{"id":"https://openalex.org/W4398226214","doi":"https://doi.org/10.1109/tase.2024.3403130","title":"Time-Varying Formation-Containment Control via PDE Backstepping Technique","display_name":"Time-Varying Formation-Containment Control via PDE Backstepping Technique","publication_year":2024,"publication_date":"2024-05-22","ids":{"openalex":"https://openalex.org/W4398226214","doi":"https://doi.org/10.1109/tase.2024.3403130"},"language":"en","primary_location":{"id":"doi:10.1109/tase.2024.3403130","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tase.2024.3403130","pdf_url":null,"source":{"id":"https://openalex.org/S34881539","display_name":"IEEE Transactions on Automation Science and Engineering","issn_l":"1545-5955","issn":["1545-5955","1558-3783"],"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 Automation Science and Engineering","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/A5051751030","display_name":"Jiachun Sun","orcid":null},"institutions":[{"id":"https://openalex.org/I1327237609","display_name":"Ministry of Education of the People's Republic of China","ror":"https://ror.org/01mv9t934","country_code":"CN","type":"government","lineage":["https://openalex.org/I1327237609","https://openalex.org/I4210127390"]},{"id":"https://openalex.org/I206324368","display_name":"Shaoyang University","ror":"https://ror.org/03fx09x73","country_code":"CN","type":"education","lineage":["https://openalex.org/I206324368"]},{"id":"https://openalex.org/I3124059619","display_name":"China University of Geosciences","ror":"https://ror.org/04gcegc37","country_code":"CN","type":"education","lineage":["https://openalex.org/I3124059619"]},{"id":"https://openalex.org/I4210094879","display_name":"Shandong Institute of Automation","ror":"https://ror.org/00qdtba35","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210094879","https://openalex.org/I4210142748"]},{"id":"https://openalex.org/I4210157608","display_name":"Institute of Advanced Manufacturing Technology","ror":"https://ror.org/05egxdg81","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210157608"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiachun Sun","raw_affiliation_strings":["School of Automation, China University of Geosciences, Wuhan, China","Engineering Research Center of Intelligent Technology for Geo-Exploration, Ministry of Education, Wuhan, China","Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems, Wuhan, China","Shaoyang Institute of Advanced Manufacturing Technology, Shaoyang, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Automation, China University of Geosciences, Wuhan, China","institution_ids":["https://openalex.org/I3124059619"]},{"raw_affiliation_string":"Engineering Research Center of Intelligent Technology for Geo-Exploration, Ministry of Education, Wuhan, China","institution_ids":["https://openalex.org/I1327237609"]},{"raw_affiliation_string":"Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems, Wuhan, China","institution_ids":["https://openalex.org/I4210094879"]},{"raw_affiliation_string":"Shaoyang Institute of Advanced Manufacturing Technology, Shaoyang, China","institution_ids":["https://openalex.org/I206324368","https://openalex.org/I4210157608"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060974056","display_name":"Shiqi Zheng","orcid":"https://orcid.org/0000-0003-0084-9533"},"institutions":[{"id":"https://openalex.org/I1327237609","display_name":"Ministry of Education of the People's Republic of China","ror":"https://ror.org/01mv9t934","country_code":"CN","type":"government","lineage":["https://openalex.org/I1327237609","https://openalex.org/I4210127390"]},{"id":"https://openalex.org/I206324368","display_name":"Shaoyang University","ror":"https://ror.org/03fx09x73","country_code":"CN","type":"education","lineage":["https://openalex.org/I206324368"]},{"id":"https://openalex.org/I3124059619","display_name":"China University of Geosciences","ror":"https://ror.org/04gcegc37","country_code":"CN","type":"education","lineage":["https://openalex.org/I3124059619"]},{"id":"https://openalex.org/I4210094879","display_name":"Shandong Institute of Automation","ror":"https://ror.org/00qdtba35","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210094879","https://openalex.org/I4210142748"]},{"id":"https://openalex.org/I4210157608","display_name":"Institute of Advanced Manufacturing Technology","ror":"https://ror.org/05egxdg81","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210157608"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shiqi