{"id":"https://openalex.org/W4407128249","doi":"https://doi.org/10.1109/tcns.2025.3538743","title":"Discrete-Time Formation Control With Attitude Alignment: A Geometric Approach Under Ergodic Products","display_name":"Discrete-Time Formation Control With Attitude Alignment: A Geometric Approach Under Ergodic Products","publication_year":2025,"publication_date":"2025-02-04","ids":{"openalex":"https://openalex.org/W4407128249","doi":"https://doi.org/10.1109/tcns.2025.3538743"},"language":"en","primary_location":{"id":"doi:10.1109/tcns.2025.3538743","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcns.2025.3538743","pdf_url":null,"source":{"id":"https://openalex.org/S2502544478","display_name":"IEEE Transactions on Control of Network Systems","issn_l":"2325-5870","issn":["2325-5870","2372-2533"],"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 Control of Network Systems","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/A5100702503","display_name":"Zhen Li","orcid":"https://orcid.org/0000-0002-1517-3452"},"institutions":[{"id":"https://openalex.org/I4210136859","display_name":"Xi\u2019an University of Posts and Telecommunications","ror":"https://ror.org/04jn0td46","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210136859"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhen Li","raw_affiliation_strings":["School of Automation, Xi&#x0027;an University of Posts &amp; Telecommunications, Xi&#x0027;an, China","School of Automation, Xi-an University of Posts &amp; Telecommunications, Xi-an, China"],"raw_orcid":"https://orcid.org/0000-0002-1517-3452","affiliations":[{"raw_affiliation_string":"School of Automation, Xi&#x0027;an University of Posts &amp; Telecommunications, Xi&#x0027;an, China","institution_ids":["https://openalex.org/I4210136859"]},{"raw_affiliation_string":"School of Automation, Xi-an University of Posts &amp; Telecommunications, Xi-an, China","institution_ids":["https://openalex.org/I4210136859"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028570509","display_name":"Yang Tang","orcid":"https://orcid.org/0000-0002-2750-8029"},"institutions":[{"id":"https://openalex.org/I143593769","display_name":"East China University of Science and Technology","ror":"https://ror.org/01vyrm377","country_code":"CN","type":"education","lineage":["https://openalex.org/I143593769"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yang Tang","raw_affiliation_strings":["Key Laboratory of Smart Manufacturing in Energy Chemical Process, East China University of Science and Technology, Shanghai, China"],"raw_orcid":"https://orcid.org/0000-0002-2750-8029","affiliations":[{"raw_affiliation_string":"Key Laboratory of Smart Manufacturing in Energy Chemical Process, East China University of Science and Technology, Shanghai, China","institution_ids":["https://openalex.org/I143593769"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100686420","display_name":"Wenbing Zhang","orcid":"https://orcid.org/0000-0002-4638-1502"},"institutions":[{"id":"https://openalex.org/I78978612","display_name":"Yangzhou University","ror":"https://ror.org/03tqb8s11","country_code":"CN","type":"education","lineage":["https://openalex.org/I78978612"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenbing Zhang","raw_affiliation_strings":["Department of Mathematics, Yangzhou University, Jiangsu, China"],"raw_orcid":"https://orcid.org/0000-0002-4638-1502","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Yangzhou University, Jiangsu, China","institution_ids":["https://openalex.org/I78978612"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050320202","display_name":"Yongqing Fan","orcid":"https://orcid.org/0000-0002-0329-3334"},"institutions":[{"id":"https://openalex.org/I4210136859","display_name":"Xi\u2019an University of Posts and Telecommunications","ror":"https://ror.org/04jn0td46","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210136859"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yongqing Fan","raw_affiliation_strings":["School of Automation, Xi&#x0027;an University of Posts &amp; Telecommunications, Xi&#x0027;an, China","School of Automation, Xi-an University of Posts &amp; Telecommunications, Xi-an, China"],"raw_orcid":"https://orcid.org/0000-0002-0329-3334","affiliations":[{"raw_affiliation_string":"School of Automation, Xi&#x0027;an University of Posts &amp; Telecommunications, Xi&#x0027;an, China","institution_ids":["https://openalex.org/I4210136859"]},{"raw_affiliation_string":"School of Automation, Xi-an University