{"id":"https://openalex.org/W2949413837","doi":"https://doi.org/10.1137/15m1046903","title":"Robust Feedback Switching Control: Dynamic Programming and Viscosity Solutions","display_name":"Robust Feedback Switching Control: Dynamic Programming and Viscosity Solutions","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2949413837","doi":"https://doi.org/10.1137/15m1046903","mag":"2949413837"},"language":"en","primary_location":{"id":"doi:10.1137/15m1046903","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1046903","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1409.6233","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005237318","display_name":"Erhan Bayraktar","orcid":"https://orcid.org/0000-0002-1926-4570"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Erhan Bayraktar","raw_affiliation_strings":["Department of Mathematics, University of Michigan, Ann Arbor, MI 48109"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Michigan, Ann Arbor, MI 48109","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037009650","display_name":"Andrea Cosso","orcid":"https://orcid.org/0000-0001-6020-0213"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Andrea Cosso","raw_affiliation_strings":["Dipartimento di Matematica, Politecnico di Milano, via Bonardi 9, 20133 Milano, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Politecnico di Milano, via Bonardi 9, 20133 Milano, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"last","author":{"id":null,"display_name":"Huy\u00ean Pham","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I4210102982","display_name":"Centre for Research in Engineering Surface Technology","ror":"https://ror.org/018q3fa22","country_code":"IE","type":"other","lineage":["https://openalex.org/I4210102982"]},{"id":"https://openalex.org/I4210137396","display_name":"Centre de Recherche en \u00c9conomie et Statistique","ror":"https://ror.org/0449khs19","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I142476485","https://openalex.org/I4210108488","https://openalex.org/I4210108488","https://openalex.org/I4210137396","https://openalex.org/I4210145102","https://openalex.org/I4210145102","https://openalex.org/I4210150854","https://openalex.org/I84009706"]},{"id":"https://openalex.org/I4210141270","display_name":"Center for Responsible Travel","ror":"https://ror.org/04yvfxe52","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I4210141270"]},{"id":"https://openalex.org/I4210147464","display_name":"Laboratoire de Probabilit\u00e9s et Mod\u00e8les Al\u00e9atoires","ror":"https://ror.org/04hjc7403","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210147464"]},{"id":"https://openalex.org/I84009706","display_name":"ENSAE Paris","ror":"https://ror.org/01fz7mn40","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210108488","https://openalex.org/I4210145102","https://openalex.org/I84009706"]}],"countries":["FR","IE","US"],"is_corresponding":false,"raw_author_name":"Huy\u00ean Pham","raw_affiliation_strings":["Laboratoire de Probabilit\u00e9s et Mod\u00e8les Al\u00e9atoires, CNRS, UMR 7599, Universit\u00e9 Paris Diderot, Paris, France and","CREST-ENSAE"],"affiliations":[{"raw_affiliation_string":"Laboratoire de Probabilit\u00e9s et Mod\u00e8les Al\u00e9atoires, CNRS, UMR 7599, Universit\u00e9 Paris Diderot, Paris, France and","institution_ids":["https://openalex.org/I4210147464","https://openalex.org/I204730241","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"CREST-ENSAE","institution_ids":["https://openalex.org/I84009706","https://openalex.org/I4210137396","https://openalex.org/I4210102982","https://openalex.org/I4210141270"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5005237318"],"corresponding_institution_ids":["https://openalex.org/I27837315"],"apc_list":null,"apc_paid":null,"fwci":1.8893,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.8760723,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"54","issue":"5","first_page":"2594","last_page":"2628"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9987000226974487,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9987000226974487,"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/T12137","display_name":"Economic theories and models","score":0.9763000011444092,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11976","display_name":"Capital Investment and Risk Analysis","score":0.9721999764442444,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hamilton\u2013jacobi\u2013bellman-equation","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","score":0.8929473161697388},{"id":"https://openalex.org/keywords/viscosity-solution","display_name":"Viscosity solution","score":0.8512366414070129},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.8334546089172363},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7465994954109192},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"Dynamic programming","score":0.6842081546783447},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5240964293479919},{"id":"https://openalex.org/keywords/knightian-uncertainty","display_name":"Knightian uncertainty","score":0.49945807456970215},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.49860668182373047},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.48878809809684753},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.4829949140548706},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4767359495162964},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.43938225507736206},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4118993282318115},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.3807261288166046},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.2863290309906006},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18585309386253357}],"concepts":[{"id":"https://openalex.org/C196978813","wikidata":"https://www.wikidata.org/wiki/Q3302775","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","level":3,"score":0.8929473161697388},{"id":"https://openalex.org/C88731125","wikidata":"https://www.wikidata.org/wiki/Q7935676","display_name":"Viscosity