{"id":"https://openalex.org/W2790688051","doi":"https://doi.org/10.1109/tnnls.2018.2808102","title":"Approximate Dynamic Programming: Combining Regional and Local State Following Approximations","display_name":"Approximate Dynamic Programming: Combining Regional and Local State Following Approximations","publication_year":2018,"publication_date":"2018-03-16","ids":{"openalex":"https://openalex.org/W2790688051","doi":"https://doi.org/10.1109/tnnls.2018.2808102","mag":"2790688051","pmid":"https://pubmed.ncbi.nlm.nih.gov/29771668"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2018.2808102","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2018.2808102","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 Transactions on Neural Networks and Learning Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5018956236","display_name":"Patryk Deptula","orcid":"https://orcid.org/0000-0002-2328-9148"},"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":"Patryk Deptula","raw_affiliation_strings":["Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, USA"],"raw_orcid":"https://orcid.org/0000-0002-2328-9148","affiliations":[{"raw_affiliation_string":"Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, USA","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058488295","display_name":"Joel A. Rosenfeld","orcid":"https://orcid.org/0000-0003-3219-448X"},"institutions":[{"id":"https://openalex.org/I200719446","display_name":"Vanderbilt University","ror":"https://ror.org/02vm5rt34","country_code":"US","type":"education","lineage":["https://openalex.org/I200719446"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Joel A. Rosenfeld","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, Vanderbilt University, Nashville, TN, USA"],"raw_orcid":"https://orcid.org/0000-0003-3219-448X","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, Vanderbilt University, Nashville, TN, USA","institution_ids":["https://openalex.org/I200719446"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071224574","display_name":"Rushikesh Kamalapurkar","orcid":"https://orcid.org/0000-0001-9963-5361"},"institutions":[{"id":"https://openalex.org/I115475287","display_name":"Oklahoma State University","ror":"https://ror.org/01g9vbr38","country_code":"US","type":"education","lineage":["https://openalex.org/I115475287"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rushikesh Kamalapurkar","raw_affiliation_strings":["School of Mechanical and Aerospace Engineering, Oklahoma State University, Stillwater, OK, USA"],"raw_orcid":"https://orcid.org/0000-0001-9963-5361","affiliations":[{"raw_affiliation_string":"School of Mechanical and Aerospace Engineering, Oklahoma State University, Stillwater, OK, USA","institution_ids":["https://openalex.org/I115475287"]}]},{"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, FL, USA"],"raw_orcid":"https://orcid.org/0000-0002-5091-181X","affiliations":[{"raw_affiliation_string":"Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, USA","institution_ids":["https://openalex.org/I33213144"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.7086,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.94036734,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"29","issue":"6","first_page":"2154","last_page":"2166"},"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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.9891999959945679,"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/T10675","display_name":"Mechanical Circulatory Support Devices","score":0.9585000276565552,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.6858670711517334},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6664380431175232},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.5801376700401306},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5560528039932251},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5505396127700806},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5433560013771057},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5405226945877075},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.4868618845939636},{"id":"https://openalex.org/keywords/reinforcement-learning","display_name":"Reinforcement learning","score":0.4312489628791809},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.41962310671806335},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41259095072746277},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32939088344573975},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2279825508594513},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12905827164649963},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.12629058957099915},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12364134192466736},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.07919010519981384}],"concepts":[{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.6858670711517334},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6664380431175232},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5801376700401306},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5560528039932251},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5505396127700806},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5433560013771057},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5405226945877075},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.4868618845939636},