{"id":"https://openalex.org/W2343580824","doi":"https://doi.org/10.1109/tac.2015.2504265","title":"Necessary and Sufficient Graphical Conditions for Affine Formation Control","display_name":"Necessary and Sufficient Graphical Conditions for Affine Formation Control","publication_year":2015,"publication_date":"2015-11-30","ids":{"openalex":"https://openalex.org/W2343580824","doi":"https://doi.org/10.1109/tac.2015.2504265","mag":"2343580824"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2015.2504265","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2015.2504265","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042932080","display_name":"Zhiyun Lin","orcid":"https://orcid.org/0000-0002-5523-4467"},"institutions":[{"id":"https://openalex.org/I78757542","display_name":"University of Newcastle Australia","ror":"https://ror.org/00eae9z71","country_code":"AU","type":"education","lineage":["https://openalex.org/I78757542"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Zhiyun Lin","raw_affiliation_strings":["State Key Laboratory of Industrial Control Technology, College of Electrical Engineering, University of Newcastle, Callaghan, NSW, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Industrial Control Technology, College of Electrical Engineering, University of Newcastle, Callaghan, NSW, Australia","institution_ids":["https://openalex.org/I78757542"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100356435","display_name":"Lili Wang","orcid":"https://orcid.org/0000-0003-4867-4357"},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lili Wang","raw_affiliation_strings":["Department of Electrical Engineering, Yale University, New Haven, CT, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Yale University, New Haven, CT, USA","institution_ids":["https://openalex.org/I32971472"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100370053","display_name":"Zhiyong Chen","orcid":"https://orcid.org/0000-0002-2033-4249"},"institutions":[{"id":"https://openalex.org/I78757542","display_name":"University of Newcastle Australia","ror":"https://ror.org/00eae9z71","country_code":"AU","type":"education","lineage":["https://openalex.org/I78757542"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Zhiyong Chen","raw_affiliation_strings":["School of Electrical Engineering and Computer Science, University of Newcastle, Callaghan, NSW, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering and Computer Science, University of Newcastle, Callaghan, NSW, Australia","institution_ids":["https://openalex.org/I78757542"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065677770","display_name":"Minyue Fu","orcid":"https://orcid.org/0000-0002-4659-601X"},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Minyue Fu","raw_affiliation_strings":["School of Electrical Engineering and Computer Science, Zhejiang University, Hangzhou, NSW, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering and Computer Science, Zhejiang University, Hangzhou, NSW, China","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100748568","display_name":"Zhimin Han","orcid":"https://orcid.org/0000-0002-8638-0440"},"institutions":[{"id":"https://openalex.org/I4391767838","display_name":"State Key Laboratory of Industrial Control Technology","ror":"https://ror.org/03a33a786","country_code":null,"type":"facility","lineage":["https://openalex.org/I4391767838","https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhimin Han","raw_affiliation_strings":["State Key Laboratory of Industrial Control Technology, College of Electrical Engineering, Zhejiang University, Hangzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Industrial Control Technology, College of Electrical Engineering, Zhejiang University, Hangzhou, China","institution_ids":["https://openalex.org/I4391767838"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":13.6755,"has_fulltext":false,"cited_by_count":248,"citation_normalized_percentile":{"value":0.98914525,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"61","issue":"10","first_page":"2877","last_page":"2891"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":1.0,"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":1.0,"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/T12158","display_name":"Guidance and Control Systems","score":0.9538999795913696,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9448000192642212,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.7592309713363647},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.618127167224884},{"id":"https://openalex.org/keywords/laplacian-matrix","display_name":"Laplacian matrix","score":0.5755653977394104},{"id":"https://openalex.org/keywords/undirected-graph","display_name":"Undirected graph","score":0.51092928647995},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4715198278427124},{"id":"https://openalex.org/keywords/affine-coordinate-system","display_name":"Affine coordinate system","score":0.4648894667625427},{"id":"https://openalex.org/keywords/directed-graph","display_name":"Directed graph","score":0.4591727554798126},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4587332308292389},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4511019289493561},{"id":"https://openalex.org/keywords/comparability-graph","display_name":"Comparability graph","score":0.4361095428466797},{"id":"https://openalex.org/keywords/affine-space","display_name":"Affine