{"id":"https://openalex.org/W1548287612","doi":"https://doi.org/10.1109/cdc.2002.1184884","title":"Viscosity solutions of the Bellman equation for perturbed optimal control problems with exit times","display_name":"Viscosity solutions of the Bellman equation for perturbed optimal control problems with exit times","publication_year":2003,"publication_date":"2003-08-27","ids":{"openalex":"https://openalex.org/W1548287612","doi":"https://doi.org/10.1109/cdc.2002.1184884","mag":"1548287612"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2002.1184884","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2002.1184884","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 41st IEEE Conference on Decision and Control, 2002.","raw_type":"proceedings-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/A5047541029","display_name":"Michael Malisoff","orcid":"https://orcid.org/0000-0003-0150-5046"},"institutions":[{"id":"https://openalex.org/I121820613","display_name":"Louisiana State University","ror":"https://ror.org/05ect4e57","country_code":"US","type":"education","lineage":["https://openalex.org/I121820613"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"M. Malisoff","raw_affiliation_strings":["Department of Mathematics, Louisiana State University, Baton Rouge, LA, USA","Dept. of Math., Louisiana State University, Baton Rouge, LA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Louisiana State University, Baton Rouge, LA, USA","institution_ids":["https://openalex.org/I121820613"]},{"raw_affiliation_string":"Dept. of Math., Louisiana State University, Baton Rouge, LA, USA","institution_ids":["https://openalex.org/I121820613"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5047541029"],"corresponding_institution_ids":["https://openalex.org/I121820613"],"apc_list":null,"apc_paid":null,"fwci":0.8178,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.76882928,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2","issue":null,"first_page":"2348","last_page":"2353"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9958999752998352,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9958999752998352,"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/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.991100013256073,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9890999794006348,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.7847480773925781},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.709145188331604},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.6389749646186829},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.47470536828041077},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47310757637023926},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4644681513309479},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.4436378479003906},{"id":"https://openalex.org/keywords/viscosity-solution","display_name":"Viscosity solution","score":0.42238110303878784},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.4142017066478729},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.4124374985694885},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35940390825271606},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2765663266181946}],"concepts":[{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7847480773925781},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.709145188331604},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.6389749646186829},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.47470536828041077},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47310757637023926},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4644681513309479},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.4436378479003906},{"id":"https://openalex.org/C88731125","wikidata":"https://www.wikidata.org/wiki/Q7935676","display_name":"Viscosity solution","level":2,"score":0.42238110303878784},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.4142017066478729},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.4124374985694885},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35940390825271606},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2765663266181946},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/cdc.2002.1184884","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2002.1184884","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 41st IEEE Conference on Decision and Control, 2002.","raw_type":"proceedings-article"},{"id":"pmh:oai:digitalcommons.lsu.edu:mathematics_pubs-2025","is_oa":false,"landing_page_url":"https://digitalcommons.lsu.edu/mathematics_pubs/1026","pdf_url":null,"source":{"id":"https://openalex.org/S4210169993","display_name":"Civil War Book Review","issn_l":"1528-6592","issn":["1528-6592"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310315936","host_organization_name":"Louisiana State University","host_organization_lineage":["https://openalex.org/P4310315936"],"host_organization_lineage_names":["Louisiana State University"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Publications","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.538.1016","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.538.1016","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://www.math.lsu.edu/~malisoff/papers/CDCperturbed.pdf","raw_type":"text"},{"id":"pmh:oai:repository.lsu.edu:mathematics_pubs-2025","is_oa":false,"landing_page_url":"https://repository.lsu.edu/mathematics_pubs/1026","pdf_url":null,"source":{"id":"https://openalex.org/S4210169993","display_name":"Civil War Book Review","issn_l":"1528-6592","issn":["1528-6592"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310315936","host_organization_name":"Louisiana State University","host_organization_lineage":["https://openalex.org/P4310315936"],"host_organization_lineage_names":["Louisiana State University"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Publications","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1487586009","https://openalex.org/W1495815306","https://openalex.org/W1584907262","https://openalex.org/W2010132706","https://openalex.org/W2023193505","https://openalex.org/W2049723320","https://openalex.org/W2085889587","https://openalex.org/W3098831681"],"related_works":["https://openalex.org/W2766367749","https://openalex.org/W4287078947","https://openalex.org/W1654696814","https://openalex.org/W4297940580","https://openalex.org/W2954291171","https://openalex.org/W4297409026","https://openalex.org/W2088353628","https://openalex.org/W2313187187","https://openalex.org/W2032834442","https://openalex.org/W3153900688"],"abstract_inverted_index":{"In":[0,60],"a":[1,51,83,88,164],"series":[2],"of":[3,22,33,121,146,166,181],"papers,":[4],"we":[5,63],"presented":[6],"new":[7],"theorems":[8],"characterizing":[9],"the":[10,17,23,34,38,58,71,77,102,112,117,122,129,141,179],"value":[11,113,190],"function":[12,114],"in":[13,82],"optimal":[14],"control":[15,153],"as":[16],"unique":[18,118],"bounded-from-below":[19,119],"viscosity":[20],"solution":[21,120],"corresponding":[24,123],"Bellman":[25,124],"equation":[26,125],"that":[27,37,47,73,126,150,194],"satisfies":[28],"appropriate":[29],"side":[30],"conditions.":[31],"Instead":[32],"usual":[35],"assumption":[36],"instantaneous":[39],"costs":[40],"are":[41,137,159],"uniformly":[42],"positive,":[43],"our":[44,147,176,196],"results":[45],"assumed":[46],"all":[48,74],"trajectories":[49,75,97],"satisfying":[50,76],"certain":[52],"integral":[53,78],"condition":[54,79],"must":[55,80],"asymptotically":[56],"approach":[57],"target.":[59,103,130],"this":[61,108],"note,":[62],"study":[64],"perturbed":[65],"exit":[66],"time":[67],"problems":[68,135,156,193],"which":[69,136,168,184],"have":[70],"property":[72],"stay":[81],"bounded":[84,95],"set.":[85],"This":[86],"is":[87,115,149],"weaker":[89,109],"asymptotic":[90,110],"property,":[91],"since":[92],"it":[93],"allows":[94],"oscillating":[96],"and":[98,174],"attractors":[99],"other":[100],"than":[101],"We":[104],"show":[105],"that,":[106],"under":[107],"condition,":[111],"still":[116],"vanishes":[127],"on":[128],"Our":[131],"theorem":[132,177],"applies":[133],"to":[134,163,188],"not":[138],"tractable":[139],"by":[140,172],"known":[142,161],"results.":[143],"The":[144],"significance":[145],"work":[148],"(i)":[151],"applied":[152],"abounds":[154],"with":[155],"whose":[157],"dynamics":[158],"only":[160],"up":[162],"margin":[165],"error,":[167],"can":[169,185],"be":[170,186],"represented":[171],"perturbations,":[173],"(ii)":[175],"implies":[178],"convergence":[180],"numerical":[182],"methods":[183],"used":[187],"approximate":[189],"functions":[191],"for":[192],"satisfy":[195],"relaxed":[197],"hypotheses.":[198]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}