{"id":"https://openalex.org/W2347563025","doi":null,"title":"Value Function and Optimal Trajectories for Regional Control Problems via Dynamic Programming and Pontryagin Maximum Principles","display_name":"Value Function and Optimal Trajectories for Regional Control Problems via Dynamic Programming and Pontryagin Maximum Principles","publication_year":2016,"publication_date":"2016-05-13","ids":{"openalex":"https://openalex.org/W2347563025","mag":"2347563025"},"language":"en","primary_location":{"id":"mag:2347563025","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1605.04079.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"arXiv (Cornell University)","raw_type":null},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1605.04079.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016430930","display_name":"Guy Barles A","orcid":"https://orcid.org/0000-0001-9381-4676","observed_orcids":["https://orcid.org/0000-0001-9381-4676"]},"institutions":[{"id":"https://openalex.org/I4210132217","display_name":"Laboratoire de Math\u00e9matiques et Physique Th\u00e9orique","ror":"https://ror.org/03g2c2k71","country_code":"FR","type":"facility","lineage":["https://openalex.org/I110017253","https://openalex.org/I12449238","https://openalex.org/I1294671590","https://openalex.org/I4210132217","https://openalex.org/I4210141950","https://openalex.org/I4387156285"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Guy Barles","raw_affiliation_strings":["Laboratoire de Math\u00e9matiques et Physique Th\u00e9orique"],"raw_orcid":"https://orcid.org/0000-0001-9381-4676","affiliations":[{"raw_affiliation_string":"Laboratoire de Math\u00e9matiques et Physique Th\u00e9orique","institution_ids":["https://openalex.org/I4210132217"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056038275","display_name":"Ariela Briani A","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210132217","display_name":"Laboratoire de Math\u00e9matiques et Physique Th\u00e9orique","ror":"https://ror.org/03g2c2k71","country_code":"FR","type":"facility","lineage":["https://openalex.org/I110017253","https://openalex.org/I12449238","https://openalex.org/I1294671590","https://openalex.org/I4210132217","https://openalex.org/I4210141950","https://openalex.org/I4387156285"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Ariela Briani","raw_affiliation_strings":["Laboratoire de Math\u00e9matiques et Physique Th\u00e9orique"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire de Math\u00e9matiques et Physique Th\u00e9orique","institution_ids":["https://openalex.org/I4210132217"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089339704","display_name":"Emmanuel Tr\u00e9lat","orcid":"https://orcid.org/0000-0002-0656-7003","observed_orcids":["https://orcid.org/0000-0002-0656-7003"]},"institutions":[{"id":"https://openalex.org/I4405261543","display_name":"CAGE: Contr\u00f4le et g\u00e9om\u00e9trie","ror":"https://ror.org/05fg1yv24","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4405255748","https://openalex.org/I4405257605","https://openalex.org/I4405261543"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Emmanuel Tr\u00e9lat","raw_affiliation_strings":["Control And GEometry"],"raw_orcid":"https://orcid.org/0000-0002-0656-7003","affiliations":[{"raw_affiliation_string":"Control And GEometry","institution_ids":["https://openalex.org/I4405261543"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.6176999807357788,"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"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.6176999807357788,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.17980000376701355,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.11140000075101852,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/value-function","display_name":"value function","score":0.8019999861717224},{"id":"https://openalex.org/keywords/optimal-trajectories","display_name":"optimal trajectories","score":0.9919999837875366},{"id":"https://openalex.org/keywords/pontryagin-s-maximum-principle","display_name":"Pontryagin maximum principle","score":0.8460000157356262},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"dynamic programming","score":0.8050000071525574},{"id":"https://openalex.org/keywords/bellman-principle","display_name":"Bellman principle","score":0.7429999709129333},{"id":"https://openalex.org/keywords/quantum-zeno-effect","display_name":"quantum Zeno effect","score":0.9079999923706055},{"id":"https://openalex.org/keywords/hybrid-optimal-control","display_name":"hybrid optimal control","score":0.8349999785423279}],"concepts":[{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.7817889451980591},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.7665845155715942},{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.7232294678688049},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5953167676925659},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.5891516208648682},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5869120359420776},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5386818051338196},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.5293158888816833},{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.4717336893081665},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.45796918869018555},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4565209746360779},{"id":"https://openalex.org/C31010330","wikidata":"https://www.wikidata.org/wiki/Q1914255","display_name":"Maximum