{"id":"https://openalex.org/W3014318492","doi":"https://doi.org/10.23919/acc50511.2021.9482813","title":"Reflected Schr\u00f6dinger Bridge: Density Control with Path Constraints","display_name":"Reflected Schr\u00f6dinger Bridge: Density Control with Path Constraints","publication_year":2021,"publication_date":"2021-05-25","ids":{"openalex":"https://openalex.org/W3014318492","doi":"https://doi.org/10.23919/acc50511.2021.9482813","mag":"3014318492"},"language":"en","primary_location":{"id":"doi:10.23919/acc50511.2021.9482813","is_oa":false,"landing_page_url":"https://doi.org/10.23919/acc50511.2021.9482813","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2021 American Control Conference (ACC)","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2003.13895","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044388757","display_name":"Kenneth F. Caluya","orcid":"https://orcid.org/0000-0001-5949-4066"},"institutions":[{"id":"https://openalex.org/I185103710","display_name":"University of California, Santa Cruz","ror":"https://ror.org/03s65by71","country_code":"US","type":"education","lineage":["https://openalex.org/I185103710"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kenneth F. Caluya","raw_affiliation_strings":["Department of Applied Mathematics, University of California, Santa Cruz, CA, USA","UNIVERSITY OF CALIFORNIA (SANTA CRUZ)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of California, Santa Cruz, CA, USA","institution_ids":["https://openalex.org/I185103710"]},{"raw_affiliation_string":"UNIVERSITY OF CALIFORNIA (SANTA CRUZ)","institution_ids":["https://openalex.org/I185103710"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029714029","display_name":"Abhishek Halder","orcid":"https://orcid.org/0000-0002-1509-5853"},"institutions":[{"id":"https://openalex.org/I185103710","display_name":"University of California, Santa Cruz","ror":"https://ror.org/03s65by71","country_code":"US","type":"education","lineage":["https://openalex.org/I185103710"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Abhishek Halder","raw_affiliation_strings":["Department of Applied Mathematics, University of California, Santa Cruz, CA, USA","UNIVERSITY OF CALIFORNIA (SANTA CRUZ)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of California, Santa Cruz, CA, USA","institution_ids":["https://openalex.org/I185103710"]},{"raw_affiliation_string":"UNIVERSITY OF CALIFORNIA (SANTA CRUZ)","institution_ids":["https://openalex.org/I185103710"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I185103710"],"apc_list":null,"apc_paid":null,"fwci":0.2289,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.53183188,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"1137","last_page":"1142"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9929999709129333,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9929999709129333,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T10067","display_name":"Stochastic processes and financial applications","score":0.9922000169754028,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9670000076293945,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/bridge","display_name":"Bridge (graph theory)","score":0.7000511884689331},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.6198282241821289},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.5350561738014221},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5345114469528198},{"id":"https://openalex.org/keywords/obstacle-avoidance","display_name":"Obstacle avoidance","score":0.49900317192077637},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.4932336211204529},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.4924333989620209},{"id":"https://openalex.org/keywords/obstacle","display_name":"Obstacle","score":0.4905973970890045},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4894019663333893},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48892131447792053},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4516162872314453},{"id":"https://openalex.org/keywords/stochastic-control","display_name":"Stochastic control","score":0.44926026463508606},{"id":"https://openalex.org/keywords/sample","display_name":"Sample (material)","score":0.43085533380508423},{"id":"https://openalex.org/keywords/path-integral-formulation","display_name":"Path integral formulation","score":0.4281054735183716},{"id":"https://openalex.org/keywords/schr\u00f6dingers-cat","display_name":"Schr\u00f6dinger's cat","score":0.4245254397392273},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.41814249753952026},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3466538190841675},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.20748603343963623},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19282478094100952},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.18483662605285645},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10288330912590027},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09643003344535828},{"id":"https://openalex.org/keywords/geography","display_name":"Geography","score":0.07520309090614319}],"concepts":[{"id":"https://openalex.org/C100776233","wikidata":"https://www.wikidata.org/wiki/Q2532492","display_name":"Bridge (graph theory)","level":2,"score":0.7000511884689331},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.6198282241821289},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5350561738014221},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5345114469528198},{"id":"https://openalex.org/C6683253","wikidata":"https://www.wikidata.org/wiki/Q7075535","display_name":"Obstacle avoidance","level":4,"score":0.49900317192077637},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.4932336211204529},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.4924333989620209},{"id":"https://openalex.org/C2776650193","wikidata":"https://www.wikidata.org/wiki/Q264661","display_name":"Obstacle","level":2,"score":0.4905973970890045},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4894019663333893},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48892131447792053},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4516162872314453},{"id":"https://openalex.org/C170131372","wikidata":"https://www.wikidata.org/wiki/Q7617811","display_name":"Stochastic