{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T12:30:38Z","timestamp":1762432238932,"version":"3.37.3"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2022,8,4]],"date-time":"2022-08-04T00:00:00Z","timestamp":1659571200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,8,4]],"date-time":"2022-08-04T00:00:00Z","timestamp":1659571200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Science Foundation of China","doi-asserted-by":"crossref","award":["61773082"],"award-info":[{"award-number":["61773082"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100010012","name":"National Aerospace Science Foundation of China","doi-asserted-by":"publisher","award":["61673120"],"award-info":[{"award-number":["61673120"]}],"id":[{"id":"10.13039\/501100010012","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Key Natural Science Foundation of Chongqing","award":["cstc2017jcyjBX0018"],"award-info":[{"award-number":["cstc2017jcyjBX0018"]}]},{"DOI":"10.13039\/501100012166","name":"National Key R &D Program of China","doi-asserted-by":"crossref","award":["2018YFB1600502"],"award-info":[{"award-number":["2018YFB1600502"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100012546","name":"Chongqing Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["cstc2021jcyj-bshX0035"],"award-info":[{"award-number":["cstc2021jcyj-bshX0035"]}],"id":[{"id":"10.13039\/100012546","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Key Project of CQUPT","award":["A2018-02"],"award-info":[{"award-number":["A2018-02"]}]},{"name":"Chongqing Basic and Advanced Technology Research Project","award":["cstc2018jcyjA2453"],"award-info":[{"award-number":["cstc2018jcyjA2453"]}]},{"DOI":"10.13039\/501100019085","name":"Key Laboratory of Chongqing Municipal Institutions of Higher Education","doi-asserted-by":"crossref","award":["[2017]3"],"award-info":[{"award-number":["[2017]3"]}],"id":[{"id":"10.13039\/501100019085","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Humanities and Social Sciences Research Program of Chongqing Municipal Education Commission","award":["22SKGH343"],"award-info":[{"award-number":["22SKGH343"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Complex Intell. Syst."],"published-print":{"date-parts":[[2023,2]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper, the complex dynamical networks (CDNs) with dynamic connections are regarded as an interconnected systems composed of intercoupling links\u2019 subsystem (LS) and nodes\u2019 subsystem (NS). Different from the previous researches on structural balance control of CDNs, the directed CDNs\u2019 structural balance problem is solved. Considering the state of links cannot be measured accurately in practice, we can control the nodes\u2019 state and enforce the weights of links to satisfy the conditions of structural balance via effective coupling. To achieve this aim, a coupling strategy between a predetermined matrix of the structural balance and a reference tracking target of NS is established by the correlative control method. Here, the controller in NS is used to track the reference tracking target, and indirectly let LS track the predetermined matrix and reach a structural balance by the effective coupling for directed and undirected networks. Finally, numerical simulations are presented to verify the theoretical results.