016/j.neucom.2016.11.052
10.1109/TSMC.2017.2677471
10.1109/TSMC.2016.2631659
10.1109/JPROC.2006.887293
10.1109/TAC.2010.2086550
ContentType Journal Article
Copyright Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2020
Copyright_xml – notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2020
DBID 97E
RIA
RIE
AAYXX
CITATION
7SC
7SP
7TB
8FD
FR3
H8D
JQ2
L7M
L~C
L~D
DOI 10.1109/TSMC.2018.2816060
DatabaseName IEEE Xplore (IEEE)
IEEE All-Society Periodicals Package (ASPP) 1998–Present
IEEE Electronic Library (IEL)
CrossRef
Computer and Information Systems Abstracts
Electronics & Communications Abstracts
Mechanical & Transportation Engineering Abstracts
Technology Research Database
Engineering Research Database
Aerospace Database
ProQuest Computer Science Collection
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts – Academic
Computer and Information Systems Abstracts Professional
DatabaseTitle CrossRef
Aerospace Database
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 Aerospace Database
Database_xml – sequence: 1
  dbid: RIE
  name: IEEE Electronic Library (IEL)
  url: https://proxy.k.utb.cz/login?url=https://ieeexplore.ieee.org/
  sourceTypes: Publisher
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
EISSN 2168-2232
EndPage 1558
ExternalDocumentID 10_1109_TSMC_2018_2816060
8356246
Genre orig-research
GrantInformation_xml – fundername: National Natural Science Foundation of China
  grantid: 61633016; 61304170; 61421004; 61720106012
  funderid: 10.13039/501100001809
– fundername: Natural Science Foundation of Beijing Municipality
  grantid: 4162066
  funderid: 10.13039/501100004826
– fundername: Fundamental Research Funds for the Central Universities
  grantid: FRF-TP-17-022A2
  funderid: 10.13039/501100012226
GroupedDBID 0R~
6IK
97E
AAJGR
AARMG
AASAJ
AAWTH
ABAZT
ABQJQ
ABVLG
ACGFS
ACIWK
AGQYO
AGSQL
AHBIQ
AKJIK
AKQYR
ALMA_UNASSIGNED_HOLDINGS
BEFXN
BFFAM
BGNUA
BKEBE
BPEOZ
EBS
EJD
HZ~
IFIPE
IPLJI
JAVBF
M43
O9-
OCL
PQQKQ
RIA
RIE
RNS
AAYXX
CITATION
RIG
7SC
7SP
7TB
8FD
FR3
H8D
JQ2
L7M
L~C
L~D
ID FETCH-LOGICAL-c293t-8eecc83068d4b6967c234c61b83e113fcdfaeae2a3c8a0a693e5bc619ab2a2cf3
IEDL.DBID RIE
ISSN 2168-2216
IngestDate Mon Jun 30 03:19:23 EDT 2025
Thu Apr 24 23:04:47 EDT 2025
Tue Jul 01 02:29:08 EDT 2025
Wed Aug 27 02:36:27 EDT 2025
IsPeerReviewed true
IsScholarly true
Issue 4
Language English
License https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html
https://doi.org/10.15223/policy-029
https://doi.org/10.15223/policy-037
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c293t-8eecc83068d4b6967c234c61b83e113fcdfaeae2a3c8a0a693e5bc619ab2a2cf3
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ORCID 0000-0003-1827-7684
0000-0001-7565-8788
0000-0002-1534-5840
PQID 2379351349
PQPubID 75739
PageCount 10
ParticipantIDs crossref_citationtrail_10_1109_TSMC_2018_2816060
proquest_journals_2379351349
ieee_primary_8356246
crossref_primary_10_1109_TSMC_2018_2816060
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate 2020-04-01
PublicationDateYYYYMMDD 2020-04-01
PublicationDate_xml – month: 04
  year: 2020
  text: 2020-04-01
  day: 01
PublicationDecade 2020
PublicationPlace New York
PublicationPlace_xml – name: New York
PublicationTitle IEEE transactions on systems, man, and cybernetics. Systems
PublicationTitleAbbrev TSMC
PublicationYear 2020
Publisher IEEE
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher_xml – name: IEEE
– name: The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
References ref13
ref12
ref15
ref14
ref11
ref10
ref17
ref19
ref18
podlubny (ref45) 1999
ref50
ref46
clarke (ref48) 1998
ref47
cao (ref31) 2012; 57
ref42
ref43
ref49
