{"id":"https://openalex.org/W2110175753","doi":"https://doi.org/10.1109/acc.2009.5160131","title":"Optimal control of uncertain nonlinear systems using a neural network and RISE feedback","display_name":"Optimal control of uncertain nonlinear systems using a neural network and RISE feedback","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2110175753","doi":"https://doi.org/10.1109/acc.2009.5160131","mag":"2110175753"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2009.5160131","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2009.5160131","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 American Control Conference","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/A5021562593","display_name":"K. Dupree","orcid":null},"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":true,"raw_author_name":"K. Dupree","raw_affiliation_strings":["Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, USA","Department of Mechanical And Aerospace Engineering, University of Florida, Gainesville, 32611, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, USA","institution_ids":["https://openalex.org/I33213144"]},{"raw_affiliation_string":"Department of Mechanical And Aerospace Engineering, University of Florida, Gainesville, 32611, USA","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035192244","display_name":"P. M. Patre","orcid":"https://orcid.org/0000-0001-5525-0611"},"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":"P. M. Patre","raw_affiliation_strings":["Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, USA","Department of Mechanical And Aerospace Engineering, University of Florida, Gainesville, 32611, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, USA","institution_ids":["https://openalex.org/I33213144"]},{"raw_affiliation_string":"Department of Mechanical And Aerospace Engineering, University of Florida, Gainesville, 32611, USA","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013944523","display_name":"Z. D. Wilcox","orcid":null},"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":"Z. D. Wilcox","raw_affiliation_strings":["Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, USA","Department of Mechanical And Aerospace Engineering, University of Florida, Gainesville, 32611, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, USA","institution_ids":["https://openalex.org/I33213144"]},{"raw_affiliation_string":"Department of Mechanical And Aerospace Engineering, University of Florida, Gainesville, 32611, USA","institution_ids":["https://openalex.org/I33213144"]}]},{"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":"W. E. Dixon","raw_affiliation_strings":["Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, USA","Department of Mechanical And Aerospace Engineering, University of Florida, Gainesville, 32611, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, USA","institution_ids":["https://openalex.org/I33213144"]},{"raw_affiliation_string":"Department of Mechanical And Aerospace Engineering, University of Florida, Gainesville, 32611, USA","institution_ids":["https://openalex.org/I33213144"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5021562593"],"corresponding_institution_ids":["https://openalex.org/I33213144"],"apc_list":null,"apc_paid":null,"fwci":0.6856,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.71853372,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"361","last_page":"366"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.9977999925613403,"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":0.9977999925613403,"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":0.9976000189781189,"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/T11236","display_name":"Control Systems and Identification","score":0.9966999888420105,"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/hamilton\u2013jacobi\u2013bellman-equation","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","score":0.9463927149772644},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.7038859128952026},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.6350478529930115},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.6272422075271606},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5879747271537781},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5703544616699219},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5319972634315491},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.5304471850395203},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.5028430819511414},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.48777586221694946},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4583096504211426},{"id":"https://openalex.org/keywords/feedback-linearization","display_name":"Feedback linearization","score":0.4552754759788513},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44462528824806213},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.42168182134628296},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.17901882529258728},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1039649248123169}],"concepts":[{"id":"https://openalex.org/C196978813","wikidata":"https://www.wikidata.org/wiki/Q3302775","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","level":3,"score":0.9463927149772644},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.7038859128952026},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.6350478529930115},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6272422075271606},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5879747271537781},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5703544616699219},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5319972634315491},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.5304471850395203},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.5028430819511414},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.48777586221694946},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4583096504211426},{"id":"https://openalex.org/C85736874","wikidata":"https://www.wikidata.org/wiki/Q672139","display_name":"Feedback linearization","level":3,"score":0.4552754759788513},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44462528824806213},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.42168182134628296},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.17901882529258728},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1039649248123169},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"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/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/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/acc.2009.5160131","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2009.5160131","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 American Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W5108103","https://openalex.org/W120139811","https://openalex.org/W194456869","https://openalex.org/W1483858097","https://openalex.org/W1492826595","https://openalex.org/W1522935148","https://openalex.org/W1542432808","https://openalex.org/W1576413672","https://openalex.org/W1644413845","https://openalex.org/W1988242845","https://openalex.org/W1997000456","https://openalex.org/W2010594214","https://openalex.org/W2016360498","https://openalex.org/W2017549645","https://openalex.org/W2048396933","https://openalex.org/W2071412131","https://openalex.org/W2099460294","https://openalex.org/W2101433417","https://openalex.org/W2110150788","https://openalex.org/W2138077931","https://openalex.org/W2147914308","https://openalex.org/W2154868061","https://openalex.org/W2170579465","https://openalex.org/W2278371096","https://openalex.org/W2302808317","https://openalex.org/W2534139192","https://openalex.org/W2798534591"],"related_works":["https://openalex.org/W2032834442","https://openalex.org/W3153900688","https://openalex.org/W2115544975","https://openalex.org/W2902017027","https://openalex.org/W1654696814","https://openalex.org/W4291598237","https://openalex.org/W2766998270","https://openalex.org/W4292330635","https://openalex.org/W3168988147","https://openalex.org/W4239477580"],"abstract_inverted_index":{"A":[0,107],"sufficient":[1],"condition":[2],"to":[3,10,64,78,112],"solve":[4,11],"an":[5],"optimal":[6,119],"control":[7],"problem":[8],"is":[9,30,110],"the":[12,23,52,87,105,114,117],"Hamilton-Jacobi-Bellman":[13],"(HJB)":[14],"equation.":[15],"However,":[16],"finding":[17],"a":[18,27,67,73,81,91,97],"value":[19,54],"function":[20],"that":[21],"satisfies":[22],"HJB":[24,53],"equation":[25],"for":[26],"nonlinear":[28,92],"systems":[29],"challenging.":[31],"Previous":[32],"efforts":[33,63],"have":[34,45],"utilized":[35],"feedback":[36,76],"linearization":[37],"methods":[38],"which":[39],"assume":[40],"exact":[41],"model":[42],"knowledge,":[43],"or":[44],"developed":[46,118],"neural":[47],"network":[48],"(NN)":[49],"approximations":[50],"of":[51,90,116],"function.":[55],"The":[56],"current":[57],"effort":[58],"builds":[59],"on":[60],"our":[61],"previous":[62],"illustrate":[65],"how":[66],"NN":[68],"can":[69],"be":[70],"combined":[71],"with":[72],"recent":[74],"robust":[75],"method":[77],"asymptotically":[79,95],"minimize":[80],"given":[82],"quadratic":[83],"performance":[84],"index":[85],"as":[86],"generalized":[88],"coordinates":[89],"Euler-Lagrange":[93],"system":[94],"track":[96],"desired":[98],"time-varying":[99],"trajectory":[100],"despite":[101],"general":[102],"uncertainty":[103],"in":[104],"dynamics.":[106],"Lyapunov":[108],"analysis":[109],"provided":[111],"examine":[113],"stability":[115],"controller.":[120]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