<\/jats:p>","DOI":"10.1007\/s40747-022-00840-4","type":"journal-article","created":{"date-parts":[[2022,8,4]],"date-time":"2022-08-04T18:02:37Z","timestamp":1659636157000},"page":"881-889","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Distributed tracking control of structural balance for complex dynamical networks based on the coupling targets of nodes and links"],"prefix":"10.1007","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6214-3312","authenticated-orcid":false,"given":"Zilin","family":"Gao","sequence":"first","affiliation":[]},{"given":"Yongfu","family":"Li","sequence":"additional","affiliation":[]},{"given":"Yinhe","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Qingshan","family":"Liu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,8,4]]},"reference":[{"key":"840_CR1","doi-asserted-by":"publisher","first-page":"334","DOI":"10.1016\/j.physa.2016.10.091","volume":"468","author":"F Hassanibesheli","year":"2017","unstructured":"Hassanibesheli F, Hedayatifar L, Gawronski P, Stojkow M, Zuchowska-Skiba D, Krzysztof Kulakowski K (2017) Gain and loss of esteem, direct reciprocity and Heider balance. Phys A 468:334\u2013339","journal-title":"Phys A"},{"issue":"11","key":"840_CR2","doi-asserted-by":"publisher","first-page":"4014","DOI":"10.1109\/TIP.2015.2456432","volume":"24","author":"CLP Chen","year":"2015","unstructured":"Chen CLP, Liu LC, Chen L, Tang YY, Zhou YC (2015) Weighted couple sparse representation with classified regularization for impulse noise removal. IEEE Trans Image Process 24(11):4014\u20134026","journal-title":"IEEE Trans Image Process"},{"issue":"6","key":"840_CR3","doi-asserted-by":"publisher","first-page":"2488","DOI":"10.1109\/TNNLS.2017.2696582","volume":"29","author":"YL Wei","year":"2018","unstructured":"Wei YL, Park JH, Karimi HR, Tian YC, Jung H (2018) Improved stability and stabilization results for stochastic synchronization of continuous-time Semi-Markovian jump neural networks with time-varying delay. IEEE Trans Neural Netw Learn Syst 29(6):2488\u20132501","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"issue":"7","key":"840_CR4","doi-asserted-by":"publisher","first-page":"4745","DOI":"10.1109\/TWC.2016.2545649","volume":"15","author":"HJ Kim","year":"2016","unstructured":"Kim HJ, Lee H, Ahn M, Kong HB, Lee I (2016) Joint subcarrier and power allocation methods in full duplex wireless powered communication networks for OFDM systems. IEEE Trans Wirel Commun 15(7):4745\u20134753","journal-title":"IEEE Trans Wirel Commun"},{"issue":"4","key":"840_CR5","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1007\/s40747-016-0029-1","volume":"2","author":"DN Sotiropoulos","year":"2016","unstructured":"Sotiropoulos DN, Bilanakos C, Giaglis GM (2016) Opinion formation in social networks: a time-variant and non-linear model. Complex Intell Syst 2(4):269\u2013284","journal-title":"Complex Intell Syst"},{"issue":"1","key":"840_CR6","doi-asserted-by":"publisher","first-page":"387","DOI":"10.1109\/TCSI.2020.3031663","volume":"68","author":"CM Wang","year":"2021","unstructured":"Wang CM, Chen XY, Cao JD, Qiu JL, Liu Y, Luo YP (2021) Neural network-based distributed adaptive pre-assigned finite-time consensus of multiple TCP\/AQM networks. IEEE Trans Circuits Syst I-Regul Pap 68(1):387\u2013395","journal-title":"IEEE Trans Circuits Syst I-Regul Pap"},{"issue":"11","key":"840_CR7","doi-asserted-by":"publisher","first-page":"4711","DOI":"10.1109\/TAC.2019.2902731","volume":"64","author":"YQ Wang","year":"2019","unstructured":"Wang YQ (2019) Privacy-preserving average consensus via state decomposition. IEEE Trans Autom Control 64(11):4711\u20134716","journal-title":"IEEE Trans Autom Control"},{"key":"840_CR8","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1002\/mma.7907","volume":"2021","author":"HW Liu","year":"2021","unstructured":"Liu HW, Chen XY, Qiu JL, Zhao F (2021) Finite-time synchronization of complex networks with hybrid-coupled time-varying delay via event-triggered aperiodically intermittent pinning control. Math Meth Appl Sci 2021:1\u201317. https:\/\/doi.org\/10.1002\/mma.7907","journal-title":"Math Meth Appl Sci"},{"key":"840_CR9","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1016\/j.neucom.2019.12.055","volume":"384","author":"YH Wang","year":"2020","unstructured":"Wang YH, Wang WL, Zhang LL (2020) State synchronization of controlled nodes via the dynamics of links for complex dynamical networks. Neurocomputing 