{"id":"https://openalex.org/W4410500708","doi":"https://doi.org/10.3390/e27050538","title":"Fixed-Time Cooperative Formation Control of Heterogeneous Systems Under Multiple Constraints","display_name":"Fixed-Time Cooperative Formation Control of Heterogeneous Systems Under Multiple Constraints","publication_year":2025,"publication_date":"2025-05-17","ids":{"openalex":"https://openalex.org/W4410500708","doi":"https://doi.org/10.3390/e27050538","pmid":"https://pubmed.ncbi.nlm.nih.gov/40422492"},"language":"en","primary_location":{"id":"doi:10.3390/e27050538","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27050538","pdf_url":"https://www.mdpi.com/1099-4300/27/5/538/pdf?version=1747478563","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"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":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/27/5/538/pdf?version=1747478563","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091431338","display_name":"Yandong Li","orcid":"https://orcid.org/0009-0009-2907-3645"},"institutions":[{"id":"https://openalex.org/I111971639","display_name":"Qiqihar University","ror":"https://ror.org/01khf5d59","country_code":"CN","type":"education","lineage":["https://openalex.org/I111971639"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yandong Li","raw_affiliation_strings":["College of Computer and Control Engineering, Qiqihar University, Qiqihar 161000, China","Heilongjiang Key Laboratory of Big Data Network Security Detection and Analysis, Qiqihar University, Qiqihar 161000, China"],"raw_orcid":"https://orcid.org/0009-0009-2907-3645","affiliations":[{"raw_affiliation_string":"College of Computer and Control Engineering, Qiqihar University, Qiqihar 161000, China","institution_ids":["https://openalex.org/I111971639"]},{"raw_affiliation_string":"Heilongjiang Key Laboratory of Big Data Network Security Detection and Analysis, Qiqihar University, Qiqihar 161000, China","institution_ids":["https://openalex.org/I111971639"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Wei Zhao","orcid":"https://orcid.org/0009-0002-2348-6907"},"institutions":[{"id":"https://openalex.org/I111971639","display_name":"Qiqihar University","ror":"https://ror.org/01khf5d59","country_code":"CN","type":"education","lineage":["https://openalex.org/I111971639"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Wei Zhao","raw_affiliation_strings":["College of Computer and Control Engineering, Qiqihar University, Qiqihar 161000, China","Heilongjiang Key Laboratory of Big Data Network Security Detection and Analysis, Qiqihar University, Qiqihar 161000, China","college of Computer and Control Engineering, Qiqihar University, Qiqihar 161000, China"],"raw_orcid":"https://orcid.org/0009-0002-2348-6907","affiliations":[{"raw_affiliation_string":"College of Computer and Control Engineering, Qiqihar University, Qiqihar 161000, China","institution_ids":["https://openalex.org/I111971639"]},{"raw_affiliation_string":"Heilongjiang Key Laboratory of Big Data Network Security Detection and Analysis, Qiqihar University, Qiqihar 161000, China","institution_ids":["https://openalex.org/I111971639"]},{"raw_affiliation_string":"college of Computer and Control Engineering, Qiqihar University, Qiqihar 161000, China","institution_ids":["https://openalex.org/I111971639"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109111294","display_name":"Ling Zhu","orcid":null},"institutions":[{"id":"https://openalex.org/I111971639","display_name":"Qiqihar University","ror":"https://ror.org/01khf5d59","country_code":"CN","type":"education","lineage":["https://openalex.org/I111971639"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ling Zhu","raw_affiliation_strings":["School of Mechanical and Electrical Engineering, Qiqihar University, Qiqihar 161000, China"],"raw_orcid":"https://orcid.org/0009-0005-0459-1308","affiliations":[{"raw_affiliation_string":"School of Mechanical and Electrical Engineering, Qiqihar University, Qiqihar 161000, China","institution_ids":["https://openalex.org/I111971639"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025001189","display_name":"Zehua Zhang","orcid":"https://orcid.org/0000-0002-1936-2234"},"institutions":[{"id":"https://openalex.org/I111971639","display_name":"Qiqihar University","ror":"https://ror.org/01khf5d59","country_code":"CN","type":"education","lineage":["https://openalex.org/I111971639"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zehua Zhang","raw_affiliation_strings":["College of Computer and Control Engineering, Qiqihar University, Qiqihar 161000, China","Heilongjiang Key Laboratory of Big Data Network Security Detection and