{"id":"https://openalex.org/W4376505226","doi":"https://doi.org/10.1080/00207721.2023.2210140","title":"Sub-optimal controller design for time-delay nonlinear partial differential equation systems: an extended state-dependent differential Riccati equation approach","display_name":"Sub-optimal controller design for time-delay nonlinear partial differential equation systems: an extended state-dependent differential Riccati equation approach","publication_year":2023,"publication_date":"2023-05-13","ids":{"openalex":"https://openalex.org/W4376505226","doi":"https://doi.org/10.1080/00207721.2023.2210140"},"language":"en","primary_location":{"id":"doi:10.1080/00207721.2023.2210140","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207721.2023.2210140","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/A5031011762","display_name":"Fariba Bouzari Liavoli","orcid":null},"institutions":[{"id":"https://openalex.org/I197220011","display_name":"Qazvin Islamic Azad University","ror":"https://ror.org/023kjn321","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I197220011"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Fariba Bouzari Liavoli","raw_affiliation_strings":["Department of Electrical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran","institution_ids":["https://openalex.org/I197220011"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023056265","display_name":"Ahmad Fakharian","orcid":"https://orcid.org/0000-0002-6530-2689"},"institutions":[{"id":"https://openalex.org/I197220011","display_name":"Qazvin Islamic Azad University","ror":"https://ror.org/023kjn321","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I197220011"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Ahmad Fakharian","raw_affiliation_strings":["Department of Electrical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran","institution_ids":["https://openalex.org/I197220011"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052551953","display_name":"Hamid Khaloozadeh","orcid":"https://orcid.org/0000-0002-6948-8898"},"institutions":[{"id":"https://openalex.org/I80543232","display_name":"K.N.Toosi University of Technology","ror":"https://ror.org/0433abe34","country_code":"IR","type":"education","lineage":["https://openalex.org/I80543232"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Hamid Khaloozadeh","raw_affiliation_strings":["Department of Systems and Control Engineering, K.N. Toosi University of Technology, Tehran, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Systems and Control Engineering, K.N. Toosi University of Technology, Tehran, Iran","institution_ids":["https://openalex.org/I80543232"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5023056265"],"corresponding_institution_ids":["https://openalex.org/I197220011"],"apc_list":null,"apc_paid":null,"fwci":3.295,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.91685972,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"54","issue":"8","first_page":"1815","last_page":"1840"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9975000023841858,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/riccati-equation","display_name":"Riccati equation","score":0.7742044925689697},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6886544823646545},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6681957244873047},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6335211992263794},{"id":"https://openalex.org/keywords/algebraic-riccati-equation","display_name":"Algebraic Riccati equation","score":0.5504039525985718},{"id":"https://openalex.org/keywords/first-order-partial-differential-equation","display_name":"First-order partial differential equation","score":0.4909832775592804},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.47396963834762573},{"id":"https://openalex.org/keywords/delay-differential-equation","display_name":"Delay differential equation","score":0.4731256365776062},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4680319130420685},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.44859540462493896},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.43599367141723633},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.43219423294067383},{"id":"https://openalex.org/keywords/linear-quadratic-regulator","display_name":"Linear-quadratic regulator","score":0.431412935256958},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38303959369659424},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.21672075986862183},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2039150595664978},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19247177243232727},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.15878257155418396}],"concepts":[{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.7742044925689697},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6886544823646545},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6681957244873047},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6335211992263794},{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.5504039525985718},{"id":"https://openalex.org/C64057670","wikidata":"https://www.wikidata.org/wiki/Q4381442","display_name":"First-order