of Posts &amp; Telecommunications, Xi-an, China","institution_ids":["https://openalex.org/I4210136859"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074290686","display_name":"Tingwen Huang","orcid":"https://orcid.org/0000-0001-9610-846X"},"institutions":[{"id":"https://openalex.org/I180726961","display_name":"Shenzhen University","ror":"https://ror.org/01vy4gh70","country_code":"CN","type":"education","lineage":["https://openalex.org/I180726961"]},{"id":"https://openalex.org/I4210152380","display_name":"Shenzhen Technology University","ror":"https://ror.org/04qzpec27","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210152380"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tingwen Huang","raw_affiliation_strings":["Faculty of Computer Science and Control Engineering, Shenzhen University of Advanced Technology, Shenzhen, China","Faculty of Computer Science and Control Engineering, Shenzhen University of Advanced Technology, Shenzhen, PR China"],"raw_orcid":"https://orcid.org/0000-0001-9610-846X","affiliations":[{"raw_affiliation_string":"Faculty of Computer Science and Control Engineering, Shenzhen University of Advanced Technology, Shenzhen, China","institution_ids":["https://openalex.org/I4210152380","https://openalex.org/I180726961"]},{"raw_affiliation_string":"Faculty of Computer Science and Control Engineering, Shenzhen University of Advanced Technology, Shenzhen, PR China","institution_ids":["https://openalex.org/I4210152380","https://openalex.org/I180726961"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5100702503"],"corresponding_institution_ids":["https://openalex.org/I4210136859"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0195041,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"12","issue":"2","first_page":"1793","last_page":"1804"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9768000245094299,"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/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9768000245094299,"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/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9725000262260437,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9538000226020813,"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/control","display_name":"Control (management)","score":0.5435578227043152},{"id":"https://openalex.org/keywords/ergodic-theory","display_name":"Ergodic theory","score":0.5150992274284363},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4801730215549469},{"id":"https://openalex.org/keywords/control-system","display_name":"Control system","score":0.45449745655059814},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.42684367299079895},{"id":"https://openalex.org/keywords/control-engineering","display_name":"Control engineering","score":0.32700496912002563},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.308720201253891},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.22751763463020325},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.18323639035224915},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.12239602208137512}],"concepts":[{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.5435578227043152},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.5150992274284363},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4801730215549469},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.45449745655059814},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.42684367299079895},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.32700496912002563},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.308720201253891},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.22751763463020325},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.18323639035224915},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.12239602208137512},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcns.2025.3538743","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcns.2025.3538743","pdf_url":null,"source":{"id":"https://openalex.org/S2502544478","display_name":"IEEE Transactions on Control of Network Systems","issn_l":"2325-5870","issn":["2325-5870","2372-2533"],"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 Control of Network Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7200000286102295,"display_name":"Climate