{"id":"https://openalex.org/W2885657237","doi":"https://doi.org/10.1007/s10957-018-1363-9","title":"Optimal Leader\u2013Follower Control for the Fractional Opinion Formation Model","display_name":"Optimal Leader\u2013Follower Control for the Fractional Opinion Formation Model","publication_year":2018,"publication_date":"2018-08-10","ids":{"openalex":"https://openalex.org/W2885657237","doi":"https://doi.org/10.1007/s10957-018-1363-9","mag":"2885657237"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-018-1363-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-018-1363-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-018-1363-9.pdf","source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10957-018-1363-9.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035657559","display_name":"Ricardo Almeida","orcid":"https://orcid.org/0000-0002-1305-2411"},"institutions":[{"id":"https://openalex.org/I60858718","display_name":"University of Aveiro","ror":"https://ror.org/00nt41z93","country_code":"PT","type":"education","lineage":["https://openalex.org/I60858718"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Ricardo Almeida","raw_affiliation_strings":["Center for Research and Development in Mathematics ad Applications (CIDMA), Department of Mathematics, University of Aveiro, Aveiro, Portugal"],"affiliations":[{"raw_affiliation_string":"Center for Research and Development in Mathematics ad Applications (CIDMA), Department of Mathematics, University of Aveiro, Aveiro, Portugal","institution_ids":["https://openalex.org/I60858718"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076441274","display_name":"Agnieszka B. Malinowska","orcid":"https://orcid.org/0000-0002-1309-8583"},"institutions":[{"id":"https://openalex.org/I1323121030","display_name":"Bialystok University of Technology","ror":"https://ror.org/02bzfsy61","country_code":"PL","type":"education","lineage":["https://openalex.org/I1323121030"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Agnieszka B. Malinowska","raw_affiliation_strings":["Faculty of Computer Science, Bialystok University of Technology, Bia\u0142ystok, Poland"],"affiliations":[{"raw_affiliation_string":"Faculty of Computer Science, Bialystok University of Technology, Bia\u0142ystok, Poland","institution_ids":["https://openalex.org/I1323121030"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078176392","display_name":"Tatiana Odzijewicz","orcid":"https://orcid.org/0000-0002-4354-9293"},"institutions":[{"id":"https://openalex.org/I18193975","display_name":"SGH Warsaw School of Economics","ror":"https://ror.org/032cph770","country_code":"PL","type":"education","lineage":["https://openalex.org/I18193975"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Tatiana Odzijewicz","raw_affiliation_strings":["Department of Mathematics and Mathematical Economics, Warsaw School of Economics, Warsaw, Poland"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Mathematical Economics, Warsaw School of Economics, Warsaw, Poland","institution_ids":["https://openalex.org/I18193975"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5076441274"],"corresponding_institution_ids":["https://openalex.org/I1323121030"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":1.9968,"has_fulltext":true,"cited_by_count":31,"citation_normalized_percentile":{"value":0.86853961,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"182","issue":"3","first_page":"1171","last_page":"1185"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"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":0.9983999729156494,"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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9947999715805054,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.690488338470459},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.6186739802360535},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.617965042591095},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.599065363407135},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.5873193740844727},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5542181134223938},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5048187375068665},{"id":"https://openalex.org/keywords/integrator","display_name":"Integrator","score":0.49693992733955383},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.45097488164901733},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.42600536346435547},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3490539491176605},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.08287054300308228},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07502087950706482}],"concepts":[{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.690488338470459},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6186739802360535},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.617965042591095},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.599065363407135},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.5873193740844727},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5542181134223938},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5048187375068665},{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.49693992733955383},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.45097488164901733},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.42600536346435547},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3490539491176605},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.08287054300308228},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07502087950706482},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10957-018-1363-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-018-1363-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-018-1363-9.pdf","source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:joptap:v:182:y:2019:i:3:d:10.1007_s10957-018-1363-9","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-018-1363-9","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:ria.ua.pt:10773/26319","is_oa":true,"landing_page_url":"http://hdl.handle.net/10773/26319","pdf_url":null,"source":{"id":"https://openalex.org/S4306402433","display_name":"Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT)","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"journal