{"id":"https://openalex.org/W3009484445","doi":"https://doi.org/10.1109/lcsys.2020.2977927","title":"Sparse Learning-Based Approximate Dynamic Programming With Barrier Constraints","display_name":"Sparse Learning-Based Approximate Dynamic Programming With Barrier Constraints","publication_year":2020,"publication_date":"2020-03-03","ids":{"openalex":"https://openalex.org/W3009484445","doi":"https://doi.org/10.1109/lcsys.2020.2977927","mag":"3009484445"},"language":"en","primary_location":{"id":"doi:10.1109/lcsys.2020.2977927","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lcsys.2020.2977927","pdf_url":null,"source":{"id":"https://openalex.org/S4306422535","display_name":"IEEE Control Systems Letters","issn_l":"2475-1456","issn":["2475-1456"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Control Systems Letters","raw_type":"journal-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/A5027840499","display_name":"Max L. Greene","orcid":"https://orcid.org/0000-0003-2733-0344"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Max L. Greene","raw_affiliation_strings":["Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, USA"],"raw_orcid":"https://orcid.org/0000-0003-2733-0344","affiliations":[{"raw_affiliation_string":"Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, USA","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018956236","display_name":"Patryk Deptula","orcid":"https://orcid.org/0000-0002-2328-9148"},"institutions":[{"id":"https://openalex.org/I1343143571","display_name":"Draper Laboratory","ror":"https://ror.org/04378d909","country_code":"US","type":"funder","lineage":["https://openalex.org/I1343143571"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Patryk Deptula","raw_affiliation_strings":["Perception and Autonomy Group Charles Stark Draper Laboratory, Inc., Cambridge, USA"],"raw_orcid":"https://orcid.org/0000-0002-2328-9148","affiliations":[{"raw_affiliation_string":"Perception and Autonomy Group Charles Stark Draper Laboratory, Inc., Cambridge, USA","institution_ids":["https://openalex.org/I1343143571"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045042598","display_name":"Scott Nivison","orcid":"https://orcid.org/0000-0002-5738-2535"},"institutions":[{"id":"https://openalex.org/I2801461044","display_name":"Eglin Air Force Base","ror":"https://ror.org/002c7zk35","country_code":"US","type":"government","lineage":["https://openalex.org/I1330347796","https://openalex.org/I2801461044","https://openalex.org/I4210089612","https://openalex.org/I4210102105"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Scott Nivison","raw_affiliation_strings":["Munitions Directorate, Air Force Research Laboratory, Eglin AFB, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Munitions Directorate, Air Force Research Laboratory, Eglin AFB, USA","institution_ids":["https://openalex.org/I2801461044"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032651215","display_name":"Warren E. Dixon","orcid":"https://orcid.org/0000-0002-5091-181X"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Warren E. Dixon","raw_affiliation_strings":["Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, USA"],"raw_orcid":"https://orcid.org/0000-0002-5091-181X","affiliations":[{"raw_affiliation_string":"Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, USA","institution_ids":["https://openalex.org/I33213144"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2045,"currency":"USD","value_usd":2045},"apc_paid":null,"fwci":2.9899,"has_fulltext":false,"cited_by_count":40,"citation_normalized_percentile":{"value":0.9262621,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"4","issue":"3","first_page":"743","last_page":"748"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.9998999834060669,"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/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.9998999834060669,"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/T10675","display_name":"Mechanical Circulatory Support Devices","score":0.982699990272522,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.9624999761581421,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6080816388130188},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5822370648384094},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"Dynamic programming","score":0.5732148885726929},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.5660189986228943},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.5485624670982361},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.508738100528717},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4422897398471832},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4406234622001648},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.43815872073173523},{"id":"https://openalex.org/keywords/classification-of-discontinuities","display_name":"Classification of discontinuities","score":0.4316719174385071},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.4309844374656677},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.422821581363678},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.4187813997268677},{"id":"https://openalex.org/keywords/control-lyapunov-function","display_name":"Control-Lyapunov function","score":0.41747021675109863},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.4135763645172119},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.3558623790740967},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.27800655364990234},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.25566983222961426},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.21117714047431946},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.1631268560886383},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.14452573657035828},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1328861117362976}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6080816388130188},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5822370648384094},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.5732148885726929},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.5660189986228943},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.5485624670982361},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.508738100528717},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4422897398471832},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4406234622001648},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.43815872073173523},{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.4316719174385071},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.4309844374656677},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.422821581363678},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.4187813997268677},{"id":"https://openalex.org/C201030206","wikidata":"https://www.wikidata.org/wiki/Q5165805","display_name":"Control-Lyapunov