partial differential equation","level":3,"score":0.4909832775592804},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.47396963834762573},{"id":"https://openalex.org/C147504518","wikidata":"https://www.wikidata.org/wiki/Q2146125","display_name":"Delay differential equation","level":3,"score":0.4731256365776062},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4680319130420685},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.44859540462493896},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.43599367141723633},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.43219423294067383},{"id":"https://openalex.org/C98779006","wikidata":"https://www.wikidata.org/wiki/Q2520550","display_name":"Linear-quadratic regulator","level":3,"score":0.431412935256958},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38303959369659424},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.21672075986862183},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2039150595664978},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19247177243232727},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.15878257155418396},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00207721.2023.2210140","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207721.2023.2210140","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:54:y:2023:i:8:p:1815-1840","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1080/00207721.2023.2210140","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":[{"display_name":"Peace, Justice and strong institutions","score":0.6600000262260437,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W585700782","https://openalex.org/W636879645","https://openalex.org/W1503437626","https://openalex.org/W1996545061","https://openalex.org/W1996909963","https://openalex.org/W2019870189","https://openalex.org/W2029382655","https://openalex.org/W2047397174","https://openalex.org/W2050025137","https://openalex.org/W2052005863","https://openalex.org/W2055027817","https://openalex.org/W2065236818","https://openalex.org/W2067156923","https://openalex.org/W2070024986","https://openalex.org/W2072425162","https://openalex.org/W2075889787","https://openalex.org/W2337334738","https://openalex.org/W2553259921","https://openalex.org/W2783707692","https://openalex.org/W2805198874","https://openalex.org/W2904138759","https://openalex.org/W2936648092","https://openalex.org/W2962913568","https://openalex.org/W2964637086","https://openalex.org/W2969342520","https://openalex.org/W2980163112","https://openalex.org/W2992411408","https://openalex.org/W3041250999","https://openalex.org/W3047093050","https://openalex.org/W3084100068","https://openalex.org/W3089240736","https://openalex.org/W3094291660","https://openalex.org/W3105727068","https://openalex.org/W3126426912","https://openalex.org/W3154491491","https://openalex.org/W3161997542","https://openalex.org/W3192523917","https://openalex.org/W3193483929","https://openalex.org/W4206318793","https://openalex.org/W4213062467","https://openalex.org/W4292079189"],"related_works":["https://openalex.org/W2005019312","https://openalex.org/W2547959172","https://openalex.org/W2018296362","https://openalex.org/W2002357820","https://openalex.org/W197349956","https://openalex.org/W2997206142","https://openalex.org/W2804494800","https://openalex.org/W2027962246","https://openalex.org/W2244442793","https://openalex.org/W2116228702"],"abstract_inverted_index":{"In":[0,43],"this":[1,44],"article,":[2],"a":[3,17,63,67,100],"sub-optimal":[4,75],"controller":[5],"based":[6,90],"on":[7,79,91],"Extended":[8],"State-Dependent":[9,38],"Differential":[10,23],"Riccati":[11],"Equation":[12,24],"(ESDDRE)":[13],"is":[14,41,82,96],"suggested":[15],"for":[16,34,111],"class":[18],"of":[19,86,121],"time-delay":[20,48,113],"nonlinear":[21,114],"Partial":[22],"(PDE)":[25],"systems.":[26],"At":[27],"first,":[28],"an":[29],"extended":[30],"pseudo":[31],"linearisation":[32],"presentation":[33],"parameterisation":[35],"form":[36],"using":[37,99],"Coefficients":[39],"(SDC)":[40],"proposed.":[42],"presentation,":[45],"all":[46],"the":[47,71,74,80,87,92,118,122],"parts":[49],"are":[50],"placed":[51],"in":[52,58],"system":[53,89],"matrices":[54],"as":[55,57],"well":[56],"input":[59],"vectors.":[60],"By":[61],"defining":[62],"cost":[64],"function":[65,103],"and":[66,104],"Hamiltonian":[68],"related":[69],"to":[70],"PDE":[72,115],"systems,":[73],"control":[76,94,124],"law":[77],"regarded":[78],"ESDDRE":[81,93],"obtained.":[83],"The":[84],"stability":[85],"closed-loop":[88],"approach":[95],"ensured":[97],"by":[98],"proper":[101],"Lyapunov":[102],"also":[105],"Poincar\u00e9":[106],"inequality.":[107],"Numerical":[108],"simulation":[109],"results":[110],"three":[112],"systems":[116],"illustrate":[117],"appropriate":[119],"performance":[120],"proposed":[123],"approach.":[125]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}