{"id":"https://openalex.org/W2887042745","doi":"https://doi.org/10.1080/00207179.2018.1506888","title":"Numerical solution of some initial optimal control problems using the reproducing kernel Hilbert space technique","display_name":"Numerical solution of some initial optimal control problems using the reproducing kernel Hilbert space technique","publication_year":2018,"publication_date":"2018-07-31","ids":{"openalex":"https://openalex.org/W2887042745","doi":"https://doi.org/10.1080/00207179.2018.1506888","mag":"2887042745"},"language":"en","primary_location":{"id":"doi:10.1080/00207179.2018.1506888","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207179.2018.1506888","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"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 Control","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/A5017126060","display_name":"Fereshteh Toutian Isfahani","orcid":null},"institutions":[{"id":"https://openalex.org/I112536369","display_name":"Yazd University","ror":"https://ror.org/02x99ac45","country_code":"IR","type":"education","lineage":["https://openalex.org/I112536369"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"F. Toutian Isfahani","raw_affiliation_strings":["Department of Mathematics, Yazd University, Yazd, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Yazd University, Yazd, Iran","institution_ids":["https://openalex.org/I112536369"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026699953","display_name":"Reza Mokhtari","orcid":"https://orcid.org/0000-0002-1420-0949"},"institutions":[{"id":"https://openalex.org/I170013655","display_name":"Isfahan University of Technology","ror":"https://ror.org/00af3sa43","country_code":"IR","type":"education","lineage":["https://openalex.org/I170013655"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"R. Mokhtari","raw_affiliation_strings":["Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran","institution_ids":["https://openalex.org/I170013655"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109482552","display_name":"Ghasem Barid Loghmani","orcid":null},"institutions":[{"id":"https://openalex.org/I112536369","display_name":"Yazd University","ror":"https://ror.org/02x99ac45","country_code":"IR","type":"education","lineage":["https://openalex.org/I112536369"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"G. B. Loghmani","raw_affiliation_strings":["Department of Mathematics, Yazd University, Yazd, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Yazd University, Yazd, Iran","institution_ids":["https://openalex.org/I112536369"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084388978","display_name":"Maryam Mohammadi","orcid":"https://orcid.org/0009-0007-4485-8446"},"institutions":[{"id":"https://openalex.org/I181744264","display_name":"Kharazmi University","ror":"https://ror.org/05hsgex59","country_code":"IR","type":"education","lineage":["https://openalex.org/I181744264"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"M. Mohammadi","raw_affiliation_strings":["Department of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran","institution_ids":["https://openalex.org/I181744264"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5109482552"],"corresponding_institution_ids":["https://openalex.org/I112536369"],"apc_list":null,"apc_paid":null,"fwci":2.7306,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.8983599,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"93","issue":"6","first_page":"1345","last_page":"1352"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9980000257492065,"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":0.9980000257492065,"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/T13855","display_name":"Aerospace Engineering and Control Systems","score":0.9979000091552734,"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/T11082","display_name":"Spacecraft Dynamics and Control","score":0.9958000183105469,"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/reproducing-kernel-hilbert-space","display_name":"Reproducing kernel Hilbert space","score":0.7864639759063721},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.7508832812309265},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7305995225906372},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.6945224404335022},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.6743885278701782},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6159353256225586},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.6121962070465088},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5566481351852417},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.5466816425323486},{"id":"https://openalex.org/keywords/state-variable","display_name":"State variable","score":0.5040208697319031},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5018153190612793},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.46655505895614624},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.43766531348228455},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4206574559211731},{"id":"https://openalex.org/keywords/representer-theorem","display_name":"Representer theorem","score":0.4182165265083313},{"id":"https://openalex.org/keywords/control-variable","display_name":"Control variable","score":0.41709643602371216},{"id":"https://openalex.org/keywords/kernel-method","display_name":"Kernel method","score":0.3462541401386261},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2608698606491089},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22363576292991638},{"id":"https://openalex.org/keywords/kernel-embedding-of-distributions","display_name":"Kernel embedding of distributions","score":0.20207899808883667}],"concepts":[{"id":"https://openalex.org/C80884492","wikidata":"https://www.wikidata.org/wiki/Q3345678","display_name":"Reproducing kernel Hilbert