{"id":"https://openalex.org/W2117717397","doi":"https://doi.org/10.1109/cdc.2010.5717676","title":"Optimal control of affine nonlinear continuous-time systems using an online Hamilton-Jacobi-Isaacs formulation","display_name":"Optimal control of affine nonlinear continuous-time systems using an online Hamilton-Jacobi-Isaacs formulation","publication_year":2010,"publication_date":"2010-12-01","ids":{"openalex":"https://openalex.org/W2117717397","doi":"https://doi.org/10.1109/cdc.2010.5717676","mag":"2117717397"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2010.5717676","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2010.5717676","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"49th IEEE Conference on Decision and Control (CDC)","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/A5045417097","display_name":"Travis Dierks","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"T. Dierks","raw_affiliation_strings":["DRS Sustainment Systems, Inc., Saint Louis, MO, USA","DRS Sustainment System, Inc., 201 Evans Lane, St. Louis, MO 63121, USA"],"affiliations":[{"raw_affiliation_string":"DRS Sustainment Systems, Inc., Saint Louis, MO, USA","institution_ids":[]},{"raw_affiliation_string":"DRS Sustainment System, Inc., 201 Evans Lane, St. Louis, MO 63121, USA","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078910343","display_name":"S. Jagannathan","orcid":"https://orcid.org/0000-0002-2310-3737"},"institutions":[{"id":"https://openalex.org/I20382870","display_name":"Missouri University of Science and Technology","ror":"https://ror.org/00scwqd12","country_code":"US","type":"education","lineage":["https://openalex.org/I20382870"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"S. Jagannathan","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Missouri University of Science and Technology, Rolla, MO, USA","Department of Electrical and Computer Engineering, Missouri University of Science and Technology, 301 W. 16th St., Rolla, 65409, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Missouri University of Science and Technology, Rolla, MO, USA","institution_ids":["https://openalex.org/I20382870"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Missouri University of Science and Technology, 301 W. 16th St., Rolla, 65409, USA","institution_ids":["https://openalex.org/I20382870"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5045417097"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":10.3704,"has_fulltext":false,"cited_by_count":88,"citation_normalized_percentile":{"value":0.98776806,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"3048","last_page":"3053"},"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/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9919999837875366,"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"}},{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9648000001907349,"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/bounded-function","display_name":"Bounded function","score":0.7324991226196289},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.6451117992401123},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5890544056892395},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.5825496912002563},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5124467015266418},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5052095055580139},{"id":"https://openalex.org/keywords/hamilton\u2013jacobi-equation","display_name":"Hamilton\u2013Jacobi equation","score":0.5030094981193542},{"id":"https://openalex.org/keywords/tracking-error","display_name":"Tracking error","score":0.4913126528263092},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45120206475257874},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.44825997948646545},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.44619259238243103},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4399668276309967},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.433908611536026},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3149850368499756},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.2533949017524719},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12355539202690125},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0767921507358551}],"concepts":[{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7324991226196289},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6451117992401123},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5890544056892395},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5825496912002563},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5124467015266418},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5052095055580139},{"id":"https://openalex.org/C2778860007","wikidata":"https://www.wikidata.org/wiki/Q1060137","display_name":"Hamilton\u2013Jacobi equation","level":2,"score":0.5030094981193542},{"id":"https://openalex.org/C183356978","wikidata":"https://www.wikidata.org/wiki/Q1779213","display_name":"Tracking error","level":3,"score":0.4913126528263092},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45120206475257874},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.44825997948646545},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.44619259238243103},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4399668276309967},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.433908611536026},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3149850368499756},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.2533949017524719},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12355539202690125},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0767921507358551},{"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/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2010.5717676","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2010.5717676","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"49th IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1517236425","https://openalex.org/W1518846109","https://openalex.org/W1596558867","https://openalex.org/W1650553268","https://openalex.org/W2037751122","https://openalex.org/W2047482409","https://openalex.org/W2068328804","https://openalex.org/W2093831009","https://openalex.org/W2098035803","https://openalex.org/W2099877034","https://openalex.org/W2109640889","https://openalex.org/W2116508132","https://openalex.org/W2121196039","https://openalex.org/W2132468772","https://openalex.org/W2495714227","https://openalex.org/W2798534591","https://openalex.org/W4244158972","https://openalex.org/W6630914634","https://openalex.org/W6722086367"],"related_works":["https://openalex.org/W4200506717","https://openalex.org/W2029860844","https://openalex.org/W1594944678","https://openalex.org/W2720912673","https://openalex.org/W2364831476","https://openalex.org/W2043759256","https://openalex.org/W575199273","https://openalex.org/W1979702477","https://openalex.org/W2107413838","https://openalex.org/W2142014702"],"abstract_inverted_index":{"Solving":[0],"the":[1,29,33,42,78,83,89,104,111,116,122,141,153,162,171,174],"Hamilton-Jacobi-Isaacs":[2],"(HJI)":[3],"equation,":[4,82],"commonly":[5],"used":[6,128],"in":[7],"H":[8],"<sub":[9],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[10],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u221e</sub>":[11],"optimal":[12,60,85,105,146,163],"control,":[13],"is":[14,45,74,98,165],"often":[15],"referred":[16],"to":[17,27,36,58,76,129,161],"as":[18],"a":[19,51],"two-player":[20],"differential":[21],"game":[22],"where":[23],"one":[24],"player":[25],"tries":[26,35],"minimize":[28],"cost":[30,106],"function":[31],"while":[32,139],"other":[34],"maximize":[37],"it.":[38],"In":[39,152],"this":[40],"paper,":[41],"HJI":[43,81],"equation":[44],"formulated":[46],"online":[47,54,123],"and":[48,62,88,110,167],"forward-in-time":[49],"using":[50],"novel":[52,94],"single":[53],"approximator":[55],"(SOLA)-based":[56],"scheme":[57],"achieve":[59],"regulation":[61],"tracking":[63],"control":[64,86,108],"of":[65,155,173],"affine":[66],"nonlinear":[67],"continuous-time":[68],"systems.":[69],"The":[70],"SOLA-based":[71],"adaptive":[72],"approach":[73,144],"designed":[75],"learn":[77],"infinite":[79],"horizon":[80],"corresponding":[84],"input,":[87,109],"worst":[90],"case":[91],"disturbance.":[92],"A":[93],"parameter":[95],"tuning":[96],"algorithm":[97],"derived":[99],"which":[100],"not":[101],"only":[102],"achieves":[103],"function,":[107],"disturbance,":[112],"but":[113],"also":[114],"ensures":[115],"system":[117],"states":[118],"remain":[119],"bounded":[120,137,150],"during":[121],"learning.":[124],"Lyapunov":[125],"methods":[126],"are":[127,134],"show":[130],"that":[131],"all":[132],"signals":[133,143,164],"uniformly":[135],"ultimately":[136],"(UUB)":[138],"ensuring":[140],"approximated":[142],"their":[145],"values":[147],"with":[148],"small":[149],"error.":[151],"absence":[154],"OLA":[156],"reconstruction":[157],"errors,":[158],"asymptotic":[159],"convergence":[160],"demonstrated,":[166],"simulation":[168],"results":[169],"illustrate":[170],"effectiveness":[172],"approach.":[175]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":11},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":15}],"updated_date":"2026-02-26T08:16:20.718346","created_date":"2025-10-10T00:00:00"}