384:225\u2013230","journal-title":"Neurocomputing"},{"issue":"11","key":"840_CR10","doi-asserted-by":"publisher","first-page":"2318","DOI":"10.1109\/TSMC.2018.2815560","volume":"49","author":"YJ Liu","year":"2019","unstructured":"Liu YJ, Park JH, Fang F (2019) Global exponential stability of delayed neural networks based on a new integral inequality. IEEE Trans Syst Man Cybern -Syst 49(11):2318\u20132325","journal-title":"IEEE Trans Syst Man Cybern -Syst"},{"issue":"5","key":"840_CR11","doi-asserted-by":"publisher","first-page":"1771","DOI":"10.1073\/pnas.1013213108","volume":"108","author":"SA Marvel","year":"2011","unstructured":"Marvel SA, Kleinberg J, Kleinberg RD, Strogatz SH (2011) Continuous-time model of structural balance. Proc Natl Acad Sci U S A 108(5):1771\u20131776","journal-title":"Proc Natl Acad Sci U S A"},{"key":"840_CR12","doi-asserted-by":"publisher","first-page":"3325","DOI":"10.1140\/epjst\/e2015-50087-9","volume":"224","author":"S Wongkaew","year":"2015","unstructured":"Wongkaew S, Caponigro M, Kulakowski K, Borzi A (2015) On the control of the Heider balance model. Eur Phys J-Spec Top 224:3325\u20133342","journal-title":"Eur Phys J-Spec Top"},{"issue":"1","key":"840_CR13","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0191941","volume":"13","author":"ZL Gao","year":"2018","unstructured":"Gao ZL, Wang YH (2018) The structural balance analysis of complex dynamical networks based on nodes\u2019 dynamical couplings. PLoS ONE 13(1):e0191941","journal-title":"PLoS ONE"},{"issue":"1","key":"840_CR14","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1080\/00223980.1946.9917275","volume":"21","author":"F Heider","year":"1946","unstructured":"Heider F (1946) Attitudes and cognitive organization. J Psychol 21(1):107\u2013112","journal-title":"J Psychol"},{"issue":"5","key":"840_CR15","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1037\/h0046049","volume":"63","author":"D Cartwright","year":"1956","unstructured":"Cartwright D, Harary F (1956) Structural balance: a generalization of Heider\u2019s theory. Psychol Rev 63(5):277\u2013293","journal-title":"Psychol Rev"},{"issue":"1\u20132","key":"840_CR16","doi-asserted-by":"publisher","first-page":"130","DOI":"10.1016\/j.physd.2006.09.028","volume":"224","author":"T Antal","year":"2006","unstructured":"Antal T, Krapivsky PL, Redner S (2006) Social balance on networks: the dynamics of friendship and enmity. Phys D 224(1\u20132):130\u2013136","journal-title":"Phys D"},{"issue":"3","key":"840_CR17","doi-asserted-by":"publisher","first-page":"565","DOI":"10.1142\/S0218202515400060","volume":"25","author":"S Wongkaew","year":"2015","unstructured":"Wongkaew S, Caponigro M, Borzi A (2015) On the control through leadership of the Hegselmann-Krause opinion formation model. Math Models Meth Appl Sci 25(3):565\u2013585","journal-title":"Math Models Meth Appl Sci"},{"issue":"7","key":"840_CR18","doi-asserted-by":"publisher","first-page":"3169","DOI":"10.1109\/TAC.2020.3018435","volume":"66","author":"PA Cisneros-Velarde","year":"2021","unstructured":"Cisneros-Velarde PA, Friedkin NE, Proskurnikov AV, Bullo F (2021) Structural balance via gradient flows over signed graphs. IEEE Trans Autom Control 66(7):3169\u20133183","journal-title":"IEEE Trans Autom Control"},{"key":"840_CR19","doi-asserted-by":"publisher","first-page":"717","DOI":"10.1007\/s41980-019-00286-4","volume":"46","author":"YL Shang","year":"2020","unstructured":"Shang YL (2020) On the structural balance dynamics under perceived sentiment. Bull Iran Math Soc 46:717\u2013724","journal-title":"Bull Iran Math Soc"},{"key":"840_CR20","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2019.108580","volume":"110","author":"WJ Mei","year":"2019","unstructured":"Mei WJ, Cisneros-Velarde P, Chen G, Friedkin NE, Bullo F (2019) Dynamic social balance and convergent appraisals via homophily and influence mechanisms. Automatica 