{"id":"https://openalex.org/W3048785731","doi":"https://doi.org/10.1080/00207721.2020.1803442","title":"Boundary state and output feedbacks for underactuated systems of coupled time-fractional PDEs with different space-dependent diffusivity","display_name":"Boundary state and output feedbacks for underactuated systems of coupled time-fractional PDEs with different space-dependent diffusivity","publication_year":2020,"publication_date":"2020-08-11","ids":{"openalex":"https://openalex.org/W3048785731","doi":"https://doi.org/10.1080/00207721.2020.1803442","mag":"3048785731"},"language":"en","primary_location":{"id":"doi:10.1080/00207721.2020.1803442","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207721.2020.1803442","pdf_url":null,"source":{"id":"https://openalex.org/S129640837","display_name":"International Journal of Systems Science","issn_l":"0020-7721","issn":["0020-7721","1464-5319"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Systems Science","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/A5100359220","display_name":"Juan Chen","orcid":"https://orcid.org/0000-0002-9384-9059"},"institutions":[{"id":"https://openalex.org/I4210153482","display_name":"Changzhou University","ror":"https://ror.org/04ymgwq66","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210153482"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Juan Chen","raw_affiliation_strings":["Aliyun School of Big Data, Changzhou University, Changzhou, Jiangsu, People's Republic of China"],"raw_orcid":"https://orcid.org/0000-0002-9384-9059","affiliations":[{"raw_affiliation_string":"Aliyun School of Big Data, Changzhou University, Changzhou, Jiangsu, People's Republic of China","institution_ids":["https://openalex.org/I4210153482"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062879647","display_name":"Aleksei Tepljakov","orcid":"https://orcid.org/0000-0002-7158-8484"},"institutions":[{"id":"https://openalex.org/I111112146","display_name":"Tallinn University of Technology","ror":"https://ror.org/0443cwa12","country_code":"EE","type":"education","lineage":["https://openalex.org/I111112146"]}],"countries":["EE"],"is_corresponding":false,"raw_author_name":"Aleksei Tepljakov","raw_affiliation_strings":["Department of Computer Systems, Tallinn University of Technology, Tallinn, Estonia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Systems, Tallinn University of Technology, Tallinn, Estonia","institution_ids":["https://openalex.org/I111112146"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061791014","display_name":"Eduard Petlenkov","orcid":"https://orcid.org/0000-0003-2167-6280"},"institutions":[{"id":"https://openalex.org/I111112146","display_name":"Tallinn University of Technology","ror":"https://ror.org/0443cwa12","country_code":"EE","type":"education","lineage":["https://openalex.org/I111112146"]}],"countries":["EE"],"is_corresponding":false,"raw_author_name":"Eduard Petlenkov","raw_affiliation_strings":["Department of Computer Systems, Tallinn University of Technology, Tallinn, Estonia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Systems, Tallinn University of Technology, Tallinn, Estonia","institution_ids":["https://openalex.org/I111112146"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004899662","display_name":"Bo Zhuang","orcid":"https://orcid.org/0000-0002-5362-7347"},"institutions":[{"id":"https://openalex.org/I151013683","display_name":"Binzhou University","ror":"https://ror.org/05frpfj73","country_code":"CN","type":"education","lineage":["https://openalex.org/I151013683"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bo Zhuang","raw_affiliation_strings":["School of Information Engineering, Binzhou University, Binzhou, Shandong, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information Engineering, Binzhou University, Binzhou, Shandong, People's Republic of China","institution_ids":["https://openalex.org/I151013683"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100359220"],"corresponding_institution_ids":["https://openalex.org/I4210153482"],"apc_list":null,"apc_paid":null,"fwci":1.3406,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.80653549,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"51","issue":"15","first_page":"2922","last_page":"2942"},"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":1.0,"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":1.0,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9994000196456909,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7106449604034424},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6269335150718689},{"id":"https://openalex.org/keywords/underactuation","display_name":"Underactuation","score":0.5646197199821472},{"id":"https://openalex.org/keywords/backstepping","display_name":"Backstepping","score":0.5230987071990967},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.49715855717658997},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.49243053793907166},{"id":"https://openalex.org/keywords/observer","display_name":"Observer (physics)","score":0.44502827525138855},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.432951956987381},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.42989397048950195},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.4259633719921112},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.418088436126709},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.41758596897125244},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4050338566303253},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.21125373244285583},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1910073459148407},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.12445127964019775},{"id":"https://openalex.org/keywords/adaptive-control","display_name":"Adaptive control","score":0.08348298072814941}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7106449604034424},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6269335150718689},{"id":"https://openalex.org/C88337583","wikidata":"https://www.wikidata.org/wiki/Q7883433","display_name":"Underactuation","level":3,"score":0.5646197199821472},{"id":"https://openalex.org/C72218879","wikidata":"https://www.wikidata.org/wiki/Q4839759","display_name":"Backstepping","level":4,"score":0.5230987071990967},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.49715855717658997},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.49243053793907166},{"id":"https://openalex.org/C2780704645","wikidata":"https://www.wikidata.org/wiki/Q9251458","display_name":"Observer (physics)","level":2,"score":0.44502827525138855},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.432951956987381},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.42989397048950195},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.4259633719921112},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.418088436126709},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.41758596897125244},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4050338566303253},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.21125373244285583},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1910073459148407},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.12445127964019775},{"id":"https://openalex.org/C107464732","wikidata":"https://www.wikidata.org/wiki/Q235781","display_name":"Adaptive control","level":3,"score":0.08348298072814941},{"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00207721.2020.1803442","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207721.2020.1803442","pdf_url":null,"source":{"id":"https://openalex.org/S129640837","display_name":"International Journal of Systems Science","issn_l":"0020-7721","issn":["0020-7721","1464-5319"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Systems Science","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:taf:tsysxx:v:51:y:2020:i:15:p:2922-2942","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1080/00207721.2020.1803442","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G481259056","display_name":null,"funder_award_id":"CA15225","funder_id":"https://openalex.org/F4320320366","funder_display_name":"European Cooperation in Science and Technology"},{"id":"https://openalex.org/G5168270418","display_name":"Intelligent Control Systems for Industry 4.0","funder_award_id":"PRG658","funder_id":"https://openalex.org/F4320321090","funder_display_name":"Eesti Teadusagentuur"},{"id":"https://openalex.org/G744207293","display_name":null,"funder_award_id":"61807016","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320320366","display_name":"European Cooperation in Science and Technology","ror":"https://ror.org/01bstzn19"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321090","display_name":"Eesti Teadusagentuur","ror":"https://ror.org/00jjeja18"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W56786142","https://openalex.org/W1498121547","https://openalex.org/W1538686203","https://openalex.org/W1584611818","https://openalex.org/W1602967628","https://openalex.org/W1970761971","https://openalex.org/W1984569254","https://openalex.org/W2000800671","https://openalex.org/W2004202105","https://openalex.org/W2018912503","https://openalex.org/W2019091709","https://openalex.org/W2028776471","https://openalex.org/W2030959812","https://openalex.org/W2044988885","https://openalex.org/W2058860728","https://openalex.org/W2078854980","https://openalex.org/W2103660039","https://openalex.org/W2114990297","https://openalex.org/W2119967247","https://openalex.org/W2121855948","https://openalex.org/W2142366499","https://openalex.org/W2192767319","https://openalex.org/W2313006060","https://openalex.org/W2334095483","https://openalex.org/W2338309093","https://openalex.org/W2351511374","https://openalex.org/W2499641798","https://openalex.org/W2734910713","https://openalex.org/W2749610394","https://openalex.org/W2763112268","https://openalex.org/W2782251405","https://openalex.org/W2787959293","https://openalex.org/W2796097038","https://openalex.org/W2808914739","https://openalex.org/W2896621584","https://openalex.org/W2898426056","https://openalex.org/W2901506668","https://openalex.org/W2938010592","https://openalex.org/W2947233008","https://openalex.org/W2952000941","https://openalex.org/W2963411237","https://openalex.org/W2964026536","https://openalex.org/W3002671726","https://openalex.org/W3007442310","https://openalex.org/W3009695939","https://openalex.org/W3016826875","https://openalex.org/W3019775607","https://openalex.org/W4252280335"],"related_works":["https://openalex.org/W1765905465","https://openalex.org/W2793080664","https://openalex.org/W2186140227","https://openalex.org/W2132535444","https://openalex.org/W2500162090","https://openalex.org/W2046770915","https://openalex.org/W2217718355","https://openalex.org/W2369318130","https://openalex.org/W3205444542","https://openalex.org/W1498122250"],"abstract_inverted_index":{"This":[0],"paper":[1],"considers":[2],"the":[3,45,53,72,75,83,87,91,94,121,124,128,131],"boundary":[4,46,77,103],"stabilisation":[5,108],"problem":[6],"of":[7,11,39,56,86,93,101,123],"an":[8,137],"underactuated":[9,30],"system":[10,55,89],"coupled":[12],"time-fractional":[13],"partial":[14],"differential":[15],"equations":[16,41],"(PDEs)":[17],"with":[18,90],"different":[19],"space-dependent":[20],"diffusivity":[21],"by":[22],"state":[23],"and":[24,37,105],"observer-based":[25],"output":[26,106],"feedback.":[27],"For":[28],"this":[29],"system,":[31],"there":[32],"are":[33,42,109],"n":[34,40,57],"fractional":[35,58,114],"equations,":[36],"n\u22121":[38,49],"actuated":[43],"at":[44],"inputs,":[47],"i.e.":[48],"available":[50],"inputs":[51],"control":[52,68],"entire":[54],"equations.":[59,70],"In":[60],"other":[61],"words,":[62],"we":[63],"do":[64],"not":[65,136],"need":[66],"to":[67,81,119],"all":[69],"Using":[71],"backstepping":[73],"mapping,":[74],"Dirichlet":[76],"controller":[78],"is":[79,117],"derived":[80],"enable":[82],"Mittag\u2013Leffler":[84,99],"stability":[85],"closed-loop":[88],"aid":[92],"Lyapunov":[95],"direct":[96],"method.":[97],"The":[98],"convergence":[100],"designed":[102],"observer":[104],"feedback":[107],"subsequently":[110],"proved.":[111],"Finally,":[112],"a":[113],"numerical":[115],"example":[116],"provided":[118],"support":[120],"effectiveness":[122],"proposed":[125],"synthesis":[126],"for":[127],"case":[129],"when":[130],"kernel":[132],"matrix":[133],"PDE":[134],"has":[135],"explicit":[138],"solution.":[139]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2020,"cited_by_count":1}],"updated_date":"2026-06-22T08:00:12.763002","created_date":"2025-10-10T00:00:00"}
