{"id":"https://openalex.org/W2327668930","doi":"https://doi.org/10.1109/tac.2016.2547979","title":"An Iterative Method for Nonlinear Stochastic Optimal Control Based on Path Integrals","display_name":"An Iterative Method for Nonlinear Stochastic Optimal Control Based on Path Integrals","publication_year":2016,"publication_date":"2016-03-29","ids":{"openalex":"https://openalex.org/W2327668930","doi":"https://doi.org/10.1109/tac.2016.2547979","mag":"2327668930"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2016.2547979","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2016.2547979","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic 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/A5006166354","display_name":"Satoshi Satoh","orcid":"https://orcid.org/0000-0003-4017-5123"},"institutions":[{"id":"https://openalex.org/I113306721","display_name":"Hiroshima University","ror":"https://ror.org/03t78wx29","country_code":"JP","type":"education","lineage":["https://openalex.org/I113306721"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Satoshi Satoh","raw_affiliation_strings":["Division of Mechanical Systems and Applied Mechanics, Faculty of Engineering, Hiroshima University, Higashi-Hiroshima, Japan"],"affiliations":[{"raw_affiliation_string":"Division of Mechanical Systems and Applied Mechanics, Faculty of Engineering, Hiroshima University, Higashi-Hiroshima, Japan","institution_ids":["https://openalex.org/I113306721"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050819882","display_name":"Hilbert J. Kappen","orcid":"https://orcid.org/0000-0002-5728-3676"},"institutions":[{"id":"https://openalex.org/I145872427","display_name":"Radboud University Nijmegen","ror":"https://ror.org/016xsfp80","country_code":"NL","type":"education","lineage":["https://openalex.org/I145872427"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Hilbert J. Kappen","raw_affiliation_strings":["Department of Biophysics, Radboud University Nijmegen, Nijmegen, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Department of Biophysics, Radboud University Nijmegen, Nijmegen, The Netherlands","institution_ids":["https://openalex.org/I145872427"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015646653","display_name":"Masami Saeki","orcid":"https://orcid.org/0000-0002-4162-0201"},"institutions":[{"id":"https://openalex.org/I113306721","display_name":"Hiroshima University","ror":"https://ror.org/03t78wx29","country_code":"JP","type":"education","lineage":["https://openalex.org/I113306721"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Masami Saeki","raw_affiliation_strings":["Division of Mechanical Systems and Applied Mechanics, Faculty of Engineering, Hiroshima University, Higashi-Hiroshima, Japan"],"affiliations":[{"raw_affiliation_string":"Division of Mechanical Systems and Applied Mechanics, Faculty of Engineering, Hiroshima University, Higashi-Hiroshima, Japan","institution_ids":["https://openalex.org/I113306721"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5006166354"],"corresponding_institution_ids":["https://openalex.org/I113306721"],"apc_list":null,"apc_paid":null,"fwci":1.8571,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.84865985,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"62","issue":"1","first_page":"262","last_page":"276"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9958999752998352,"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"}},"topics":[{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9958999752998352,"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/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.9916999936103821,"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"}},{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9868000149726868,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/mathematics","display_name":"Mathematics","score":0.7781347632408142},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5695531368255615},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5540006160736084},{"id":"https://openalex.org/keywords/path-integral-formulation","display_name":"Path integral formulation","score":0.5536195635795593},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5510679483413696},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.520223081111908},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4941733181476593},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.4751336872577667},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4562188386917114},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.45342397689819336},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.4491628110408783},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39240598678588867},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32491570711135864},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1439799964427948}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7781347632408142},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5695531368255615},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5540006160736084},{"id":"https://openalex.org/C154018700","wikidata":"https://www.wikidata.org/wiki/Q898323","display_name":"Path integral