{"id":"https://openalex.org/W4213224558","doi":"https://doi.org/10.3390/e24020305","title":"Optimal UAV Formation Tracking Control with Dynamic Leading Velocity and Network-Induced Delays","display_name":"Optimal UAV Formation Tracking Control with Dynamic Leading Velocity and Network-Induced Delays","publication_year":2022,"publication_date":"2022-02-21","ids":{"openalex":"https://openalex.org/W4213224558","doi":"https://doi.org/10.3390/e24020305","pmid":"https://pubmed.ncbi.nlm.nih.gov/35205598"},"language":"en","primary_location":{"id":"doi:10.3390/e24020305","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24020305","pdf_url":"https://www.mdpi.com/1099-4300/24/2/305/pdf?version=1645525828","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/1099-4300/24/2/305/pdf?version=1645525828","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084779219","display_name":"Zhuwei Wang","orcid":"https://orcid.org/0000-0002-2880-3329"},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhuwei Wang","raw_affiliation_strings":["Faculty of Information Technology, Beijing University of Technology, Beijing 100124, China"],"raw_orcid":"https://orcid.org/0000-0002-2880-3329","affiliations":[{"raw_affiliation_string":"Faculty of Information Technology, Beijing University of Technology, Beijing 100124, China","institution_ids":["https://openalex.org/I37796252"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028650902","display_name":"Mengjiao Xu","orcid":null},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Mengjiao Xu","raw_affiliation_strings":["Faculty of Information Technology, Beijing University of Technology, Beijing 100124, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Information Technology, Beijing University of Technology, Beijing 100124, China","institution_ids":["https://openalex.org/I37796252"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063375819","display_name":"Lihan Liu","orcid":"https://orcid.org/0000-0002-0689-2332"},"institutions":[{"id":"https://openalex.org/I176432857","display_name":"Beijing Wuzi University","ror":"https://ror.org/00bd1d647","country_code":"CN","type":"education","lineage":["https://openalex.org/I176432857"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Lihan Liu","raw_affiliation_strings":["School of Information, Beijing Wuzi University, Beijing 101149, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information, Beijing Wuzi University, Beijing 101149, China","institution_ids":["https://openalex.org/I176432857"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062252654","display_name":"Chao Fang","orcid":"https://orcid.org/0000-0002-3989-3964"},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]},{"id":"https://openalex.org/I4210155350","display_name":"Purple Mountain Laboratories","ror":"https://ror.org/04zcbk583","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210155350"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chao Fang","raw_affiliation_strings":["Faculty of Information Technology, Beijing University of Technology, Beijing 100124, China","Purple Mountain Laboratory: Networking, Communications and Security, Nanjing 210096, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Information Technology, Beijing University of Technology, Beijing 100124, China","institution_ids":["https://openalex.org/I37796252"]},{"raw_affiliation_string":"Purple Mountain Laboratory: Networking, Communications and Security, Nanjing 210096, China","institution_ids":["https://openalex.org/I4210155350"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013105152","display_name":"Yang Sun","orcid":"https://orcid.org/0000-0001-8470-3982"},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yang Sun","raw_affiliation_strings":["Faculty of Information Technology, Beijing University of Technology, Beijing 100124, China"],"raw_orcid":"https://orcid.org/0000-0001-8470-3982","affiliations":[{"raw_affiliation_string":"Faculty of Information Technology, Beijing University of Technology, Beijing 100124, China","institution_ids":["https://openalex.org/I37796252"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101790570","display_name":"Hua\u2010Min Chen","orcid":"https://orcid.org/0000-0002-2799-6464"},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huamin Chen","raw_affiliation_strings":["Faculty of Information Technology, Beijing University of Technology, Beijing 100124, China"],"raw_orcid":"https://orcid.org/0000-0002-2799-6464","affiliations":[{"raw_affiliation_string":"Faculty of Information Technology, Beijing University of Technology, Beijing 100124, China","institution_ids":["https://openalex.org/I37796252"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5063375819"],"corresponding_institution_ids":["https://openalex.org/I176432857"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":3.6135,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.93159534,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"24","issue":"2","first_page":"305","last_page":"305"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11133","display_name":"UAV Applications and Optimization","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11133","display_name":"UAV Applications and Optimization","score":0.9998000264167786,"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9994999766349792,"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":0.9677000045776367,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.7273094058036804},{"id":"https://openalex.org/keywords/tracking","display_name":"Tracking (education)","score":0.6315827369689941},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5821080803871155},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.568304181098938},{"id":"https://openalex.org/keywords/position","display_name":"Position (finance)","score":0.54340660572052},{"id":"https://openalex.org/keywords/tracking-error","display_name":"Tracking error","score":0.4720861613750458},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.47069787979125977},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3330819606781006},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3063734173774719}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.7273094058036804},{"id":"https://openalex.org/C2775936607","wikidata":"https://www.wikidata.org/wiki/Q466845","display_name":"Tracking (education)","level":2,"score":0.6315827369689941},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5821080803871155},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.568304181098938},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.54340660572052},{"id":"https://openalex.org/C183356978","wikidata":"https://www.wikidata.org/wiki/Q1779213","display_name":"Tracking error","level":3,"score":0.4720861613750458},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.47069787979125977},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3330819606781006},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3063734173774719},{"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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e24020305","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24020305","pdf_url":"https://www.mdpi.com/1099-4300/24/2/305/pdf?version=1645525828","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:35205598","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/35205598","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:a1685a1619c248d7b910e6720b4f6d66","is_oa":true,"landing_page_url":"https://doaj.org/article/a1685a1619c248d7b910e6720b4f6d66","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 24, Iss 2, p 305 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/24/2/305/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e24020305","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Entropy; Volume 24; Issue 2; Pages: 305","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:8871154","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/8871154","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e24020305","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24020305","pdf_url":"https://www.mdpi.com/1099-4300/24/2/305/pdf?version=1645525828","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/G5367626508","display_name":null,"funder_award_id":"61901011","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5750651708","display_name":null,"funder_award_id":"62001011","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6976746248","display_name":null,"funder_award_id":"L202016","funder_id":"https://openalex.org/F4320322919","funder_display_name":"Natural Science Foundation of Beijing Municipality"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322919","display_name":"Natural Science Foundation of Beijing Municipality","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4213224558.pdf"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W1980755499","https://openalex.org/W1983818779","https://openalex.org/W2042733674","https://openalex.org/W2066544832","https://openalex.org/W2095712111","https://openalex.org/W2105850748","https://openalex.org/W2119693819","https://openalex.org/W2140665365","https://openalex.org/W2142714685","https://openalex.org/W2150336603","https://openalex.org/W2278415548","https://openalex.org/W2294622247","https://openalex.org/W2302167001","https://openalex.org/W2327622231","https://openalex.org/W2342656438","https://openalex.org/W2512487235","https://openalex.org/W2522615148","https://openalex.org/W2533738230","https://openalex.org/W2571149404","https://openalex.org/W2599854673","https://openalex.org/W2762304185","https://openalex.org/W2795219039","https://openalex.org/W2797090510","https://openalex.org/W2808472015","https://openalex.org/W2907962963","https://openalex.org/W2909440388","https://openalex.org/W2924288577","https://openalex.org/W2962691117","https://openalex.org/W2963569053","https://openalex.org/W2963580658","https://openalex.org/W2963638537","https://openalex.org/W2969429360","https://openalex.org/W2987256267","https://openalex.org/W3084461364","https://openalex.org/W3084579523","https://openalex.org/W3106792093"],"related_works":["https://openalex.org/W2996812256","https://openalex.org/W2525543468","https://openalex.org/W2026490863","https://openalex.org/W1996877595","https://openalex.org/W2366743900","https://openalex.org/W2389929639","https://openalex.org/W2369313712","https://openalex.org/W2380496977","https://openalex.org/W2351548249","https://openalex.org/W2099967431"],"abstract_inverted_index":{"With":[0],"the":[1,7,19,39,51,67,86,90,93,105,125,131,136,154,159,166,183,186,200],"rapid":[2],"development":[3],"of":[4,9,26,43,71,88,99,104,112,168,185,202],"UAV":[5,11,72,189],"technology,":[6],"research":[8],"optimal":[10,52,108,188],"formation":[12,29,53,109],"tracking":[13,30,110],"has":[14],"been":[15],"extensively":[16],"studied.":[17],"However,":[18],"high":[20],"maneuverability":[21],"and":[22,48,59,95,101,123,149,165,195],"dynamic":[23,41,61,133,196],"network":[24],"topology":[25],"UAVs":[27],"make":[28],"control":[31,54,62,169,197],"much":[32],"more":[33],"difficult.":[34],"In":[35],"this":[36],"paper,":[37],"considering":[38],"highly":[40],"features":[42],"uncertain":[44,141],"time-varying":[45,142],"leader":[46,137],"velocity":[47,100],"network-induced":[49,203],"delays,":[50],"algorithms":[55],"for":[56],"both":[57,193],"near-equilibrium":[58,113,194],"general":[60,132,160],"cases":[63,114,198],"are":[64,75,127,147],"developed.":[65],"First,":[66],"discrete-time":[68],"error":[69],"dynamics":[70,157],"leader-follower":[73],"models":[74],"analyzed.":[76],"Next,":[77],"a":[78,119],"linear":[79],"quadratic":[80],"optimization":[81],"problem":[82,111],"is":[83,115,151],"formulated":[84],"with":[85],"objective":[87],"minimizing":[89],"errors":[91],"between":[92],"desired":[94],"actual":[96,177],"states":[97],"consisting":[98],"position":[102],"information":[103],"follower.":[106],"The":[107],"addressed":[116],"by":[117],"using":[118,176],"backward":[120],"recursion":[121],"method,":[122],"then":[124],"results":[126],"further":[128],"extended":[129],"to":[130,158],"case":[134,161],"where":[135],"moves":[138],"at":[139],"an":[140],"velocity.":[143],"Additionally,":[144],"angle":[145],"deviations":[146],"investigated,":[148],"it":[150],"proved":[152],"that":[153],"similar":[155],"state":[156],"can":[162,172],"be":[163,173],"derived":[164],"principle":[167],"strategy":[170],"design":[171],"maintained.":[174],"By":[175],"real-world":[178],"data,":[179],"numerical":[180],"experiments":[181],"verify":[182],"effectiveness":[184],"proposed":[187],"formation-tracking":[190],"algorithm":[191],"in":[192,199],"presence":[201],"delays.":[204]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}