Zheng","raw_affiliation_strings":["School of Automation, China University of Geosciences, Wuhan, China","Engineering Research Center of Intelligent Technology for Geo-Exploration, Ministry of Education, Wuhan, China","Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems, Wuhan, China","Shaoyang Institute of Advanced Manufacturing Technology, Shaoyang, China"],"raw_orcid":"https://orcid.org/0000-0003-0084-9533","affiliations":[{"raw_affiliation_string":"School of Automation, China University of Geosciences, Wuhan, China","institution_ids":["https://openalex.org/I3124059619"]},{"raw_affiliation_string":"Engineering Research Center of Intelligent Technology for Geo-Exploration, Ministry of Education, Wuhan, China","institution_ids":["https://openalex.org/I1327237609"]},{"raw_affiliation_string":"Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems, Wuhan, China","institution_ids":["https://openalex.org/I4210094879"]},{"raw_affiliation_string":"Shaoyang Institute of Advanced Manufacturing Technology, Shaoyang, China","institution_ids":["https://openalex.org/I206324368","https://openalex.org/I4210157608"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084993350","display_name":"Choon Ki Ahn","orcid":"https://orcid.org/0000-0003-0993-9658"},"institutions":[{"id":"https://openalex.org/I197347611","display_name":"Korea University","ror":"https://ror.org/047dqcg40","country_code":"KR","type":"education","lineage":["https://openalex.org/I197347611"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Choon Ki Ahn","raw_affiliation_strings":["School of Electrical Engineering, Korea University, Seoul, South Korea"],"raw_orcid":"https://orcid.org/0000-0003-0993-9658","affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, Korea University, Seoul, South Korea","institution_ids":["https://openalex.org/I197347611"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5098761998","display_name":"Yifeng Zha","orcid":"https://orcid.org/0009-0000-6129-9067"},"institutions":[{"id":"https://openalex.org/I1327237609","display_name":"Ministry of Education of the People's Republic of China","ror":"https://ror.org/01mv9t934","country_code":"CN","type":"government","lineage":["https://openalex.org/I1327237609","https://openalex.org/I4210127390"]},{"id":"https://openalex.org/I206324368","display_name":"Shaoyang University","ror":"https://ror.org/03fx09x73","country_code":"CN","type":"education","lineage":["https://openalex.org/I206324368"]},{"id":"https://openalex.org/I3124059619","display_name":"China University of Geosciences","ror":"https://ror.org/04gcegc37","country_code":"CN","type":"education","lineage":["https://openalex.org/I3124059619"]},{"id":"https://openalex.org/I4210094879","display_name":"Shandong Institute of Automation","ror":"https://ror.org/00qdtba35","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210094879","https://openalex.org/I4210142748"]},{"id":"https://openalex.org/I4210157608","display_name":"Institute of Advanced Manufacturing Technology","ror":"https://ror.org/05egxdg81","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210157608"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yifeng Zha","raw_affiliation_strings":["School of Automation, China University of Geosciences, Wuhan, China","Engineering Research Center of Intelligent Technology for Geo-Exploration, Ministry of Education, Wuhan, China","Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems, Wuhan, China","Shaoyang Institute of Advanced Manufacturing Technology, Shaoyang, China"],"raw_orcid":"https://orcid.org/0009-0000-6129-9067","affiliations":[{"raw_affiliation_string":"School of Automation, China University of Geosciences, Wuhan, China","institution_ids":["https://openalex.org/I3124059619"]},{"raw_affiliation_string":"Engineering Research Center of Intelligent Technology for Geo-Exploration, Ministry of Education, Wuhan, China","institution_ids":["https://openalex.org/I1327237609"]},{"raw_affiliation_string":"Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems, Wuhan, China","institution_ids":["https://openalex.org/I4210094879"]},{"raw_affiliation_string":"Shaoyang Institute of Advanced Manufacturing Technology, Shaoyang, China","institution_ids":["https://openalex.org/I206324368","https://openalex.org/I4210157608"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100739668","display_name":"Peng Shi","orcid":"https://orcid.org/0000-0001-8218-586X"},"institutions":[{"id":"https://openalex.org/I103356709","display_name":"Obuda