{"id":"https://openalex.org/W2156195399","doi":"https://doi.org/10.1109/cdc.2014.7039666","title":"Solving the Hamilton-Jacobi-Bellman equation for a stochastic system with state constraints","display_name":"Solving the Hamilton-Jacobi-Bellman equation for a stochastic system with state constraints","publication_year":2014,"publication_date":"2014-12-01","ids":{"openalex":"https://openalex.org/W2156195399","doi":"https://doi.org/10.1109/cdc.2014.7039666","mag":"2156195399"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2014.7039666","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2014.7039666","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"53rd IEEE Conference on Decision and Control","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/A5064697824","display_name":"Per Rutquist","orcid":null},"institutions":[{"id":"https://openalex.org/I66862912","display_name":"Chalmers University of Technology","ror":"https://ror.org/040wg7k59","country_code":"SE","type":"education","lineage":["https://openalex.org/I66862912"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Per Rutquist","raw_affiliation_strings":["Tomlab Optimization AB, V\u00e4ster\u00e5s and Chalmers University of Technology"],"affiliations":[{"raw_affiliation_string":"Tomlab Optimization AB, V\u00e4ster\u00e5s and Chalmers University of Technology","institution_ids":["https://openalex.org/I66862912"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050466193","display_name":"Torsten Wik","orcid":"https://orcid.org/0000-0002-5234-8426"},"institutions":[{"id":"https://openalex.org/I66862912","display_name":"Chalmers University of Technology","ror":"https://ror.org/040wg7k59","country_code":"SE","type":"education","lineage":["https://openalex.org/I66862912"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Torsten Wik","raw_affiliation_strings":["Department of Signals and Systems, Chalmers University of Technology, Goteborg, Sweden"],"affiliations":[{"raw_affiliation_string":"Department of Signals and Systems, Chalmers University of Technology, Goteborg, Sweden","institution_ids":["https://openalex.org/I66862912"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086639334","display_name":"Claes Breitholtz","orcid":null},"institutions":[{"id":"https://openalex.org/I66862912","display_name":"Chalmers University of Technology","ror":"https://ror.org/040wg7k59","country_code":"SE","type":"education","lineage":["https://openalex.org/I66862912"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Claes Breitholtz","raw_affiliation_strings":["Department of Signals and Systems, Chalmers University of Technology, Goteborg, Sweden"],"affiliations":[{"raw_affiliation_string":"Department of Signals and Systems, Chalmers University of Technology, Goteborg, Sweden","institution_ids":["https://openalex.org/I66862912"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5064697824"],"corresponding_institution_ids":["https://openalex.org/I66862912"],"apc_list":null,"apc_paid":null,"fwci":1.763,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.87690385,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"1840","last_page":"1845"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9894000291824341,"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"}},"topics":[{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9894000291824341,"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"}},{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9857000112533569,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9839000105857849,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hamilton\u2013jacobi\u2013bellman-equation","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","score":0.9789122939109802},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.608113706111908},{"id":"https://openalex.org/keywords/hamilton\u2013jacobi-equation","display_name":"Hamilton\u2013Jacobi equation","score":0.5961319208145142},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.5138221383094788},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5116055607795715},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.48102766275405884},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.48062795400619507},{"id":"https://openalex.org/keywords/viscosity-solution","display_name":"Viscosity solution","score":0.47620829939842224},{"id":"https://openalex.org/keywords/linear-quadratic-gaussian-control","display_name":"Linear-quadratic-Gaussian control","score":0.4716590642929077},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4556558132171631},{"id":"https://openalex.org/keywords/stochastic-control","display_name":"Stochastic