formulation","level":3,"score":0.5536195635795593},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5510679483413696},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.520223081111908},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4941733181476593},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.4751336872577667},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4562188386917114},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.45342397689819336},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.4491628110408783},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39240598678588867},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32491570711135864},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1439799964427948},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tac.2016.2547979","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2016.2547979","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},{"id":"pmh:ru:oai:repository.ubn.ru.nl:2066/165896","is_oa":false,"landing_page_url":"http://hdl.handle.net/2066/165896","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Automatic Control, 62, 262 - 276","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.6499999761581421}],"awards":[{"id":"https://openalex.org/G2256499016","display_name":null,"funder_award_id":"Grant-in-Aid for Young Scientists (","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G2290966971","display_name":"A new solution method for nonlinear stochastic optimal control based on stochastic analysis and statistical mechanics and  its application to learning control","funder_award_id":"24760338","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G3236194794","display_name":null,"funder_award_id":"Grant-in-Aid","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G3348058139","display_name":null,"funder_award_id":"Grant-in-Aid for Young Scien","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G3459562248","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G4367772926","display_name":null,"funder_award_id":"Grant-in-Aid for Young Scientists","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G4873009569","display_name":null,"funder_award_id":"Grant-in-Aid for Young Scientists (B)","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G4874944895","display_name":null,"funder_award_id":"-in-Aid","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G7469498077","display_name":"\u96fb\u5b50\u9855\u5fae\u93e1\u306b\u3088\u308b\u30a4\u30cd\u840e\u7e2e\u75c5\u30a6\u30a3\u30eb\u30b9\u7c92\u5b50\u306e\u5fae\u7d30\u69cb\u9020\u306b\u95a2\u3059\u308b\u7814\u7a76","funder_award_id":"476033","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W10636524","https://openalex.org/W103048554","https://openalex.org/W1489872560","https://openalex.org/W1507126399","https://openalex.org/W1525883337","https://openalex.org/W1536233603","https://openalex.org/W1558902221","https://openalex.org/W1613865483","https://openalex.org/W1925816294","https://openalex.org/W1980115416","https://openalex.org/W1985529856","https://openalex.org/W1995502176","https://openalex.org/W2025752438","https://openalex.org/W2026659355","https://openalex.org/W2043880592","https://openalex.org/W2047090868","https://openalex.org/W2061230119","https://openalex.org/W2063996763","https://openalex.org/W2066557929","https://openalex.org/W2108631580","https://openalex.org/W2112507254","https://openalex.org/W2121156749","https://openalex.org/W2167697140","https://openalex.org/W2170316986","https://openalex.org/W2323465150","https://openalex.org/W2327668930","https://openalex.org/W3005581722","https://openalex.org/W4206537305","https://openalex.org/W4210791600","https://openalex.org/W4300810540","https://openalex.org/W6636453219","https://openalex.org/W6640290305","https://openalex.org/W6645308989"],"related_works":["https://openalex.org/W3127842299","https://openalex.org/W1497853864","https://openalex.org/W4254377558","https://openalex.org/W2494568668","https://openalex.org/W1859674131","https://openalex.org/W2783417900","https://openalex.org/W1544506386","https://openalex.org/W1527804034","https://openalex.org/W4247445069","https://openalex.org/W2889455557"],"abstract_inverted_index":{"This":[0],"paper":[1],"proposes":[2],"a":[3,27,38,57,61,78],"new":[4],"iterative":[5],"solution":[6,68],"method":[7,53,98],"for":[8,25,60,112],"nonlinear":[9,39],"stochastic":[10,28],"optimal":[11],"control":[12],"problems":[13],"based":[14],"on":[15],"path":[16,88],"integral":[17,89],"analysis.":[18,90],"First,":[19],"we":[20,76],"provide":[21],"an":[22],"iteration":[23,48,84,115],"law":[24],"solving":[26],"Hamilton-Jacobi-Bellman":[29],"(SHJB)":[30],"equation":[31,42,120],"associated":[32],"to":[33],"this":[34],"problem,":[35],"which":[36],"is":[37,54,69,99,121],"partial":[40],"differential":[41],"(PDE)":[43],"of":[44,50,95,110,129],"second":[45],"order.":[46],"Each":[47],"procedure":[49],"the":[51,72,87,92,96,108,113,118,127,130],"proposed":[52,97,114,131],"represented":[55],"by":[56,71,85],"Cauchy":[58],"problem":[59],"linear":[62],"parabolic":[63],"PDE,":[64],"and":[65,117],"its":[66],"explicit":[67],"given":[70],"Feynman-Kac":[73],"formula.":[74],"Second,":[75],"derive":[77],"suboptimal":[79],"feedback":[80],"controller":[81],"at":[82],"each":[83],"using":[86],"Third,":[91],"convergence":[93],"property":[94],"investigated.":[100],"Here,":[101],"some":[102],"conditions":[103],"are":[104],"provided":[105],"so":[106],"that":[107],"sequence":[109],"solutions":[111],"converges,":[116],"SHJB":[119],"satisfied.":[122],"Finally,":[123],"numerical":[124],"simulations":[125],"demonstrate":[126],"effectiveness":[128],"method.":[132]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}