University","ror":"https://ror.org/00ax71d21","country_code":"HU","type":"education","lineage":["https://openalex.org/I103356709"]},{"id":"https://openalex.org/I5681781","display_name":"The University of Adelaide","ror":"https://ror.org/00892tw58","country_code":"AU","type":"education","lineage":["https://openalex.org/I5681781"]}],"countries":["AU","HU"],"is_corresponding":false,"raw_author_name":"Peng Shi","raw_affiliation_strings":["School of Electrical and Mechanical Engineering, The University of Adelaide, Adelaide, SA, Australia","Research and Innovation Centre, Obuda University, Budapest, Hungary"],"raw_orcid":"https://orcid.org/0000-0001-8218-586X","affiliations":[{"raw_affiliation_string":"School of Electrical and Mechanical Engineering, The University of Adelaide, Adelaide, SA, Australia","institution_ids":["https://openalex.org/I5681781"]},{"raw_affiliation_string":"Research and Innovation Centre, Obuda University, Budapest, Hungary","institution_ids":["https://openalex.org/I103356709"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":8,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.4896,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.80169134,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"22","issue":null,"first_page":"3911","last_page":"3921"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9832000136375427,"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"}},"topics":[{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9832000136375427,"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"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9692000150680542,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9535999894142151,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/backstepping","display_name":"Backstepping","score":0.8083091974258423},{"id":"https://openalex.org/keywords/containment","display_name":"Containment (computer programming)","score":0.7113658785820007},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6139686703681946},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.46468472480773926},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4493713974952698},{"id":"https://openalex.org/keywords/control-engineering","display_name":"Control engineering","score":0.4001936614513397},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.32164788246154785},{"id":"https://openalex.org/keywords/adaptive-control","display_name":"Adaptive control","score":0.24745142459869385},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10695889592170715}],"concepts":[{"id":"https://openalex.org/C72218879","wikidata":"https://www.wikidata.org/wiki/Q4839759","display_name":"Backstepping","level":4,"score":0.8083091974258423},{"id":"https://openalex.org/C2777019822","wikidata":"https://www.wikidata.org/wiki/Q390066","display_name":"Containment (computer programming)","level":2,"score":0.7113658785820007},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6139686703681946},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.46468472480773926},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4493713974952698},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.4001936614513397},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.32164788246154785},{"id":"https://openalex.org/C107464732","wikidata":"https://www.wikidata.org/wiki/Q235781","display_name":"Adaptive control","level":3,"score":0.24745142459869385},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10695889592170715},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tase.2024.3403130","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tase.2024.3403130","pdf_url":null,"source":{"id":"https://openalex.org/S34881539","display_name":"IEEE Transactions on Automation Science and Engineering","issn_l":"1545-5955","issn":["1545-5955","1558-3783"],"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 Automation Science and Engineering","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1030557703","display_name":null,"funder_award_id":"52375520","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6862166440","display_name":"Insect-inspired flapping wing robots: autonomous flight control systems","funder_award_id":"DP240101140","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322120","display_name":"National Research Foundation of