principle","level":3,"score":0.4565041661262512},{"id":"https://openalex.org/C7707877","wikidata":"https://www.wikidata.org/wiki/Q33378","display_name":"Zeno's paradoxes","level":2,"score":0.4477729797363281},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.43376338481903076},{"id":"https://openalex.org/C2982888158","wikidata":"https://www.wikidata.org/wiki/Q5165874","display_name":"Control function","level":3,"score":0.42473796010017395},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4236396551132202},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.41755837202072144},{"id":"https://openalex.org/C142730499","wikidata":"https://www.wikidata.org/wiki/Q934367","display_name":"Function space","level":2,"score":0.4135141670703888},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40571269392967224},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.34405529499053955},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.14141437411308289},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09104940295219421},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.07443258166313171},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:2347563025","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1605.04079.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"arXiv (Cornell University)","raw_type":null}],"best_oa_location":{"id":"mag:2347563025","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1605.04079.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"arXiv (Cornell University)","raw_type":null},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W230866137","https://openalex.org/W1006433933","https://openalex.org/W1126041682","https://openalex.org/W1487586009","https://openalex.org/W1494380031","https://openalex.org/W1505284970","https://openalex.org/W1513745936","https://openalex.org/W1528856837","https://openalex.org/W1558492509","https://openalex.org/W1587799944","https://openalex.org/W1595765050","https://openalex.org/W1969823226","https://openalex.org/W1972272978","https://openalex.org/W1973664921","https://openalex.org/W1982415574","https://openalex.org/W1992238136","https://openalex.org/W1992513717","https://openalex.org/W1997500459","https://openalex.org/W2009353114","https://openalex.org/W2013596005","https://openalex.org/W2021200307","https://openalex.org/W2031281152","https://openalex.org/W2056261501","https://openalex.org/W2057794519","https://openalex.org/W2068864491","https://openalex.org/W2071623514","https://openalex.org/W2082522457","https://openalex.org/W2083122976","https://openalex.org/W2090718664","https://openalex.org/W2092078242","https://openalex.org/W2106780336","https://openalex.org/W2118115577","https://openalex.org/W2118590834","https://openalex.org/W2120666720","https://openalex.org/W2130980192","https://openalex.org/W2152185829","https://openalex.org/W2160032004","https://openalex.org/W2612727995","https://openalex.org/W2734379426","https://openalex.org/W2913332731","https://openalex.org/W2963868582"],"related_works":["https://openalex.org/W2964126589","https://openalex.org/W2143847391","https://openalex.org/W2530325632","https://openalex.org/W2008063200","https://openalex.org/W4296423347","https://openalex.org/W7099872266","https://openalex.org/W4224145368","https://openalex.org/W7096603212","https://openalex.org/W2461142177","https://openalex.org/W4391330383"],"abstract_inverted_index":{"In":[0],"this":[1,61,95],"paper":[2],"we":[3,120],"study":[4,52],"the":[5,17,20,31,47,51,57,69,73,86,111,127,131],"optimal":[6,11,76,135],"trajectories":[7,77,108],"for":[8,126],"regional,":[9],"deterministic":[10],"control":[12,136],"problems,":[13],"i.e.,":[14],"problems":[15],"where":[16],"dynamics":[18],"and":[19,34,56,63],"cost":[21],"functional":[22],"can":[23],"be":[24],"completely":[25],"different":[26,87],"in":[27,60,102,130],"two":[28],"regions":[29],"of":[30,53,83,93,117,133],"state":[32],"space":[33],"therefore":[35],"present":[36],"discontinuities":[37],"at":[38],"their":[39],"interface.":[40],"Our":[41],"first":[42],"aim":[43],"is":[44,96],"to":[45,67],"prove":[46],"classical":[48],"link":[49],"between":[50,85],"optimality":[54],"conditions":[55],"Bell-man":[58],"approach":[59],"framework,":[62],"then":[64],"exploit":[65],"it":[66],"recover":[68],"value":[70,128],"function":[71,129],"under":[72],"assumption":[74,100],"that":[75],"have":[78],"only":[79],"a":[80,97,115,122],"countable":[81],"number":[82],"switchings":[84],"regions.":[88],"From":[89],"an":[90],"application":[91],"point":[92],"view":[94],"very":[98],"reasonable":[99],"because":[101],"practice":[103],"one":[104],"never":[105],"implements":[106],"chattering":[107],"(i.e.,":[109],"enjoying":[110],"Zeno":[112],"phenomenon).":[113],"As":[114],"consequence":[116],"our":[118],"description":[119],"obtain":[121],"new":[123],"regularity":[124],"result":[125],"framework":[132],"hybrid":[134],"problems.":[137]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":3}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2016-06-24T00:00:00"}