ren (ref16) 2011
ref8
ref7
ref9
ref4
ref3
ref6
ref5
ref40
ref35
ref34
ref37
ref36
ref30
ref32
cao (ref23) 2011
ref2
ref1
ref39
ref38
xue (ref33) 2002
ref24
ref26
ref25
ref20
ref22
ref21
ref28
ref27
ref29
hartman (ref44) 1982
horn (ref41) 1987
References_xml – ident: ref17
  doi: 10.1016/j.automatica.2006.06.015
– ident: ref6
  doi: 10.1109/TCYB.2015.2494738
– ident: ref2
  doi: 10.1016/j.automatica.2013.02.024
– ident: ref10
  doi: 10.1016/j.automatica.2011.06.020
– ident: ref50
  doi: 10.1109/ACCESS.2017.2723462
– ident: ref29
  doi: 10.1080/00207179.2014.944872
– ident: ref22
  doi: 10.1016/j.automatica.2009.07.012
– year: 1999
  ident: ref45
  publication-title: Fractional Differential Equations
– ident: ref42
  doi: 10.1080/00207170802123895
– ident: ref34
  doi: 10.1177/1077546306070608
– ident: ref43
  doi: 10.1080/00029890.1949.11990209
– year: 1982
  ident: ref44
  publication-title: Ordinary Differential Equations
– start-page: 4020
  year: 2011
  ident: ref23
  article-title: Finite-time consensus of multi-agent networks with inherent nonlinear dynamics under an undirected interaction graph
  publication-title: Proc Amer Control Conf
– ident: ref35
  doi: 10.1051/proc:1998006
– start-page: 3228
  year: 2002
  ident: ref33
  article-title: A comparative introduction of four fractional order controllers
  publication-title: Proc 4th World Congr Intell Control Autom
– ident: ref14
  doi: 10.3390/app7070713
– volume: 57
  start-page: 33
  year: 2012
  ident: ref31
  article-title: Distributed coordinated tracking with reduced interaction via a variable structure approach
  publication-title: IEEE Trans Autom Control
  doi: 10.1109/TAC.2011.2146830
– ident: ref5
  doi: 10.1016/j.automatica.2011.03.014
– ident: ref4
  doi: 10.1109/TAC.2005.864190
– ident: ref36
  doi: 10.1016/j.sysconle.2010.01.008
– ident: ref39
  doi: 10.1109/81.983876
– ident: ref46
  doi: 10.1002/rnc.1565
– ident: ref7
  doi: 10.1109/TSMC.2016.2564929
– year: 1998
  ident: ref48
  publication-title: Nonsmooth Analysis and Control Theory
– ident: ref27
  doi: 10.1109/TNNLS.2015.2424225
– year: 1987
  ident: ref41
  publication-title: Matrix Analysis
– ident: ref3
  doi: 10.1109/TSMC.2016.2577578
– ident: ref20
  doi: 10.1109/TAC.2010.2041610
– ident: ref24
  doi: 10.1016/j.automatica.2011.02.045
– ident: ref40
  doi: 10.1017/CBO9780511608704
– year: 2011
  ident: ref16
  publication-title: Distributed Coordination of Multi-agent Networks Emergent Problems Models and Issues
  doi: 10.1007/978-0-85729-169-1
– ident: ref49
  doi: 10.1155/2017/3465076
– ident: ref12
  doi: 10.1109/TAC.2013.2270873
– ident: ref25
  doi: 10.1080/00207721.2010.517857
– ident: ref18
  doi: 10.1016/j.automatica.2011.05.013
– ident: ref32
  doi: 10.1109/TAC.2012.2208295
– ident: ref8
  doi: 10.1109/TSMC.2017.2660883
– ident: ref13
  doi: 10.1109/TAC.2016.2522647
– ident: ref9
  doi: 10.1109/TNN.2010.2050601
– ident: ref47
  doi: 10.1016/j.sysconle.2012.01.012
– ident: ref26
  doi: 10.1016/j.automatica.2015.11.005
– ident: ref30
  doi: 10.1109/TMECH.2009.2014057
– ident: ref1
  doi: 10.1109/TAC.2005.846556
– ident: ref38
  doi: 10.1109/TAC.2016.2560145
– ident: ref21
  doi: 10.1016/j.sysconle.2011.05.009
– ident: ref37
  doi: 10.1016/j.neucom.2016.11.052
– ident: ref11
  doi: 10.1109/TSMC.2017.2677471
– ident: ref28
  doi: 10.1109/TSMC.2016.2631659
– ident: ref15
  doi: 10.1109/JPROC.2006.887293
– ident: ref19
  doi: 10.1109/TAC.2010.2086550
SSID ssj0001286306
Score 2.4978201
Snippet The application of the fast sliding-mode control technique on solving consensus problems of fractional-order multiagent systems is investigated. The design and...
