{"id":"https://openalex.org/W4403446275","doi":"https://doi.org/10.1109/tcyb.2024.3473295","title":"Retracted: Multiple Transformation Matrix-Based Adaptive Projective Vortex Formation Tracking for Multiagent Systems With a Leader of Completely Unknown Input","display_name":"Retracted: Multiple Transformation Matrix-Based Adaptive Projective Vortex Formation Tracking for Multiagent Systems With a Leader of Completely Unknown Input","publication_year":2024,"publication_date":"2024-10-16","ids":{"openalex":"https://openalex.org/W4403446275","doi":"https://doi.org/10.1109/tcyb.2024.3473295","pmid":"https://pubmed.ncbi.nlm.nih.gov/39412965"},"language":"en","primary_location":{"id":"doi:10.1109/tcyb.2024.3473295","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2024.3473295","pdf_url":null,"source":{"id":"https://openalex.org/S4210191041","display_name":"IEEE Transactions on Cybernetics","issn_l":"2168-2267","issn":["2168-2267","2168-2275"],"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 Cybernetics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5067780753","display_name":"Xiangyang Du","orcid":"https://orcid.org/0009-0004-1024-257X"},"institutions":[{"id":"https://openalex.org/I151727225","display_name":"Harbin Engineering University","ror":"https://ror.org/03x80pn82","country_code":"CN","type":"education","lineage":["https://openalex.org/I151727225"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiangyang Du","raw_affiliation_strings":["Harbin Engineering University","College of Mathematical Sciences, Harbin Engineering University, Harbin, China"],"raw_orcid":"https://orcid.org/0009-0004-1024-257X","affiliations":[{"raw_affiliation_string":"Harbin Engineering University","institution_ids":["https://openalex.org/I151727225"]},{"raw_affiliation_string":"College of Mathematical Sciences, Harbin Engineering University, Harbin, China","institution_ids":["https://openalex.org/I151727225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040210816","display_name":"Jihong Shen","orcid":"https://orcid.org/0000-0002-2333-3428"},"institutions":[{"id":"https://openalex.org/I151727225","display_name":"Harbin Engineering University","ror":"https://ror.org/03x80pn82","country_code":"CN","type":"education","lineage":["https://openalex.org/I151727225"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jihong Shen","raw_affiliation_strings":["Harbin Engineering University","College of Mathematical Sciences, Harbin Engineering University, Harbin, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Harbin Engineering University","institution_ids":["https://openalex.org/I151727225"]},{"raw_affiliation_string":"College of Mathematical Sciences, Harbin Engineering University, Harbin, China","institution_ids":["https://openalex.org/I151727225"]}]},{"author_position":"last","author":{"id":null,"display_name":"Shujuan Wang","orcid":"https://orcid.org/0009-0000-6736-4974"},"institutions":[{"id":"https://openalex.org/I151727225","display_name":"Harbin Engineering University","ror":"https://ror.org/03x80pn82","country_code":"CN","type":"education","lineage":["https://openalex.org/I151727225"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shujuan Wang","raw_affiliation_strings":["Harbin Engineering University","College of Mathematical Sciences, Harbin Engineering University, Harbin, China"],"raw_orcid":"https://orcid.org/0009-0000-6736-4974","affiliations":[{"raw_affiliation_string":"Harbin Engineering University","institution_ids":["https://openalex.org/I151727225"]},{"raw_affiliation_string":"College of Mathematical Sciences, Harbin Engineering University, Harbin, China","institution_ids":["https://openalex.org/I151727225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I151727225"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12964878,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"55","issue":"8","first_page":"3573","last_page":"3583"},"is_retracted":true,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10462","display_name":"Reinforcement Learning in Robotics","score":0.9430999755859375,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.9430999755859375,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11195","display_name":"Simulation Techniques and Applications","score":0.9006999731063843,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.7016066908836365},{"id":"https://openalex.org/keywords/multi-agent-system","display_name":"Multi-agent system","score":0.6087033152580261},{"id":"https://openalex.org/keywords/tracking","display_name":"Tracking (education)","score":0.5585938692092896},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5422753095626831},{"id":"https://openalex.org/keywords/projective-test","display_name":"Projective test","score":0.518527626991272},{"id":"https://openalex.org/keywords/vortex","display_name":"Vortex","score":0.5117611885070801},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4331071674823761},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3703436851501465},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.36573493480682373},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3177873492240906},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2850799262523651},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1905471384525299},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.1330505907535553},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.1104675829410553},{"id":"https://openalex.org/keywords/psychology","display_name":"Psychology","score":0.10695838928222656},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.06865403056144714},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.06438630819320679}],"concepts":[{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.7016066908836365},{"id":"https://openalex.org/C41550386","wikidata":"https://www.wikidata.org/wiki/Q529909","display_name":"Multi-agent