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.4312489628791809},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41962310671806335},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41259095072746277},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32939088344573975},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2279825508594513},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12905827164649963},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.12629058957099915},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12364134192466736},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.07919010519981384},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/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":2,"locations":[{"id":"doi:10.1109/tnnls.2018.2808102","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2018.2808102","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 Transactions on Neural Networks and Learning Systems","raw_type":"journal-article"},{"id":"pmid:29771668","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/29771668","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on neural networks and learning systems","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"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/G4309261220","display_name":"Adaptive dynamic programming for uncertain nonlinear systems through coupling of nonlinear analysis and data-based learning","funder_award_id":"1509516","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"},{"id":"https://openalex.org/F4320332201","display_name":"Office of the Secretary of Defense","ror":"https://ror.org/00q4sx826"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W1483858097","https://openalex.org/W1486164486","https://openalex.org/W1527736490","https://openalex.org/W1540245649","https://openalex.org/W1580348315","https://openalex.org/W1597405158","https://openalex.org/W1601719319","https://openalex.org/W1698155719","https://openalex.org/W1749408314","https://openalex.org/W1977671496","https://openalex.org/W1981146152","https://openalex.org/W1983523797","https://openalex.org/W1988242845","https://openalex.org/W1995273480","https://openalex.org/W1997603681","https://openalex.org/W2002007892","https://openalex.org/W2039762773","https://openalex.org/W2052305027","https://openalex.org/W2067603665","https://openalex.org/W2081514674","https://openalex.org/W2085194340","https://openalex.org/W2086975818","https://openalex.org/W2104843094","https://openalex.org/W2113501460","https://openalex.org/W2121863487","https://openalex.org/W2157577161","https://openalex.org/W2160698719","https://openalex.org/W2165726932","https://openalex.org/W2214816543","https://openalex.org/W2241799117","https://openalex.org/W2292860354","https://openalex.org/W2343912161","https://openalex.org/W2403413656","https://openalex.org/W2476385022","https://openalex.org/W2476930474","https://openalex.org/W2509783950","https://openalex.org/W2535973186","https://openalex.org/W2602493242","https://openalex.org/W2735449579","https://openalex.org/W3141455185","https://openalex.org/W4214717370","https://openalex.org/W4251512373","https://openalex.org/W4285719527","https://openalex.org/W6628910748","https://openalex.org/W6728517856"],"related_works":["https://openalex.org/W4306904969","https://openalex.org/W2138720691","https://openalex.org/W4362501864","https://openalex.org/W4380318855","https://openalex.org/W2031695474","https://openalex.org/W2024136090","https://openalex.org/W2386410636","https://openalex.org/W3038962357","https://openalex.org/W2025663273","https://openalex.org/W3099153698"],"abstract_inverted_index":{"An":[0],"infinite-horizon":[1],"optimal":[2],"regulation":[3],"problem":[4],"for":[5,141],"a":[6,14,21,47,62,71,83,98,134],"control-affine":[7],"deterministic":[8],"system":[9,126],"is":[10,80,131],"solved":[11],"online":[12],"using":[13,82,133],"local":[15,63],"state":[16,67,96],"following":[17],"(StaF)":[18],"kernel":[19,53],"and":[20,90,145,153],"regional":[22],"model-based":[23],"reinforcement":[24],"learning":[25],"(R-MBRL)":[26],"method":[27],"to":[28,41,56,114,128,149],"approximate":[29,42,57],"the":[30,43,51,58,66,77,88,91,95,101,103,111,115,125,129,151,156],"value":[31,44,59,78,104],"function.":[32],"Unlike":[33],"traditional":[34],"methods":[35],"such":[36],"as":[37],"R-MBRL":[38,116],"that":[39,68],"aim":[40],"function":[45,60,79,105],"over":[46],"large":[48],"compact":[49,72],"set,":[50],"StaF":[52,112],"approach":[54,113],"aims":[55],"in":[61],"neighborhood":[64,99],"of":[65,87,124,155],"travels":[69],"within":[70],"set.":[73],"In":[74],"this":[75],"paper,":[76],"approximated":[81,109],"state-dependent":[84],"convex":[85],"combination":[86],"StaF-based":[89],"R-MBRL-based":[92],"approximations.":[93],"As":[94],"enters":[97],"containing":[100],"origin,":[102],"transitions":[106],"from":[107],"being":[108],"by":[110],"approach.":[117],"Semiglobal":[118],"uniformly":[119],"ultimately":[120],"bounded":[121],"(SGUUB)":[122],"convergence":[123],"states":[127],"origin":[130],"established":[132],"Lyapunov-based":[135],"analysis.":[136],"Simulation":[137],"results":[138],"are":[139],"provided":[140],"two,":[142],"three,":[143],"six,":[144],"ten-state":[146],"dynamical":[147],"systems":[148],"demonstrate":[150],"scalability":[152],"performance":[154],"developed":[157],"method.":[158]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}