control","level":3,"score":0.44926026463508606},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.43085533380508423},{"id":"https://openalex.org/C154018700","wikidata":"https://www.wikidata.org/wiki/Q898323","display_name":"Path integral formulation","level":3,"score":0.4281054735183716},{"id":"https://openalex.org/C194800363","wikidata":"https://www.wikidata.org/wiki/Q8588","display_name":"Schr\u00f6dinger's cat","level":2,"score":0.4245254397392273},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.41814249753952026},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3466538190841675},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.20748603343963623},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19282478094100952},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18483662605285645},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10288330912590027},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09643003344535828},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.07520309090614319},{"id":"https://openalex.org/C19966478","wikidata":"https://www.wikidata.org/wiki/Q4810574","display_name":"Mobile robot","level":3,"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/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"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/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.23919/acc50511.2021.9482813","is_oa":false,"landing_page_url":"https://doi.org/10.23919/acc50511.2021.9482813","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2021 American Control Conference (ACC)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:2003.13895","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2003.13895","pdf_url":"https://arxiv.org/pdf/2003.13895","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":null},{"id":"mag:3014318492","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/2003.13895","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2003.13895","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2003.13895","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2003.13895","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2003.13895","pdf_url":"https://arxiv.org/pdf/2003.13895","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":null},"sustainable_development_goals":[{"score":0.6899999976158142,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[{"id":"https://openalex.org/G5750029926","display_name":"AMPS: Optimal Transport Algorithms for Stochastic Uncertainty Management in Modern Power Systems","funder_award_id":"1923278","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3014318492.pdf","grobid_xml":"https://content.openalex.org/works/W3014318492.grobid-xml"},"referenced_works_count":48,"referenced_works":["https://openalex.org/W112023339","https://openalex.org/W561749035","https://openalex.org/W1520121751","https://openalex.org/W1520803780","https://openalex.org/W1585160083","https://openalex.org/W1858982327","https://openalex.org/W1964110293","https://openalex.org/W1970030120","https://openalex.org/W1985506636","https://openalex.org/W2018158804","https://openalex.org/W2045384647","https://openalex.org/W2059900018","https://openalex.org/W2071048859","https://openalex.org/W2074918857","https://openalex.org/W2092038977","https://openalex.org/W2097415784","https://openalex.org/W2103226217","https://openalex.org/W2151849802","https://openalex.org/W2176624840","https://openalex.org/W2236237046","https://openalex.org/W2299620045","https://openalex.org/W2502449663","https://openalex.org/W2503537357","https://openalex.org/W2513846512","https://openalex.org/W2519388618","https://openalex.org/W2565432921","https://openalex.org/W2624897282","https://openalex.org/W2735823378","https://openalex.org/W2791122645","https://openalex.org/W2791804925","https://openalex.org/W2927396997","https://openalex.org/W2963198158","https://openalex.org/W2964076623","https://openalex.org/W2964229334","https://openalex.org/W2964269742","https://openalex.org/W2973202360","https://openalex.org/W2976757820","https://openalex.org/W2988326897","https://openalex.org/W3012068377","https://openalex.org/W3105663536","https://openalex.org/W3110204697","https://openalex.org/W3129947101","https://openalex.org/W4233742192","https://openalex.org/W4236779604","https://openalex.org/W4245164763","https://openalex.org/W4302928681","https://openalex.org/W6631219977","https://openalex.org/W6823297717"],"related_works":["https://openalex.org/W3183437454","https://openalex.org/W3098408365","https://openalex.org/W2148829083","https://openalex.org/W2015614846","https://openalex.org/W2171650454","https://openalex.org/W2079403996","https://openalex.org/W3009950647","https://openalex.org/W2951011180","https://openalex.org/W2547466557","https://openalex.org/W3127653057","https://openalex.org/W3102312891","https://openalex.org/W1981487261","https://openalex.org/W1997251742","https://openalex.org/W1531545095","https://openalex.org/W2042240095","https://openalex.org/W2090793317","https://openalex.org/W2010778846","https://openalex.org/W2329625325","https://openalex.org/W2741345629","https://openalex.org/W2148519327"],"abstract_inverted_index":{"How":[0],"to":[1,10,16,58,68,91],"steer":[2],"a":[3,17,80],"given":[4],"joint":[5],"state":[6,23,29,59],"probability":[7],"density":[8,51],"function":[9],"another":[11],"over":[12],"finite":[13],"horizon":[14],"subject":[15,57],"controlled":[18],"stochastic":[19],"dynamics":[20],"with":[21],"hard":[22],"(sample":[24],"path)":[25],"constraints?":[26],"In":[27,39],"applications,":[28],"constraints":[30],"may":[31],"encode":[32],"safety":[33],"requirements":[34],"such":[35],"as":[36],"obstacle":[37],"avoidance.":[38],"this":[40],"paper,":[41],"we":[42],"perform":[43],"the":[44,63,70,75,93],"feedback":[45],"synthesis":[46],"for":[47,74],"minimum":[48],"control":[49],"effort":[50],"steering":[52],"(a.k.a.":[53],"Schr\u00f6dinger":[54,66],"bridge)":[55],"problem":[56],"constraints.":[60],"We":[61],"extend":[62],"theory":[64],"of":[65],"bridges":[67],"account":[69],"reflecting":[71],"boundary":[72],"conditions":[73],"sample":[76],"paths,":[77],"and":[78],"provide":[79],"computational":[81],"framework":[82],"building":[83],"on":[84,88],"our":[85],"previous":[86],"work":[87],"proximal":[89],"recursions,":[90],"solve":[92],"same.":[94]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-07-01T08:55:40.977307","created_date":"2025-10-10T00:00:00"}