110:108580","journal-title":"Automatica"},{"issue":"3","key":"840_CR21","doi-asserted-by":"publisher","first-page":"725","DOI":"10.1007\/s11424-020-8093-4","volume":"33","author":"ZL Gao","year":"2020","unstructured":"Gao ZL, Wang YH, Peng Y, Liu LZ, Chen HG (2020) Adaptive control of the structural balance for a class of complex dynamical networks. J Syst Sci Complex 33(3):725\u2013742","journal-title":"J Syst Sci Complex"},{"issue":"24","key":"840_CR22","doi-asserted-by":"publisher","first-page":"1850267","DOI":"10.1142\/S0217979218502673","volume":"32","author":"ZL Gao","year":"2018","unstructured":"Gao ZL, Wang YH, Zhang LL, Huang YY, Wang WL (2018) The dynamic behaviors of nodes driving the structural balance for complex dynamical networks via adaptive decentralized control. Int J Mod Phys B 32(24):1850267","journal-title":"Int J Mod Phys B"},{"issue":"10","key":"840_CR23","doi-asserted-by":"publisher","first-page":"2050352","DOI":"10.1142\/S0217984920503522","volume":"34","author":"LZ Liu","year":"2020","unstructured":"Liu LZ, Wang YH, Chen HG, Gao ZL (2020) Structural balance for discrete-time complex dynamical network associated with the controlled nodes. Mod Phys Lett B 34(10):2050352","journal-title":"Mod Phys Lett B"},{"issue":"8","key":"840_CR24","doi-asserted-by":"publisher","first-page":"1153","DOI":"10.1016\/S0005-1098(00)00025-X","volume":"36","author":"P Tsiotras","year":"2000","unstructured":"Tsiotras P, Luo JH (2000) Control of underactuated spacecraft with bounded inputs. Automatica 36(8):1153\u20131169","journal-title":"Automatica"},{"issue":"2","key":"840_CR25","doi-asserted-by":"publisher","first-page":"272","DOI":"10.1080\/00207721.2016.1179816","volume":"48","author":"TT Gao","year":"2017","unstructured":"Gao TT, Huang JS, Zhou Y, Song YD (2017) Robust adaptive tracking control of an underactuated ship with guaranteed transient performance. Int J Syst Sci 48(2):272\u2013279","journal-title":"Int J Syst Sci"},{"issue":"10","key":"840_CR26","doi-asserted-by":"publisher","first-page":"3471","DOI":"10.1109\/TAC.2018.2794885","volume":"63","author":"B Lu","year":"2018","unstructured":"Lu B, Fang YC, Sun N (2018) Continuous sliding mode control strategy for a class of nonlinear underactuated systems. IEEE Trans Autom Control 63(10):3471\u20133478","journal-title":"IEEE Trans Autom Control"},{"issue":"2","key":"840_CR27","first-page":"79","volume":"58","author":"M Stulrajter","year":"2007","unstructured":"Stulrajter M, Hrabovcova V, Franko M (2007) Permanent magnets synchronous motor control theory. J Electr Eng 58(2):79\u201384","journal-title":"J Electr Eng"},{"issue":"11","key":"840_CR28","doi-asserted-by":"publisher","first-page":"5222","DOI":"10.1109\/TNNLS.2020.3027312","volume":"32","author":"X Zhang","year":"2021","unstructured":"Zhang X, Zhou WN, Karimi HR, Sun YQ (2021) Finite- and fixed-time cluster synchronization of nonlinearly coupled delayed neural networks via pinning control. IEEE Trans Neural Netw Learn Syst 32(11):5222\u20135231","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"840_CR29","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2021.110805","volume":"145","author":"L Shi","year":"2021","unstructured":"Shi L, Zhang CM, Zhong SM (2021) Synchronization of singular complex networks with time-varying delay via pinning control and linear feedback control. Chaos, Solitons Fractals 145:110805","journal-title":"Chaos, Solitons Fractals"},{"key":"840_CR30","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2019.104981","volume":"80","author":"Y Pei","year":"2019","unstructured":"Pei Y, Bohner M, Pi DC (2019) Impulsive synchronization of time-scales complex networks with time-varying topology. Commun Nonlinear Sci Numer Simulat 80:104981","journal-title":"Commun Nonlinear Sci Numer Simulat"},{"key":"840_CR31","first-page":"510","volume":"259","author":"LL Zhang","year":"2015","unstructured":"Zhang LL, Wang YH, Huang YY, Chen XS (2015) Delay-dependent