solution","level":2,"score":0.8512366414070129},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.8334546089172363},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7465994954109192},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.6842081546783447},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5240964293479919},{"id":"https://openalex.org/C2779652836","wikidata":"https://www.wikidata.org/wiki/Q1548830","display_name":"Knightian uncertainty","level":3,"score":0.49945807456970215},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.49860668182373047},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.48878809809684753},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.4829949140548706},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4767359495162964},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.43938225507736206},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4118993282318115},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.3807261288166046},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2863290309906006},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18585309386253357},{"id":"https://openalex.org/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","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/C2780522230","wikidata":"https://www.wikidata.org/wiki/Q1140419","display_name":"Ambiguity","level":2,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/15m1046903","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1046903","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1409.6233","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1409.6233","pdf_url":"https://arxiv.org/pdf/1409.6233","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:HAL:hal-01066954v2","is_oa":true,"landing_page_url":"https://hal.science/hal-01066954","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2016","raw_type":"Preprints, Working Papers, ..."},{"id":"pmh:oai:cris.unibo.it:11585/610837","is_oa":false,"landing_page_url":"http://hdl.handle.net/11585/610837","pdf_url":null,"source":{"id":"https://openalex.org/S4306402579","display_name":"Archivio istituzionale della ricerca (Alma Mater Studiorum Universit\u00e0 di Bologna)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210117483","host_organization_name":"Istituto di Ematologia di Bologna","host_organization_lineage":["https://openalex.org/I4210117483"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:re.public.polimi.it:11311/1007149","is_oa":true,"landing_page_url":"http://hdl.handle.net/11311/1007149","pdf_url":null,"source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1409.6233","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1409.6233","pdf_url":"https://arxiv.org/pdf/1409.6233","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3486263863","display_name":null,"funder_award_id":"DMS-0955463","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1723047861","https://openalex.org/W1966660110","https://openalex.org/W1969088168","https://openalex.org/W1972434283","https://openalex.org/W1980753586","https://openalex.org/W1988747288","https://openalex.org/W1998407679","https://openalex.org/W2005746928","https://openalex.org/W2032168766","https://openalex.org/W2040009667","https://openalex.org/W2071447885","https://openalex.org/W2072321868","https://openalex.org/W2074741901","https://openalex.org/W2088471261","https://openalex.org/W2098244917","https://openalex.org/W2106203939","https://openalex.org/W2108101768","https://openalex.org/W2119993310","https://openalex.org/W2124430714","https://openalex.org/W2140171702","https://openalex.org/W2142044708","https://openalex.org/W2157509603","https://openalex.org/W2592216957","https://openalex.org/W2953358932","https://openalex.org/W2963548356","https://openalex.org/W3105343238","https://openalex.org/W3121892982","https://openalex.org/W3122516375","https://openalex.org/W3125380953","https://openalex.org/W4243590097"],"related_works":["https://openalex.org/W2032834442","https://openalex.org/W1654696814","https://openalex.org/W3153900688","https://openalex.org/W4297940580","https://openalex.org/W4297409026","https://openalex.org/W2115544975","https://openalex.org/W1992466143","https://openalex.org/W2144074296","https://openalex.org/W2949413837","https://openalex.org/W51876359"],"abstract_inverted_index":{"We":[0,67],"consider":[1],"a":[2,24,62,81,87,100,123],"robust":[3,131],"switching":[4,22,28,133],"control":[5,134],"problem.":[6,66,135],"The":[7,34,52],"controller":[8],"only":[9],"observes":[10],"the":[11,14,43,50,69,95,105,109,112,117,125,130],"evolution":[12],"of":[13,27,49,89,108],"state":[15],"process,":[16],"and":[17,76,84,120],"thus":[18],"uses":[19],"feedback":[20,132],"(closed-loop)":[21],"strategies,":[23],"nonstandard":[25],"class":[26],"controls":[29,40],"introduced":[30],"in":[31,73],"this":[32,74,103],"paper.":[33],"adverse":[35],"player":[36],"(nature)":[37],"chooses":[38],"open-loop":[39],"that":[41,78],"represent":[42],"so-called":[44],"Knightian":[45],"uncertainty,":[46],"i.e.,":[47],"misspecifications":[48],"model.":[51],"(half)":[53],"game":[54,110],"switcher":[55],"versus":[56],"nature":[57],"is":[58],"then":[59],"formulated":[60],"as":[61,111,122],"two-step":[63],"(robust)":[64],"optimization":[65],"develop":[68],"stochastic":[70],"Perron's":[71],"method":[72],"framework,":[75],"prove":[77],"it":[79],"produces":[80],"viscosity":[82,114],"subsolution":[83],"supersolution":[85],"to":[86,116],"system":[88],"HJB":[90,118],"variational":[91],"inequalities,":[92],"which":[93],"envelop":[94],"value":[96,106],"function.":[97],"Together":[98],"with":[99],"comparison":[101],"principle,":[102],"characterizes":[104],"function":[107],"unique":[113],"solution":[115],"equation,":[119],"shows":[121],"by-product":[124],"dynamic":[126],"programming":[127],"principle":[128],"for":[129]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4}],"updated_date":"2026-04-17T18:11:37.981687","created_date":"2025-10-10T00:00:00"}