{"id":"https://openalex.org/W4288064487","doi":"https://doi.org/10.1109/tac.2022.3194040","title":"Approximate Optimal Trajectory Tracking With Sparse Bellman Error Extrapolation","display_name":"Approximate Optimal Trajectory Tracking With Sparse Bellman Error Extrapolation","publication_year":2022,"publication_date":"2022-07-27","ids":{"openalex":"https://openalex.org/W4288064487","doi":"https://doi.org/10.1109/tac.2022.3194040"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2022.3194040","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2022.3194040","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","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/I1295339012","display_name":"Boeing (United States)","ror":"https://ror.org/04sm5zn07","country_code":"US","type":"company","lineage":["https://openalex.org/I1295339012"]},{"id":"https://openalex.org/I2800865783","display_name":"Aurora Flight Sciences (United States)","ror":"https://ror.org/0110df420","country_code":"US","type":"company","lineage":["https://openalex.org/I2800865783"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Max L. Greene","raw_affiliation_strings":["Aurora Flight Sciences, a Boeing Company, Cambridge, MA, USA"],"raw_orcid":"https://orcid.org/0000-0003-2733-0344","affiliations":[{"raw_affiliation_string":"Aurora Flight Sciences, a Boeing Company, Cambridge, MA, USA","institution_ids":["https://openalex.org/I1295339012","https://openalex.org/I2800865783"]}]},{"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":["Charles Stark Draper Laboratory, Inc., Cambridge, MA, USA"],"raw_orcid":"https://orcid.org/0000-0002-2328-9148","affiliations":[{"raw_affiliation_string":"Charles Stark Draper Laboratory, Inc., Cambridge, MA, 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/I2802946424","display_name":"Johns Hopkins University Applied Physics Laboratory","ror":"https://ror.org/029pp9z10","country_code":"US","type":"facility","lineage":["https://openalex.org/I145311948","https://openalex.org/I2802946424"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Scott Nivison","raw_affiliation_strings":["Johns Hopkins University Applied Physics Laboratory, Fort Walton Beach, FL, USA"],"raw_orcid":"https://orcid.org/0000-0002-5738-2535","affiliations":[{"raw_affiliation_string":"Johns Hopkins University Applied Physics Laboratory, Fort Walton Beach, FL, USA","institution_ids":["https://openalex.org/I2802946424"]}]},{"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":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2195,"currency":"USD","value_usd":2195},"apc_paid":null,"fwci":1.0766,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.79100064,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"68","issue":"6","first_page":"3618","last_page":"3624"},"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/T12277","display_name":"Frequency Control in Power Systems","score":0.9728000164031982,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.944599986076355,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/extrapolation","display_name":"Extrapolation","score":0.7624905109405518},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.6092011332511902},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5368016362190247},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"Dynamic programming","score":0.5135262608528137},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4936574399471283},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.4927399456501007},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.491269052028656},{"id":"https://openalex.org/keywords/function-approximation","display_name":"Function approximation","score":0.4900871515274048},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.47602608799934387},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4394649565219879},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.43876805901527405},{"id":"https://openalex.org/keywords/classification-of-discontinuities","display_name":"Classification of discontinuities","score":0.42206305265426636},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39568910002708435},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.30962252616882324},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1501067876815796}],"concepts":[{"id":"https://openalex.org/C132459708","wikidata":"https://www.wikidata.org/wiki/Q744069","display_name":"Extrapolation","level":2,"score":0.7624905109405518},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.6092011332511902},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5368016362190247},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.5135262608528137},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4936574399471283},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.4927399456501007},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