synchronization for non-diffusively coupled time-varying complex dynamical networks. Appl Math Comput 259:510\u2013522","journal-title":"Appl Math Comput"},{"issue":"4","key":"840_CR32","doi-asserted-by":"publisher","first-page":"2969","DOI":"10.1007\/s11071-017-3425-1","volume":"88","author":"YH Xu","year":"2017","unstructured":"Xu YH, Zhou WN, Zhang JC, Sun W, Tong DB (2017) Topology identification of complex delayed dynamical networks with multiple response systems. Nonlinear Dyn 88(4):2969\u20132981","journal-title":"Nonlinear Dyn"},{"issue":"4","key":"840_CR33","doi-asserted-by":"publisher","first-page":"935","DOI":"10.1109\/TAC.2012.2224251","volume":"58","author":"C Altafini","year":"2013","unstructured":"Altafini C (2013) Consensus problems on networks with antagonistic interactions. IEEE Trans Autom Control 58(4):935\u2013946","journal-title":"IEEE Trans Autom Control"},{"key":"840_CR34","first-page":"46","volume":"194","author":"D Bahuguna","year":"2007","unstructured":"Bahuguna D, Ujlayan A, Pandey DN (2007) Advanced type coupled matrix Riccati differential equation systems with Kronecker product. Appl Math Comput 194:46\u201353","journal-title":"Appl Math Comput"},{"issue":"1","key":"840_CR35","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1109\/TCST.2006.883345","volume":"15","author":"PR Pagilla","year":"2006","unstructured":"Pagilla PR, Siraskar NB, Dwivedula RV (2006) Decentralized control of web processing lines. IEEE Trans Control Syst Technol 15(1):106\u2013117","journal-title":"IEEE Trans Control Syst Technol"},{"issue":"4","key":"840_CR36","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1049\/iet-cta.2008.0118","volume":"3","author":"NR Abjadi","year":"2009","unstructured":"Abjadi NR, Soltani J, Askari J, Markadeh GRA (2009) Nonlinear sliding-mode control of a multi-motor web-winding system without tension control. IET Contr Theory Appl 3(4):419\u2013427","journal-title":"IET Contr Theory Appl"},{"issue":"5","key":"840_CR37","doi-asserted-by":"publisher","first-page":"1001","DOI":"10.1142\/S0218127402004851","volume":"12","author":"JH Lv","year":"2002","unstructured":"Lv JH, Chen GR, Zhang SC (2002) Dynamical analysis of a new chaotic attractor. Int. J. Bifurcation Chaos 12(5):1001\u20131015","journal-title":"Int. J. Bifurcation Chaos"},{"issue":"19","key":"840_CR38","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.103.198701","volume":"103","author":"SA Marvel","year":"2009","unstructured":"Marvel SA, Strogatz SH, Kleinberg JM (2009) Energy landscape of social balance. Phys Rev Lett 103(19):198701","journal-title":"Phys Rev Lett"}],"container-title":["Complex &amp; Intelligent Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-022-00840-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40747-022-00840-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-022-00840-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,22]],"date-time":"2023-02-22T18:02:42Z","timestamp":1677088962000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40747-022-00840-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,4]]},"references-count":38,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,2]]}},"alternative-id":["840"],"URL":"https:\/\/doi.org\/10.1007\/s40747-022-00840-4","relation":{},"ISSN":["2199-4536","2198-6053"],"issn-type":[{"type":"print","value":"2199-4536"},{"type":"electronic","value":"2198-6053"}],"subject":[],"published":{"date-parts":[[2022,8,4]]},"assertion":[{"value":"27 February 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 July 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 August 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The work described has not been submitted elsewhere for publication, in whole or in part, and all the authors listed have approved the manuscript that is enclosed. Moreover, the authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflicts of interest"}}]}}