Analysis, Qiqihar University, Qiqihar 161000, China","college of Computer and Control Engineering, Qiqihar University, Qiqihar 161000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Computer and Control Engineering, Qiqihar University, Qiqihar 161000, China","institution_ids":["https://openalex.org/I111971639"]},{"raw_affiliation_string":"Heilongjiang Key Laboratory of Big Data Network Security Detection and Analysis, Qiqihar University, Qiqihar 161000, China","institution_ids":["https://openalex.org/I111971639"]},{"raw_affiliation_string":"college of Computer and Control Engineering, Qiqihar University, Qiqihar 161000, China","institution_ids":["https://openalex.org/I111971639"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113010580","display_name":"Yuan Guo","orcid":"https://orcid.org/0000-0001-6997-2316"},"institutions":[{"id":"https://openalex.org/I55022517","display_name":"Heilongjiang University","ror":"https://ror.org/04zyhq975","country_code":"CN","type":"education","lineage":["https://openalex.org/I55022517"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuan Guo","raw_affiliation_strings":["School of Computer and Big Data, Heilongjiang University, Harbin 150080, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer and Big Data, Heilongjiang University, Harbin 150080, China","institution_ids":["https://openalex.org/I55022517"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I111971639"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10579494,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"27","issue":"5","first_page":"538","last_page":"538"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9767000079154968,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9750000238418579,"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-theory","display_name":"Control theory (sociology)","score":0.7567719221115112},{"id":"https://openalex.org/keywords/sliding-mode-control","display_name":"Sliding mode control","score":0.5969729423522949},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5897756814956665},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.5886191725730896},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5193549394607544},{"id":"https://openalex.org/keywords/actuator","display_name":"Actuator","score":0.5106585621833801},{"id":"https://openalex.org/keywords/lyapunov-stability","display_name":"Lyapunov stability","score":0.4999527931213379},{"id":"https://openalex.org/keywords/mode","display_name":"Mode (computer interface)","score":0.4753513038158417},{"id":"https://openalex.org/keywords/protocol","display_name":"Protocol (science)","score":0.44496655464172363},{"id":"https://openalex.org/keywords/tracking","display_name":"Tracking (education)","score":0.418714314699173},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.27524957060813904},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.0910457968711853},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.071787029504776}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.7567719221115112},{"id":"https://openalex.org/C36662352","wikidata":"https://www.wikidata.org/wiki/Q6008560","display_name":"Sliding mode control","level":3,"score":0.5969729423522949},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5897756814956665},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.5886191725730896},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5193549394607544},{"id":"https://openalex.org/C172707124","wikidata":"https://www.wikidata.org/wiki/Q423488","display_name":"Actuator","level":2,"score":0.5106585621833801},{"id":"https://openalex.org/C2776829284","wikidata":"https://www.wikidata.org/wiki/Q1341651","display_name":"Lyapunov stability","level":3,"score":0.4999527931213379},{"id":"https://openalex.org/C48677424","wikidata":"https://www.wikidata.org/wiki/Q6888088","display_name":"Mode (computer interface)","level":2,"score":0.4753513038158417},{"id":"https://openalex.org/C2780385302","wikidata":"https://www.wikidata.org/wiki/Q367158","display_name":"Protocol (science)","level":3,"score":0.44496655464172363},{"id":"https://openalex.org/C2775936607","wikidata":"https://www.wikidata.org/wiki/Q466845","display_name":"Tracking (education)","level":2,"score":0.418714314699173},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.27524957060813904},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0910457968711853},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.071787029504776},{"id":"https://openalex.org/C19417346","wikidata":"https://www.wikidata.org/wiki/Q7922","display_name":"Pedagogy","level":1,"score":0.0},{"id":"https://openalex.org/C142724271","wikidata":"https://www.wikidata.org/wiki/Q7208","display_name":"Pathology","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C204787440","wikidata":"https://www.wikidata.org/wiki/Q188504","display_name":"Alternative