control","score":0.44464555382728577},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.4263920485973358},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29966992139816284}],"concepts":[{"id":"https://openalex.org/C196978813","wikidata":"https://www.wikidata.org/wiki/Q3302775","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","level":3,"score":0.9789122939109802},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.608113706111908},{"id":"https://openalex.org/C2778860007","wikidata":"https://www.wikidata.org/wiki/Q1060137","display_name":"Hamilton\u2013Jacobi equation","level":2,"score":0.5961319208145142},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.5138221383094788},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5116055607795715},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.48102766275405884},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.48062795400619507},{"id":"https://openalex.org/C88731125","wikidata":"https://www.wikidata.org/wiki/Q7935676","display_name":"Viscosity solution","level":2,"score":0.47620829939842224},{"id":"https://openalex.org/C204495892","wikidata":"https://www.wikidata.org/wiki/Q1798304","display_name":"Linear-quadratic-Gaussian control","level":3,"score":0.4716590642929077},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4556558132171631},{"id":"https://openalex.org/C170131372","wikidata":"https://www.wikidata.org/wiki/Q7617811","display_name":"Stochastic control","level":3,"score":0.44464555382728577},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.4263920485973358},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29966992139816284},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/cdc.2014.7039666","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2014.7039666","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"53rd IEEE Conference on Decision and Control","raw_type":"proceedings-article"},{"id":"pmh:oai:research.chalmers.se:214484","is_oa":false,"landing_page_url":"https://research.chalmers.se/en/publication/214484","pdf_url":null,"source":{"id":"https://openalex.org/S4306402469","display_name":"Chalmers Research (Chalmers University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66862912","host_organization_name":"Chalmers University of Technology","host_organization_lineage":["https://openalex.org/I66862912"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W162444011","https://openalex.org/W655138999","https://openalex.org/W1521930086","https://openalex.org/W1805381866","https://openalex.org/W1972904523","https://openalex.org/W1996743636","https://openalex.org/W2010475424","https://openalex.org/W2015673634","https://openalex.org/W2022144657","https://openalex.org/W2026659355","https://openalex.org/W2163709604","https://openalex.org/W2178598128","https://openalex.org/W2341171179","https://openalex.org/W2795744704","https://openalex.org/W3021722416","https://openalex.org/W4242891646","https://openalex.org/W6643468503","https://openalex.org/W6649475019"],"related_works":["https://openalex.org/W2962695587","https://openalex.org/W2754120543","https://openalex.org/W4301305831","https://openalex.org/W2358967034","https://openalex.org/W2963548356","https://openalex.org/W2094032802","https://openalex.org/W2383239293","https://openalex.org/W1964620550","https://openalex.org/W3153900688","https://openalex.org/W575255019"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,6,15,32,38,46,50,73,90],"method":[3,105],"for":[4,14,68,120],"finding":[5],"stationary":[7],"solution":[8,85],"to":[9],"the":[10,28,52,58,69,104,114,121],"Hamilton-Jacobi-Bellman":[11],"(HJB)":[12],"equation":[13,30],"stochastic":[16],"system":[17,78],"with":[18,79,89],"state":[19,80],"constraints.":[20,81],"A":[21,82],"variable":[22],"transformation":[23],"is":[24,86,123],"introduced":[25],"which":[26,101],"turns":[27],"HJB":[29,60],"into":[31],"combination":[33],"of":[34,40,57,72,94,116],"an":[35],"eigenvalue":[36],"problem,":[37],"set":[39],"partial":[41],"differential":[42],"equations":[43],"(PDEs),":[44],"and":[45],"point-wise":[47],"equation.":[48],"As":[49],"result":[51],"difficult":[53],"infinite":[54],"boundary":[55],"conditions":[56],"original":[59],"becomes":[61],"homogeneous.":[62],"To":[63],"illustrate,":[64],"we":[65],"numerically":[66],"solve":[67],"optimal":[70],"control":[71],"Linear":[74],"Quadratic":[75],"Gaussian":[76],"(LQG)":[77],"reasonably":[83],"accurate":[84],"obtained":[87],"even":[88],"very":[91],"small":[92],"number":[93],"collocation":[95],"points":[96],"(three":[97],"in":[98],"each":[99],"dimension),":[100],"suggests":[102],"that":[103],"could":[106],"be":[107],"used":[108],"on":[109],"high":[110],"order":[111],"systems,":[112],"mitigating":[113],"curse":[115],"dimensionality.":[117],"Source":[118],"code":[119],"example":[122],"available":[124],"online.":[125]},"counts_by_year":[{"year":2020,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}