{"id":"https://openalex.org/W3160644820","doi":"https://doi.org/10.3390/sym13060920","title":"Leader-Following Regional Multiple-Bipartite Consensus for Networked Lagrangian Systems with Coopetition Interactions","display_name":"Leader-Following Regional Multiple-Bipartite Consensus for Networked Lagrangian Systems with Coopetition Interactions","publication_year":2021,"publication_date":"2021-05-21","ids":{"openalex":"https://openalex.org/W3160644820","doi":"https://doi.org/10.3390/sym13060920","mag":"3160644820"},"language":"en","primary_location":{"id":"doi:10.3390/sym13060920","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13060920","pdf_url":"https://www.mdpi.com/2073-8994/13/6/920/pdf?version=1621580814","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/13/6/920/pdf?version=1621580814","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042618615","display_name":"Tiehui Zhang","orcid":"https://orcid.org/0000-0003-1282-4974"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]},{"id":"https://openalex.org/I4210127530","display_name":"Jining University","ror":"https://ror.org/037rvh518","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210127530"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tiehui Zhang","raw_affiliation_strings":["College of Elementary Education, Jining University, Jining 273155, China","School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200444, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Elementary Education, Jining University, Jining 273155, China","institution_ids":["https://openalex.org/I4210127530"]},{"raw_affiliation_string":"School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200444, China","institution_ids":["https://openalex.org/I113940042"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100780078","display_name":"Hengyu Li","orcid":"https://orcid.org/0000-0002-2243-5908"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hengyu Li","raw_affiliation_strings":["School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200444, China"],"raw_orcid":"https://orcid.org/0000-0002-2243-5908","affiliations":[{"raw_affiliation_string":"School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200444, China","institution_ids":["https://openalex.org/I113940042"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029751926","display_name":"Zhaoyan Wang","orcid":"https://orcid.org/0000-0002-0977-0920"},"institutions":[{"id":"https://openalex.org/I4210127530","display_name":"Jining University","ror":"https://ror.org/037rvh518","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210127530"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhaoyan Wang","raw_affiliation_strings":["Department of Mathematics, Jining University, Jining 273155, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Jining University, Jining 273155, China","institution_ids":["https://openalex.org/I4210127530"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086702173","display_name":"Shaorong Xie","orcid":"https://orcid.org/0000-0002-8016-9310"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shaorong Xie","raw_affiliation_strings":["School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200444, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200444, China","institution_ids":["https://openalex.org/I113940042"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100780078"],"corresponding_institution_ids":["https://openalex.org/I113940042"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.1299,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.50112937,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"13","issue":"6","first_page":"920","last_page":"920"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.7559853196144104},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5959009528160095},{"id":"https://openalex.org/keywords/graph-theory","display_name":"Graph theory","score":0.5666638016700745},{"id":"https://openalex.org/keywords/lagrangian","display_name":"Lagrangian","score":0.5663087368011475},{"id":"https://openalex.org/keywords/coopetition","display_name":"Coopetition","score":0.5032677054405212},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.48175954818725586},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.43707531690597534},{"id":"https://openalex.org/keywords/multi-agent-system","display_name":"Multi-agent system","score":0.4368845820426941},{"id":"https://openalex.org/keywords/directed-graph","display_name":"Directed graph","score":0.43245142698287964},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4195474088191986},{"id":"https://openalex.org/keywords/decentralised-system","display_name":"Decentralised system","score":0.41793137788772583},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3983273506164551},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3727344274520874},{"id":"https://openalex.org/keywords/distributed-computing","display_name":"Distributed computing","score":0.3324418067932129},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.30677828192710876},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.29376664757728577},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.24537894129753113},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.17768555879592896},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.16804128885269165},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.15733537077903748},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1429349184036255},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10459202527999878},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08333176374435425}],"concepts":[{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.7559853196144104},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5959009528160095},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.5666638016700745},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.5663087368011475},{"id":"https://openalex.org/C2777216475","wikidata":"https://www.wikidata.org/wiki/Q615782","display_name":"Coopetition","level":3,"score":0.5032677054405212},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.48175954818725586},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.43707531690597534},{"id":"https://openalex.org/C41550386","wikidata":"https://www.wikidata.org/wiki/Q529909","display_name":"Multi-agent