space","level":3,"score":0.7864639759063721},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.7508832812309265},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7305995225906372},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6945224404335022},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.6743885278701782},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6159353256225586},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.6121962070465088},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5566481351852417},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.5466816425323486},{"id":"https://openalex.org/C129537906","wikidata":"https://www.wikidata.org/wiki/Q7603913","display_name":"State variable","level":2,"score":0.5040208697319031},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5018153190612793},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.46655505895614624},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.43766531348228455},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4206574559211731},{"id":"https://openalex.org/C172623408","wikidata":"https://www.wikidata.org/wiki/Q7314263","display_name":"Representer theorem","level":5,"score":0.4182165265083313},{"id":"https://openalex.org/C153240184","wikidata":"https://www.wikidata.org/wiki/Q3243772","display_name":"Control variable","level":2,"score":0.41709643602371216},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.3462541401386261},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2608698606491089},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22363576292991638},{"id":"https://openalex.org/C134517425","wikidata":"https://www.wikidata.org/wiki/Q16000131","display_name":"Kernel embedding of distributions","level":4,"score":0.20207899808883667},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00207179.2018.1506888","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207179.2018.1506888","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"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 Control","raw_type":"journal-article"},{"id":"pmh:oai:www.research.unipd.it:11577/3468698","is_oa":false,"landing_page_url":"https://hdl.handle.net/11577/3468698","pdf_url":null,"source":{"id":"https://openalex.org/S4306402547","display_name":"Padua Research Archive (University of Padova)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I138689650","host_organization_name":"University of Padua","host_organization_lineage":["https://openalex.org/I138689650"],"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":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":55,"referenced_works":["https://openalex.org/W357773498","https://openalex.org/W565431999","https://openalex.org/W1514799972","https://openalex.org/W1527525543","https://openalex.org/W1929307632","https://openalex.org/W1967416910","https://openalex.org/W1985249384","https://openalex.org/W1986280275","https://openalex.org/W1995326656","https://openalex.org/W1996247133","https://openalex.org/W2000226979","https://openalex.org/W2002666445","https://openalex.org/W2010050675","https://openalex.org/W2013324146","https://openalex.org/W2014822975","https://openalex.org/W2017977027","https://openalex.org/W2020498805","https://openalex.org/W2022648092","https://openalex.org/W2029874783","https://openalex.org/W2031291057","https://openalex.org/W2033408818","https://openalex.org/W2034438020","https://openalex.org/W2043848760","https://openalex.org/W2049125855","https://openalex.org/W2053391813","https://openalex.org/W2055443629","https://openalex.org/W2057437701","https://openalex.org/W2059586616","https://openalex.org/W2068170870","https://openalex.org/W2100571430","https://openalex.org/W2107345353","https://openalex.org/W2120688585","https://openalex.org/W2122410365","https://openalex.org/W2128370777","https://openalex.org/W2131820185","https://openalex.org/W2134298283","https://openalex.org/W2137740319","https://openalex.org/W2140630087","https://openalex.org/W2145487433","https://openalex.org/W2161137845","https://openalex.org/W2188556074","https://openalex.org/W2190591480","https://openalex.org/W2334591577","https://openalex.org/W2407894843","https://openalex.org/W2441384902","https://openalex.org/W2489467106","https://openalex.org/W2596467784","https://openalex.org/W2596553520","https://openalex.org/W2772687319","https://openalex.org/W2787991034","https://openalex.org/W2974720244","https://openalex.org/W3022423118","https://openalex.org/W3123320253","https://openalex.org/W3135608841","https://openalex.org/W4400944146"],"related_works":["https://openalex.org/W2038278625","https://openalex.org/W2392804273","https://openalex.org/W1517937628","https://openalex.org/W2964184113","https://openalex.org/W2896419989","https://openalex.org/W4298112926","https://openalex.org/W2094771605","https://openalex.org/W2154558852","https://openalex.org/W2119647995","https://openalex.org/W2887042745"],"abstract_inverted_index":{"In":[0,17],"this":[1,45],"paper,":[2],"we":[3,48],"present":[4,51],"a":[5,10,32,35,57],"general":[6],"technique":[7],"for":[8],"solving":[9],"class":[11],"of":[12,22,31,44,83,100],"linear/nonlinear":[13],"optimal":[14,53,69],"control":[15,54,70],"problems.":[16],"fact,":[18],"an":[19],"analytical":[20],"solution":[21],"the":[23,29,42,52,67,75,84,96,101],"state":[24,72],"variable":[25,55],"is":[26,63,78,86],"represented":[27],"in":[28,34,56],"form":[30],"series":[33,46,58],"reproducing":[36],"kernel":[37],"Hilbert":[38],"space.":[39],"Sometimes":[40],"with":[41],"aid":[43],"form,":[47],"can":[49],"also":[50,87],"form.":[59],"An":[60],"iterative":[61],"method":[62,85],"given":[64],"to":[65,94],"obtain":[66],"approximate":[68],"and":[71,74,98],"variables":[73],"cost":[76],"functional":[77],"numerically":[79],"obtained.":[80],"Convergence":[81],"analysis":[82],"provided.":[88],"Several":[89],"numerical":[90],"examples":[91],"are":[92],"tested":[93],"demonstrate":[95],"applicability":[97],"efficiency":[99],"method.":[102]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":2}],"updated_date":"2026-04-15T08:11:43.952461","created_date":"2025-10-10T00:00:00"}