space","score":0.30977118015289307},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.2300478219985962},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.19326376914978027},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.1417233645915985}],"concepts":[{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.7592309713363647},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.618127167224884},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.5755653977394104},{"id":"https://openalex.org/C3018234147","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Undirected graph","level":3,"score":0.51092928647995},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4715198278427124},{"id":"https://openalex.org/C95565831","wikidata":"https://www.wikidata.org/wiki/Q382698","display_name":"Affine coordinate system","level":4,"score":0.4648894667625427},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.4591727554798126},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4587332308292389},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4511019289493561},{"id":"https://openalex.org/C198414033","wikidata":"https://www.wikidata.org/wiki/Q5155607","display_name":"Comparability graph","level":5,"score":0.4361095428466797},{"id":"https://openalex.org/C173110770","wikidata":"https://www.wikidata.org/wiki/Q382698","display_name":"Affine space","level":3,"score":0.30977118015289307},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.2300478219985962},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19326376914978027},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.1417233645915985}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tac.2015.2504265","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2015.2504265","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},{"id":"pmh:uon:29254","is_oa":false,"landing_page_url":"http://hdl.handle.net/1959.13/1343842","pdf_url":null,"source":{"id":"https://openalex.org/S4377196471","display_name":"NOVA (University of Newcastle Australia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I78757542","host_organization_name":"University of Newcastle Australia","host_organization_lineage":["https://openalex.org/I78757542"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"journal article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8499081890","display_name":null,"funder_award_id":"61273113","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1964537835","https://openalex.org/W1967509640","https://openalex.org/W1980755499","https://openalex.org/W1981692507","https://openalex.org/W1993227633","https://openalex.org/W1994596188","https://openalex.org/W2009942238","https://openalex.org/W2021437094","https://openalex.org/W2027524385","https://openalex.org/W2033931769","https://openalex.org/W2068640222","https://openalex.org/W2074796812","https://openalex.org/W2081952013","https://openalex.org/W2088103590","https://openalex.org/W2099175737","https://openalex.org/W2107850743","https://openalex.org/W2114871659","https://openalex.org/W2115206688","https://openalex.org/W2118909312","https://openalex.org/W2123876595","https://openalex.org/W2128202699","https://openalex.org/W2130532917","https://openalex.org/W2133503839","https://openalex.org/W2145206324","https://openalex.org/W2147326597","https://openalex.org/W2162496869","https://openalex.org/W2165744313","https://openalex.org/W2245154713","https://openalex.org/W4252959020","https://openalex.org/W4299945841","https://openalex.org/W6653062677","https://openalex.org/W6671038618","https://openalex.org/W6676412311","https://openalex.org/W6691039924"],"related_works":["https://openalex.org/W2546891199","https://openalex.org/W2606958405","https://openalex.org/W3022853753","https://openalex.org/W2052402162","https://openalex.org/W2077954576","https://openalex.org/W2951009501","https://openalex.org/W2798263748","https://openalex.org/W2751476518","https://openalex.org/W2067039815","https://openalex.org/W3128259744"],"abstract_inverted_index":{"This":[0],"paper":[1,75],"introduces":[2],"a":[3,20,32,43,103],"new":[4],"multi-agent":[5],"control":[6,12,58],"problem,":[7,13],"called":[8],"an":[9,77,83,97],"affine":[10,57,78,98],"formation":[11,79,99],"with":[14,29,51,130],"the":[15,56,90,107,114,131],"objective":[16],"of":[17,27,46],"asymptotically":[18],"reaching":[19],"configuration":[21],"that":[22,76],"preserves":[23],"collinearity":[24],"and":[25,87,111,138],"ratios":[26],"distances":[28],"respect":[30],"to":[31],"target":[33],"configuration.":[34],"Suppose":[35],"each":[36],"agent":[37],"updates":[38],"its":[39,47],"own":[40],"state":[41],"using":[42],"weighted":[44],"sum":[45],"neighbor's":[48],"relative":[49],"states":[50],"possibly":[52],"negative":[53,139],"weights.":[54,140],"Then":[55],"problem":[59],"can":[60],"be":[61],"solved":[62],"for":[63],"either":[64],"undirected":[65,84,91],"or":[66],"directed":[67,104,115],"interaction":[68,132],"graphs.":[69],"It":[70],"is":[71,80,93,100,117,123],"shown":[72],"in":[73,106],"this":[74],"stabilizable":[81,101],"over":[82,102],"graph":[85,92,105,116],"if":[86,89,110,113],"only":[88,112],"universally":[94],"rigid,":[95],"while":[96],"d-dimensional":[108],"space":[109],"(d":[118],"+":[119],"1)-rooted.":[120],"Rigorous":[121],"analysis":[122],"provided,":[124],"mainly":[125],"relying":[126],"on":[127],"Laplacian":[128],"associated":[129],"graph,":[133],"which":[134],"contain":[135],"both":[136],"positive":[137]},"counts_by_year":[{"year":2026,"cited_by_count":12},{"year":2025,"cited_by_count":30},{"year":2024,"cited_by_count":39},{"year":2023,"cited_by_count":31},{"year":2022,"cited_by_count":25},{"year":2021,"cited_by_count":20},{"year":2020,"cited_by_count":24},{"year":2019,"cited_by_count":27},{"year":2018,"cited_by_count":26},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}