function","level":5,"score":0.41747021675109863},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4135763645172119},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3558623790740967},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27800655364990234},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.25566983222961426},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.21117714047431946},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.1631268560886383},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.14452573657035828},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1328861117362976},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","level":1,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/lcsys.2020.2977927","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lcsys.2020.2977927","pdf_url":null,"source":{"id":"https://openalex.org/S4306422535","display_name":"IEEE Control Systems Letters","issn_l":"2475-1456","issn":["2475-1456"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Control Systems Letters","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/17","score":0.4000000059604645,"display_name":"Partnerships for the goals"}],"awards":[{"id":"https://openalex.org/G1257962346","display_name":null,"funder_award_id":"#FA9550-19-1-0169","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G28741391","display_name":null,"funder_award_id":"FA9550-18-1-0109","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G4297280941","display_name":null,"funder_award_id":"N00014-13-1-0151","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G6588266790","display_name":null,"funder_award_id":"1762829","funder_id":"https://openalex.org/F4320335353","funder_display_name":"National Science Foundation of Sri Lanka"}],"funders":[{"id":"https://openalex.org/F4320335353","display_name":"National Science Foundation of Sri Lanka","ror":"https://ror.org/010xaa060"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W1540245649","https://openalex.org/W1574514837","https://openalex.org/W1578936488","https://openalex.org/W1592648094","https://openalex.org/W1607353007","https://openalex.org/W1891170951","https://openalex.org/W1914756871","https://openalex.org/W1968908471","https://openalex.org/W1972149633","https://openalex.org/W1977671496","https://openalex.org/W1983523797","https://openalex.org/W1998683434","https://openalex.org/W2003183707","https://openalex.org/W2013895638","https://openalex.org/W2032631296","https://openalex.org/W2086975818","https://openalex.org/W2097253853","https://openalex.org/W2104843094","https://openalex.org/W2107308405","https://openalex.org/W2109987654","https://openalex.org/W2111034649","https://openalex.org/W2116508132","https://openalex.org/W2145956080","https://openalex.org/W2156387975","https://openalex.org/W2157577161","https://openalex.org/W2570540139","https://openalex.org/W2766918150","https://openalex.org/W2781919638","https://openalex.org/W2790688051","https://openalex.org/W2795039172","https://openalex.org/W2800330509","https://openalex.org/W2887138972","https://openalex.org/W2971473345","https://openalex.org/W2996568167","https://openalex.org/W3010713425","https://openalex.org/W4238000550","https://openalex.org/W4301747304","https://openalex.org/W6682889407"],"related_works":["https://openalex.org/W4255265352","https://openalex.org/W4239477580","https://openalex.org/W2952594763","https://openalex.org/W4285537323","https://openalex.org/W1932159282","https://openalex.org/W2090698372","https://openalex.org/W4383890581","https://openalex.org/W2965004901","https://openalex.org/W2921905705","https://openalex.org/W4233178034"],"abstract_inverted_index":{"This":[0],"letter":[1],"provides":[2,33],"an":[3,103],"approximate":[4],"online":[5,67],"adaptive":[6],"solution":[7],"to":[8,36,49,101,140,148],"the":[9,45,57,70,73,122,125,142,145],"infinite-horizon":[10],"optimal":[11,104],"control":[12],"problem":[13],"for":[14,135],"control-affine":[15],"continuous-time":[16],"nonlinear":[17],"systems":[18],"while":[19],"formalizing":[20],"system":[21,38,46,58,139],"safety":[22,34],"using":[23,41],"barrier":[24,30,43,126],"certificates.":[25],"The":[26],"use":[27],"of":[28,69,80,124,144],"a":[29,42,53,60,78,136],"function":[31,127],"transform":[32,128],"certificates":[35],"formalize":[37],"behavior.":[39],"Specifically,":[40],"function,":[44,72],"is":[47,75,95,113],"transformed":[48],"aid":[50,65],"in":[51,59,66,87,121],"developing":[52],"controller":[54],"which":[55,115],"maintains":[56],"pre-defined":[61],"constrained":[62],"region.":[63],"To":[64],"learning":[68],"value":[71],"state-space":[74],"segmented":[76],"into":[77],"number":[79],"user-defined":[81],"segments.":[82],"Off-policy":[83],"trajectories":[84],"are":[85,133],"selected":[86],"each":[88,98,107],"segment,":[89],"and":[90,129],"sparse":[91],"Bellman":[92],"error":[93],"extrapolation":[94],"performed":[96],"within":[97,106],"respective":[99],"segment":[100],"generate":[102],"policy":[105],"segment.":[108],"A":[109],"Lyapunov-like":[110],"stability":[111],"analysis":[112],"included":[114],"proves":[116],"uniformly":[117],"ultimately":[118],"bounded":[119],"regulation":[120],"presence":[123],"discontinuities.":[130],"Simulation":[131],"results":[132],"provided":[134],"two-state":[137],"dynamical":[138],"compare":[141],"performance":[143],"developed":[146],"method":[147],"existing":[149],"methods.":[150]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":1}],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2025-10-10T00:00:00"}