.491269052028656},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.4900871515274048},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.47602608799934387},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4394649565219879},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.43876805901527405},{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.42206305265426636},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39568910002708435},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.30962252616882324},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1501067876815796},{"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2022.3194040","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2022.3194040","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_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/G5399105082","display_name":null,"funder_award_id":"N00014\u201021\u20101\u20102481","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W560518094","https://openalex.org/W1519369336","https://openalex.org/W1540245649","https://openalex.org/W1854776945","https://openalex.org/W1914756871","https://openalex.org/W1977671496","https://openalex.org/W1981146152","https://openalex.org/W2086975818","https://openalex.org/W2097253853","https://openalex.org/W2109987654","https://openalex.org/W2156387975","https://openalex.org/W2570540139","https://openalex.org/W2580909119","https://openalex.org/W2595897327","https://openalex.org/W2781919638","https://openalex.org/W2790688051","https://openalex.org/W2800330509","https://openalex.org/W2943852008","https://openalex.org/W3009484445","https://openalex.org/W3010713425","https://openalex.org/W3011457441","https://openalex.org/W3016201194","https://openalex.org/W3016893731","https://openalex.org/W3155402581","https://openalex.org/W3172934943","https://openalex.org/W3213472335","https://openalex.org/W4238000550","https://openalex.org/W4288319859","https://openalex.org/W4301747304","https://openalex.org/W6682889407","https://openalex.org/W6764053384","https://openalex.org/W6794398224","https://openalex.org/W6804409665"],"related_works":["https://openalex.org/W4239477580","https://openalex.org/W2001439412","https://openalex.org/W1524506417","https://openalex.org/W2964126589","https://openalex.org/W2716677055","https://openalex.org/W4307691181","https://openalex.org/W2188011710","https://openalex.org/W2347563025","https://openalex.org/W2107530459","https://openalex.org/W4288064487"],"abstract_inverted_index":{"This":[0],"article":[1,176],"provides":[2],"an":[3],"approximate":[4,25],"online":[5],"adaptive":[6],"solution":[7],"to":[8,69,98,135,151,185],"the":[9,40,46,52,73,90,100,109,126,139,143,153,158,167,178,186],"infinite-horizon":[10],"optimal":[11,41],"tracking":[12],"problem":[13],"for":[14],"control-affine":[15],"continuous-time":[16],"nonlinear":[17],"systems":[18],"with":[19],"uncertain":[20],"drift":[21],"dynamics.":[22],"A":[23,129],"model-based":[24,50],"dynamic":[26],"programming":[27],"(ADP)":[28],"approach,":[29],"which":[30],"is":[31,55,80,133],"facilitated":[32],"using":[33,166],"a":[34],"concurrent":[35],"learning-based":[36],"system":[37,141],"identifier,":[38],"approximates":[39],"value":[42,74],"function.":[43],"To":[44],"reduce":[45,99],"computational":[47,101],"complexity":[48],"of":[49,72,89,103,116,125,138,145,157],"ADP,":[51],"state":[53,91,127],"space":[54],"segmented":[56],"into":[57],"user-defined":[58],"segments":[59,88],"(i.e.,":[60],"regions).":[61],"Off-policy":[62],"trajectories":[63,119],"are":[64,96,120,149],"selected":[65],"within":[66],"each":[67],"segment":[68],"facilitate":[70],"learning":[71],"function":[75],"weight":[76,110],"estimates;":[77],"this":[78,175],"process":[79],"called":[81],"Bellman":[82],"error":[83],"(BE)":[84],"extrapolation.":[85,105],"Within":[86],"certain":[87,123],"space,":[92],"sparse":[93],"neural":[94],"networks":[95],"used":[97],"expense":[102],"BE":[104,118,170,188],"Discontinuities":[106],"occur":[107],"in":[108,122,142,174],"update":[111],"laws":[112],"since":[113],"different":[114],"groupings":[115],"extrapolated":[117],"active":[121],"regions":[124],"space.":[128],"Lyapunov-like":[130],"stability":[131],"analysis":[132],"presented":[134],"prove":[136],"boundedness":[137],"overall":[140],"presence":[144],"discontinuities.":[146],"Simulation":[147],"results":[148,163],"included":[150],"demonstrate":[152,164],"performance":[154],"and":[155],"validity":[156],"developed":[159,173],"method.":[160,190],"The":[161],"simulation":[162],"that":[165],"sparse,":[168],"switched":[169],"extrapolation":[171,189],"method":[172],"reduces":[177],"computation":[179],"time":[180],"by":[181],"85.6%":[182],"when":[183],"compared":[184],"traditional":[187]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1}],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2025-10-10T00:00:00"}