article"}],"best_oa_location":{"id":"doi:10.1007/s10957-018-1363-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-018-1363-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-018-1363-9.pdf","source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1195261861","display_name":null,"funder_award_id":"project UID/MAT/04","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"},{"id":"https://openalex.org/G1607522747","display_name":null,"funder_award_id":"UID/MAT/04106/2013","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"},{"id":"https://openalex.org/G1886981331","display_name":null,"funder_award_id":"project UID","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"},{"id":"https://openalex.org/G3069120617","display_name":null,"funder_award_id":"04106","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"},{"id":"https://openalex.org/G4149320474","display_name":null,"funder_award_id":"FCT-Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"},{"id":"https://openalex.org/G6751613957","display_name":null,"funder_award_id":"UID/MAT/04106/2013","funder_id":"https://openalex.org/F4320329951","funder_display_name":"Center for Research and Development in Mathematics and Applications"},{"id":"https://openalex.org/G7049410507","display_name":null,"funder_award_id":"Portuguese Foundation for Science","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"},{"id":"https://openalex.org/G878132358","display_name":null,"funder_award_id":"CIDMA","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"},{"id":"https://openalex.org/G943999617","display_name":null,"funder_award_id":"Technology","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"}],"funders":[{"id":"https://openalex.org/F4320329951","display_name":"Center for Research and Development in Mathematics and Applications","ror":null},{"id":"https://openalex.org/F4320334779","display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","ror":"https://ror.org/00snfqn58"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2885657237.pdf","grobid_xml":"https://content.openalex.org/works/W2885657237.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W193812311","https://openalex.org/W196924534","https://openalex.org/W220525228","https://openalex.org/W391578156","https://openalex.org/W861454831","https://openalex.org/W1497317027","https://openalex.org/W1568999108","https://openalex.org/W1610219664","https://openalex.org/W1967024934","https://openalex.org/W1978345715","https://openalex.org/W1982839492","https://openalex.org/W1983603428","https://openalex.org/W1994139361","https://openalex.org/W1998692453","https://openalex.org/W2016570436","https://openalex.org/W2020625830","https://openalex.org/W2022149728","https://openalex.org/W2062163287","https://openalex.org/W2067064980","https://openalex.org/W2105850748","https://openalex.org/W2112090702","https://openalex.org/W2113096089","https://openalex.org/W2120791740","https://openalex.org/W2138678265","https://openalex.org/W2143415130","https://openalex.org/W2159465607","https://openalex.org/W2165744313","https://openalex.org/W2170039048","https://openalex.org/W2299647821","https://openalex.org/W2399155880","https://openalex.org/W2516482828","https://openalex.org/W2610857016","https://openalex.org/W2761428690","https://openalex.org/W2947056241","https://openalex.org/W3099308307","https://openalex.org/W3102103731","https://openalex.org/W4210849352"],"related_works":["https://openalex.org/W2366352762","https://openalex.org/W2613964090","https://openalex.org/W2380425739","https://openalex.org/W2081322886","https://openalex.org/W2001283893","https://openalex.org/W2032860538","https://openalex.org/W2069436786","https://openalex.org/W2053079725","https://openalex.org/W2001500949","https://openalex.org/W2065518442"],"abstract_inverted_index":{"This":[0],"paper":[1],"deals":[2],"with":[3],"an":[4],"opinion":[5,44],"formation":[6],"model,":[7],"that":[8,34,62],"obeys":[9],"a":[10,19,26],"nonlinear":[11],"system":[12],"of":[13,37,45,53],"fractional-order":[14],"differential":[15],"equations.":[16],"We":[17,48],"introduce":[18],"virtual":[20],"leader":[21,60],"in":[22,68,87],"order":[23,88],"to":[24,32,66,79,89],"attain":[25],"consensus.":[27],"Sufficient":[28],"conditions":[29],"are":[30,97],"established":[31],"ensure":[33],"the":[35,43,46,51,59,63,69,81,91],"opinions":[36],"all":[38],"agents":[39],"globally":[40],"asymptotically":[41],"approach":[42],"leader.":[47],"also":[49],"address":[50],"problem":[52],"designing":[54],"optimal":[55,83],"control":[56,84],"strategies":[57],"for":[58],"so":[61],"followers":[64],"tend":[65],"consensus":[67],"most":[70],"efficient":[71],"way.":[72],"A":[73],"variational":[74],"integrator":[75],"scheme":[76],"is":[77],"applied":[78],"solve":[80],"leader\u2013follower":[82],"problem.":[85],"Finally,":[86],"verify":[90],"theoretical":[92],"analysis,":[93],"several":[94],"particular":[95],"examples":[96],"presented.":[98]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