medicine","level":2,"score":0.0},{"id":"https://openalex.org/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e27050538","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27050538","pdf_url":"https://www.mdpi.com/1099-4300/27/5/538/pdf?version=1747478563","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"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":"Entropy","raw_type":"journal-article"},{"id":"pmid:40422492","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/40422492","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":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:4923e5fcbd994edea5acd6695c40ee50","is_oa":true,"landing_page_url":"https://doaj.org/article/4923e5fcbd994edea5acd6695c40ee50","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":"Entropy, Vol 27, Iss 5, p 538 (2025)","raw_type":"article"},{"id":"pmh:oai:europepmc.org:10924035","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/12111349","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"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":null,"raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e27050538","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27050538","pdf_url":"https://www.mdpi.com/1099-4300/27/5/538/pdf?version=1747478563","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"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":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G982308803","display_name":null,"funder_award_id":"62473278","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":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4410500708.pdf","grobid_xml":"https://content.openalex.org/works/W4410500708.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W2015113370","https://openalex.org/W2017011168","https://openalex.org/W2289757616","https://openalex.org/W2343840829","https://openalex.org/W2938888561","https://openalex.org/W2939045095","https://openalex.org/W2963882535","https://openalex.org/W3132676906","https://openalex.org/W3196938143","https://openalex.org/W4220974168","https://openalex.org/W4226127943","https://openalex.org/W4242038012","https://openalex.org/W4308687980","https://openalex.org/W4323065078","https://openalex.org/W4387122334","https://openalex.org/W4390952678","https://openalex.org/W4391746568","https://openalex.org/W4393938407","https://openalex.org/W4399243463","https://openalex.org/W4399357254","https://openalex.org/W4401247288","https://openalex.org/W4403467538","https://openalex.org/W4405074271","https://openalex.org/W4406688326","https://openalex.org/W4407695845","https://openalex.org/W4408274459","https://openalex.org/W4408776302"],"related_works":["https://openalex.org/W2099333796","https://openalex.org/W2084086966","https://openalex.org/W2117379282","https://openalex.org/W2534107666","https://openalex.org/W1973429430","https://openalex.org/W2117933783","https://openalex.org/W2354493725","https://openalex.org/W1989996768","https://openalex.org/W2560479139","https://openalex.org/W4282930489"],"abstract_inverted_index":{"This":[0,74],"paper":[1],"proposes":[2],"a":[3,9,36,64,89,94],"fixed-time":[4,66,98],"formation-tracking":[5],"control":[6,70],"problem":[7],"for":[8,44],"heterogeneous":[10,46],"multi-agent":[11],"system":[12,103],"(MAS)":[13],"consisting":[14],"of":[15,100],"six":[16],"unmanned":[17,23],"aerial":[18],"vehicles":[19,25],"(UAVs)":[20],"and":[21,32,41,87],"three":[22],"ground":[24],"(UGVs)":[26],"under":[27],"actuator":[28],"attacks,":[29],"external":[30],"disturbances,":[31],"input":[33],"saturation.":[34],"First,":[35],"distributed":[37,65],"sliding":[38,52,62,68],"mode":[39,53,69],"estimator":[40],"controller":[42],"tailored":[43],"UAV-UGV":[45],"systems":[47],"are":[48],"proposed":[49],"based":[50],"on":[51],"techniques.":[54],"Second,":[55],"by":[56],"integrating":[57],"repulsive":[58],"potential":[59],"functions":[60],"with":[61],"manifolds,":[63],"adaptive":[67],"protocol":[71,75],"was":[72,104],"designed.":[73],"ensures":[76],"collision":[77],"avoidance":[78],"while":[79],"enabling":[80],"the":[81,101],"MASs":[82],"to":[83],"track":[84],"desired":[85],"trajectories":[86],"achieve":[88],"predefined":[90],"formation":[91],"configuration":[92],"within":[93],"fixed":[95],"time.":[96],"The":[97],"stability":[99],"closed-loop":[102],"rigorously":[105],"proven":[106],"via":[107],"Lyapunov":[108],"theory.":[109]},"counts_by_year":[],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}