SourceID proquest
crossref
ieee
SourceType Aggregation Database
Enrichment Source
Index Database
Publisher
StartPage 1549
SubjectTerms Algorithms
Convergence
Directed network topology
exponential finite-time consensus
fast sliding-mode algorithms
fractional-order dynamics
Graph theory
Heuristic algorithms
Liapunov functions
Lyapunov methods
Manifolds
Multi-agent systems
Multiagent systems
Protocols
Sliding mode control
Title Exponential Finite-Time Consensus of Fractional-Order Multiagent Systems
URI https://ieeexplore.ieee.org/document/8356246
https://www.proquest.com/docview/2379351349
Volume 50
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV3dS8MwED_mnvTBrylOp_TBJ7Fdm7RZ8yhjYwjTBzfYW0nSBMSxja0D8a83l3ZjfiC-lEIvcNyluV-Su98B3EbCYn4eGp8rwvw4yTu-1Cz2U60TTQ1R0p13DJ_YYBw_TpJJDe63tTBaa5d8pgN8dXf5-Vyt8aisbdECIzHbgz27cStrtXbOU1JGXStNEjHrfPusLjGjkLdHL8Mu5nGlAUkji9nDL2HI9VX5sRi7CNM_guFGtzKx5C1YFzJQH99oG_-r_DEcVlDTeyjnxgnU9OwUDnYICBsw6L0v5jNMGLKC_VfEnz4WhXjYxxObYKy8ufH6y7L6QUz9Z2Tq9FzVrsCiLK9iPD-Dcb836g78qreCr2yAL9AXSqXWYGkeS8ZZRxEaKxbJlOoookblRmihiaAqFaFgnOpE2u9cSCKIMvQc6jOr4AV4koaac214R-ZxbmGwYRZziNwwjmyBcRPCjakzVRGPY_-LaeY2ICHP0DsZeiervNOEu-2QRcm68ZdwA629FawM3YTWxp9Z9V-uMkLtepQgJePl76OuYJ_gjtrl5rSgXizX-trCjkLeuPn2CTNm09M
linkProvider IEEE
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV1LT8MwDLZ4HIADb8R49sAJ0dEmbdYc0bRqPDoObNJuVZImEgJtaA8J8euJ024aDyEuVaU6kmWn8ZfE_gxwEQqL-XlgfK4I86O4aPhSs8hPtI41NURJd96RdVi7F9314_4SXM1rYbTWLvlM1_HV3eUXQzXFo7JrixYYidgyrNq4H4dltdbCiUrCqGumSUJm3W-f1TVmGPDr7lPWxEyupE6S0KL24Esgcp1VfizHLsakW5DNtCtTS17q04msq49vxI3_VX8bNiuw6d2Us2MHlvRgFzYWKAj3oN16fxsOMGXICqbPiEB9LAvxsJMntsEYe0PjpaOy_kG8-o_I1em5ul2BZVlexXm-D7201W22_aq7gq9siJ-gN5RKrMGSIpKMs4YiNFIslAnVYUiNKozQQhNBVSICwTjVsbTfuZBEEGXoAawMrIKH4EkaaM614Q1ZRIUFwoZZ1CEKwzjyBUY1CGamzlVFPY4dMF5ztwUJeI7eydE7eeWdGlzOh7yVvBt_Ce-hteeClaFrcDLzZ179meOcULsixUjKePT7qHNYa3ezh_zhtnN_DOsE99cuU-cEViajqT61IGQiz9zc-wRrMdcc
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=Exponential+Finite-Time+Consensus+of+Fractional-Order+Multiagent+Systems&rft.jtitle=IEEE+transactions+on+systems%2C+man%2C+and+cybernetics.+Systems&rft.au=Liu%2C+Huiyang&rft.au=Cheng%2C+Long&rft.au=Tan%2C+Min&rft.au=Hou%2C+Zeng-Guang&rft.date=2020-04-01&rft.issn=2168-2216&rft.eissn=2168-2232&rft.volume=50&rft.issue=4&rft.spage=1549&rft.epage=1558&rft_id=info:doi/10.1109%2FTSMC.2018.2816060&rft.externalDBID=n%2Fa&rft.externalDocID=10_1109_TSMC_2018_2816060
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2168-2216&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2168-2216&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2168-2216&client=summon