Korea","ror":"https://ror.org/013aysd81"},{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W1493175923","https://openalex.org/W1970786657","https://openalex.org/W1994892535","https://openalex.org/W2005422895","https://openalex.org/W2011671151","https://openalex.org/W2035625658","https://openalex.org/W2060645918","https://openalex.org/W2121622973","https://openalex.org/W2123876595","https://openalex.org/W2134020191","https://openalex.org/W2141410403","https://openalex.org/W2160932744","https://openalex.org/W2310756702","https://openalex.org/W2576700979","https://openalex.org/W2793582886","https://openalex.org/W2795214178","https://openalex.org/W2893450756","https://openalex.org/W2897657295","https://openalex.org/W2917314747","https://openalex.org/W2922330498","https://openalex.org/W2962815952","https://openalex.org/W3008959010","https://openalex.org/W3028170371","https://openalex.org/W3049083478","https://openalex.org/W3087754293","https://openalex.org/W3097297555","https://openalex.org/W3097627133","https://openalex.org/W3107174227","https://openalex.org/W3112519497","https://openalex.org/W3112730247","https://openalex.org/W3114737796","https://openalex.org/W3145618612","https://openalex.org/W3168831288","https://openalex.org/W3169164188","https://openalex.org/W3209370225","https://openalex.org/W4207092385","https://openalex.org/W4220859467","https://openalex.org/W4313655176","https://openalex.org/W4322124312","https://openalex.org/W4322576650","https://openalex.org/W4362718213","https://openalex.org/W4381162772","https://openalex.org/W4381198781","https://openalex.org/W4383113679","https://openalex.org/W4385732534"],"related_works":["https://openalex.org/W2771027241","https://openalex.org/W1765905465","https://openalex.org/W2793080664","https://openalex.org/W2186140227","https://openalex.org/W2389203828","https://openalex.org/W2182708846","https://openalex.org/W2170944339","https://openalex.org/W2477888563","https://openalex.org/W1972061147","https://openalex.org/W3167722269"],"abstract_inverted_index":{"This":[0],"paper":[1],"focuses":[2],"on":[3,70,215,219],"the":[4,35,39,43,47,57,71,91,95,117,120,124,127,167,171,176,206,220],"formation-containment":[5],"(FC)":[6],"control":[7,83,222],"for":[8],"multi-agent":[9],"systems":[10],"(MASs)":[11],"with":[12,50,97,225],"long":[13,66,98,226],"input":[14,67,99,192,227],"delay":[15,100,228],"under":[16],"jointly":[17],"connected":[18],"switching":[19],"topologies.":[20],"The":[21,32,151],"considered":[22,58],"MASs":[23,59,96,197,224],"contain":[24],"one":[25],"virtual":[26,162],"leader,":[27],"multiple":[28,134,177],"leaders":[29,33,148,152],"and":[30,90,149],"followers.":[31,150],"complete":[34],"formation":[36,44,158],"first,":[37],"then":[38,170],"followers":[40,172],"move":[41,174],"into":[42,104,147,175],"created":[45],"by":[46],"leaders.":[48],"Compared":[49],"existing":[51],"FC":[52,207,216,221],"control,":[53,217],"each":[54],"agent":[55],"in":[56,196],"can":[60,101,144,173,184],"have":[61],"different":[62],"dynamics.":[63],"To":[64],"handle":[65],"delay,":[68],"based":[69],"partial":[72],"differential":[73],"equation":[74],"(PDE)":[75],"backstepping":[76],"technique,":[77],"a":[78,156,161],"new":[79,105],"distributed":[80],"predictor":[81],"feedback":[82],"method":[84,89],"is":[85,229],"proposed.":[86],"Utilizing":[87],"this":[88],"certainty":[92],"equivalence":[93],"principle,":[94],"be":[102,145,185],"mapped":[103],"coupled":[106],"ODE-PDE":[107],"target":[108],"systems.":[109],"Then,":[110],"Lyapunov-Krasovskii":[111],"functions":[112],"are":[113,211],"used":[114],"to":[115,130,137,154,164,166,199,205],"prove":[116],"stability":[118],"of":[119,126,213,223],"system.":[121],"Simulations":[122],"verify":[123],"validity":[125],"proposed":[128],"results.Note":[129],"Practitioners\u2014In":[131],"actual":[132],"applications,":[133],"agents":[135,143],"need":[136,153],"perform":[138],"complex":[139],"tasks":[140],"together.":[141],"These":[142],"divided":[146],"establish":[155],"time-varying":[157],"(TVF)":[159],"around":[160],"leader":[163],"adapt":[165],"changing":[168],"circumstances,":[169],"leaders\u2019":[178],"spanning":[179],"convex":[180],"hull":[181],"so":[182],"they":[183],"protected":[186],"from":[187],"outside":[188],"obstacles.":[189],"In":[190],"practical,":[191],"delays":[193],"frequently":[194],"occur":[195],"due":[198],"network":[200],"transmission,":[201],"which":[202],"brings":[203],"difficulties":[204],"control.":[208],"Although":[209],"there":[210],"plenty":[212],"works":[214],"research":[218],"still":[230],"lacking.":[231]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}