action","id":"https://metadata.un.org/sdg/13"}],"awards":[{"id":"https://openalex.org/G5884386629","display_name":null,"funder_award_id":"U2441245","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6442699438","display_name":null,"funder_award_id":"62293502","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7545332879","display_name":null,"funder_award_id":"62233005","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8401245427","display_name":null,"funder_award_id":"62376242","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8998959397","display_name":null,"funder_award_id":"62003262","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":35,"referenced_works":["https://openalex.org/W1564897360","https://openalex.org/W1981826826","https://openalex.org/W1992412916","https://openalex.org/W1992415540","https://openalex.org/W1993193433","https://openalex.org/W1994122308","https://openalex.org/W2002655995","https://openalex.org/W2004567337","https://openalex.org/W2016411453","https://openalex.org/W2019312235","https://openalex.org/W2033578271","https://openalex.org/W2066647300","https://openalex.org/W2124351843","https://openalex.org/W2165469059","https://openalex.org/W2292586222","https://openalex.org/W2328033575","https://openalex.org/W2796974626","https://openalex.org/W2906460993","https://openalex.org/W2908811855","https://openalex.org/W2913876491","https://openalex.org/W2940830480","https://openalex.org/W2941038413","https://openalex.org/W3014574026","https://openalex.org/W3021373970","https://openalex.org/W3032266707","https://openalex.org/W3092327471","https://openalex.org/W3130434785","https://openalex.org/W3197005105","https://openalex.org/W4206570602","https://openalex.org/W4213427794","https://openalex.org/W4226047815","https://openalex.org/W4285040449","https://openalex.org/W4312718982","https://openalex.org/W4360995563","https://openalex.org/W4375928726"],"related_works":["https://openalex.org/W2615607975","https://openalex.org/W2355865573","https://openalex.org/W2155981143","https://openalex.org/W2155245395","https://openalex.org/W2192101006","https://openalex.org/W2116800748","https://openalex.org/W2638730922","https://openalex.org/W2190465783","https://openalex.org/W2027827693","https://openalex.org/W2381267592"],"abstract_inverted_index":{"Assuming":[0],"agents":[1],"possess":[2],"sensing":[3],"capabilities":[4],"and":[5,42,104,153],"dynamics":[6],"relative":[7],"to":[8,66,89,112],"their":[9],"body":[10],"coordinate":[11],"frames,":[12],"this":[13,151],"article":[14],"addresses":[15],"a":[16,51,62,143,177],"displacement-based":[17],"strategy":[18],"for":[19,146],"discrete-time":[20,36],"formation":[21,159],"control":[22,57],"through":[23],"attitude":[24,43],"synchronization.":[25],"Unlike":[26],"the":[27,30,68,79,82,92,101,109,129,132,136,157,167,170,174,181],"Eulerian":[28],"approximation,":[29],"first":[31],"challenge":[32],"lies":[33],"in":[34,164],"developing":[35],"models":[37],"that":[38],"capture":[39],"both":[40],"position":[41],"motions,":[44],"thereby":[45],"complementing":[46],"existing":[47],"continuous-time":[48],"systems":[49,75],"with":[50,173],"discretized":[52],"version.":[53],"Then,":[54],"two":[55],"leader-following":[56,113],"protocols":[58],"are":[59,98,117],"designed,":[60],"incorporating":[61],"jointly":[63],"connected":[64],"topology":[65],"relax":[67],"connectivity":[69],"requirements.":[70],"The":[71],"analysis":[72],"of":[73,84,95,128,131,138,169],"these":[74,115],"often":[76],"relies":[77],"on":[78],"Lyapunov":[80,133],"function,":[81],"existence":[83,130],"which":[85,125],"may":[86],"be":[87,162],"hard":[88],"guarantee.":[90],"Consequently,":[91],"geometric":[93],"properties":[94,116],"several":[96],"polytopes":[97],"explored":[99],"under":[100],"dynamic":[102],"topologies":[103],"time-varying":[105],"parameters.":[106],"By":[107],"extending":[108],"ergodicity":[110],"results":[111],"scenarios,":[114],"characterized":[118],"as":[119],"positively":[120],"invariant":[121],"sets.":[122],"This":[123],"invariance,":[124],"is":[126],"independent":[127],"function":[134],"or":[135],"solvability":[137],"its":[139],"associated":[140],"criteria,":[141],"provides":[142],"beneficial":[144],"tool":[145],"analyzing":[147],"time-variant":[148],"systems.":[149],"Utilizing":[150],"invariance":[152],"some":[154],"mathematical":[155],"techniques,":[156],"desired":[158],"shape":[160],"can":[161],"achieved":[163],"cases":[165],"where":[166],"attitudes":[168],"followers":[171],"synchronize":[172],"leader.":[175],"Finally,":[176],"numerical":[178],"simulation":[179],"validates":[180],"results.":[182]},"counts_by_year":[],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