system","level":2,"score":0.6087033152580261},{"id":"https://openalex.org/C2775936607","wikidata":"https://www.wikidata.org/wiki/Q466845","display_name":"Tracking (education)","level":2,"score":0.5585938692092896},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5422753095626831},{"id":"https://openalex.org/C177846678","wikidata":"https://www.wikidata.org/wiki/Q1501864","display_name":"Projective test","level":2,"score":0.518527626991272},{"id":"https://openalex.org/C140820882","wikidata":"https://www.wikidata.org/wiki/Q732722","display_name":"Vortex","level":2,"score":0.5117611885070801},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4331071674823761},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3703436851501465},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.36573493480682373},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3177873492240906},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2850799262523651},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1905471384525299},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.1330505907535553},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.1104675829410553},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.10695838928222656},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.06865403056144714},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.06438630819320679},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C19417346","wikidata":"https://www.wikidata.org/wiki/Q7922","display_name":"Pedagogy","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tcyb.2024.3473295","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2024.3473295","pdf_url":null,"source":{"id":"https://openalex.org/S4210191041","display_name":"IEEE Transactions on Cybernetics","issn_l":"2168-2267","issn":["2168-2267","2168-2275"],"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 Cybernetics","raw_type":"journal-article"},{"id":"pmid:39412965","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/39412965","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on cybernetics","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2255795374","display_name":null,"funder_award_id":"3072024XX0205","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"}],"funders":[{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1834394711","https://openalex.org/W2028235243","https://openalex.org/W2035945038","https://openalex.org/W2038014752","https://openalex.org/W2050090436","https://openalex.org/W2088195248","https://openalex.org/W2099175737","https://openalex.org/W2282865445","https://openalex.org/W2339624293","https://openalex.org/W2522669551","https://openalex.org/W2569044767","https://openalex.org/W2614186282","https://openalex.org/W2886463928","https://openalex.org/W2909077198","https://openalex.org/W2940830480","https://openalex.org/W2976811411","https://openalex.org/W2995211006","https://openalex.org/W3011445504","https://openalex.org/W3016221081","https://openalex.org/W3035348688","https://openalex.org/W3134125274","https://openalex.org/W3135345850","https://openalex.org/W3153809019","https://openalex.org/W4205525671","https://openalex.org/W4210714139","https://openalex.org/W4211201154","https://openalex.org/W4224306019","https://openalex.org/W4241629868","https://openalex.org/W4293704324","https://openalex.org/W4296501482","https://openalex.org/W4312757523","https://openalex.org/W4361801707"],"related_works":["https://openalex.org/W4387497383","https://openalex.org/W3183948672","https://openalex.org/W3173606202","https://openalex.org/W3110381201","https://openalex.org/W2948807893","https://openalex.org/W2935909890","https://openalex.org/W2778153218","https://openalex.org/W2758277628","https://openalex.org/W1531601525","https://openalex.org/W2001489718"],"abstract_inverted_index":{"This":[0],"article":[1],"systematically":[2],"studies":[3],"projective":[4],"vortex":[5],"formation":[6],"tracking":[7],"(PVFT)":[8],"of":[9,25,42,58,65,101,120,135,154],"linear":[10,127],"multiagent":[11],"systems":[12,128],"(MASs)":[13],"on":[14,70,137],"directed":[15],"graphs":[16],"through":[17],"multiple":[18,54],"transformation":[19],"matrices,":[20],"in":[21,91],"which":[22],"the":[23,49,59,92,98,102,110,113,133,152,155],"input":[24,100],"leader":[26],"and":[27,75,86,94,109,123,139,144],"its":[28],"upper":[29],"bound":[30],"information":[31],"are":[32,79,89,141,148],"not":[33],"available":[34],"to":[35,52,96,125,129,150],"any":[36],"follower.":[37],"First,":[38],"an":[39,105],"innovative":[40],"class":[41],"distributed":[43,66,71],"adaptive":[44,83],"observer":[45,74,93],"is":[46,107,115],"designed":[47],"using":[48],"projection":[50],"matrices":[51,78],"capture":[53],"desired":[55],"virtual":[56],"signals":[57],"leader.":[60,103],"Next,":[61],"a":[62],"novel":[63],"kind":[64],"PVFT":[67],"protocol":[68,111],"based":[69],"observer,":[72],"local":[73],"coordinates":[76],"coupling":[77],"proposed.":[80],"Two":[81],"different":[82],"update":[84],"mechanisms":[85],"nonlinear":[87],"functions":[88],"introduced":[90],"controller":[95],"override":[97],"unknown":[99],"Then,":[104],"algorithm":[106,114],"given,":[108],"under":[112],"proved":[116],"from":[117],"three":[118],"processes":[119],"estimation,":[121],"aggregation,":[122],"rotation":[124,140],"enable":[126],"achieve":[130],"PVFT.":[131],"Finally,":[132],"effects":[134],"parameters":[136],"aggregation":[138],"analyzed":[142],"systematically,":[143],"several":[145],"simulation":[146],"examples":[147],"given":[149],"illustrate":[151],"reliability":[153],"results.":[156]},"counts_by_year":[],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}