system","level":2,"score":0.4368845820426941},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.43245142698287964},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4195474088191986},{"id":"https://openalex.org/C205875254","wikidata":"https://www.wikidata.org/wiki/Q17156857","display_name":"Decentralised system","level":3,"score":0.41793137788772583},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3983273506164551},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3727344274520874},{"id":"https://openalex.org/C120314980","wikidata":"https://www.wikidata.org/wiki/Q180634","display_name":"Distributed computing","level":1,"score":0.3324418067932129},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.30677828192710876},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.29376664757728577},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.24537894129753113},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.17768555879592896},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.16804128885269165},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.15733537077903748},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1429349184036255},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10459202527999878},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08333176374435425},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym13060920","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13060920","pdf_url":"https://www.mdpi.com/2073-8994/13/6/920/pdf?version=1621580814","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:f9b723de8da0445ead0486bea7c9208a","is_oa":true,"landing_page_url":"https://doaj.org/article/f9b723de8da0445ead0486bea7c9208a","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 13, Iss 6, p 920 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/6/920/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13060920","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry; Volume 13; Issue 6; Pages: 920","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym13060920","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13060920","pdf_url":"https://www.mdpi.com/2073-8994/13/6/920/pdf?version=1621580814","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Partnerships for the goals","id":"https://metadata.un.org/sdg/17","score":0.5699999928474426}],"awards":[{"id":"https://openalex.org/G2413287777","display_name":null,"funder_award_id":"61625304; 62073209; 61991415","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6445465751","display_name":null,"funder_award_id":"ZR2020KA005","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320324174","display_name":"Natural Science Foundation of Shandong Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3160644820.pdf"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W836351843","https://openalex.org/W950821216","https://openalex.org/W1120031704","https://openalex.org/W1967509640","https://openalex.org/W1979472936","https://openalex.org/W2025421018","https://openalex.org/W2055015486","https://openalex.org/W2088103590","https://openalex.org/W2101474901","https://openalex.org/W2109470906","https://openalex.org/W2165482975","https://openalex.org/W2167516879","https://openalex.org/W2167808181","https://openalex.org/W2227511020","https://openalex.org/W2512487235","https://openalex.org/W2587622940","https://openalex.org/W2593974156","https://openalex.org/W2775507451","https://openalex.org/W2786229123","https://openalex.org/W2787963636","https://openalex.org/W2790817590","https://openalex.org/W2892946647","https://openalex.org/W3015763257","https://openalex.org/W3025126133","https://openalex.org/W3101211700","https://openalex.org/W3111259590","https://openalex.org/W3135995851","https://openalex.org/W3209876736","https://openalex.org/W4243043969","https://openalex.org/W6776278055"],"related_works":["https://openalex.org/W2157861323","https://openalex.org/W2901795222","https://openalex.org/W2056883096","https://openalex.org/W2625585958","https://openalex.org/W4205673251","https://openalex.org/W2582845858","https://openalex.org/W1995329927","https://openalex.org/W2368361611","https://openalex.org/W2112081846","https://openalex.org/W1968702692"],"abstract_inverted_index":{"This":[0],"paper":[1],"investigates":[2],"the":[3,20,31,40,43,55,62,68,72,75,94],"leader-following":[4],"regional":[5,25],"multiple-bipartite":[6],"consensus":[7,26],"problems":[8],"of":[9,23,33,46,64,74,96],"networked":[10],"Lagrangian":[11],"systems":[12],"(NLSs)":[13],"in":[14,27,39,54,67],"coopetition":[15],"networks.":[16,29],"Our":[17],"framework":[18],"expands":[19],"application":[21],"scopes":[22],"traditional":[24],"cooperative":[28],"With":[30],"aid":[32],"a":[34],"novel":[35],"auxiliary":[36],"variable":[37],"embedded":[38],"control":[41,85],"protocols,":[42],"final":[44],"states":[45],"NLSs":[47],"are":[48],"guaranteed":[49],"to":[50],"realise":[51],"multi-regional":[52],"symmetry":[53],"constructed":[56],"multiple":[57],"symmetric":[58],"regions.":[59],"By":[60],"utilising":[61],"characteristic":[63],"acyclic":[65],"topology":[66],"structurally":[69],"balanced":[70],"graph,":[71],"stability":[73],"closed":[76],"system":[77],"is":[78,99],"performed":[79],"by":[80,101],"perturbation":[81],"analysis":[82,88],"theory,":[83,86,89],"nonlinear":[84],"functional":[87],"and":[90],"so":[91],"on.":[92],"Finally,":[93],"effectiveness":[95],"our":[97],"approach":[98],"verified":[100],"numerical":[102],"simulations.":[103]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2021-05-24T00:00:00"}
