{"id":"https://openalex.org/W2010158378","doi":"https://doi.org/10.1109/tac.2014.2305932","title":"Minimized Tracking Error Randomness Control for Nonlinear Multivariate and Non-Gaussian Systems Using the Generalized Density Evolution Equation","display_name":"Minimized Tracking Error Randomness Control for Nonlinear Multivariate and Non-Gaussian Systems Using the Generalized Density Evolution Equation","publication_year":2014,"publication_date":"2014-02-12","ids":{"openalex":"https://openalex.org/W2010158378","doi":"https://doi.org/10.1109/tac.2014.2305932","mag":"2010158378"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2014.2305932","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2014.2305932","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/A5101897479","display_name":"Mifeng Ren","orcid":"https://orcid.org/0000-0001-5062-0521"},"institutions":[{"id":"https://openalex.org/I153473198","display_name":"North China Electric Power University","ror":"https://ror.org/04qr5t414","country_code":"CN","type":"education","lineage":["https://openalex.org/I153473198"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Mifeng Ren","raw_affiliation_strings":["State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources and School of Control and Computer Engineering, North China Electric Power University, Beijing, China","State Key Lab. of Alternate Electr. Power Syst. with Renewable Energy Sources, North China Electr. Power Univ., Beijing, China"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources and School of Control and Computer Engineering, North China Electric Power University, Beijing, China","institution_ids":["https://openalex.org/I153473198"]},{"raw_affiliation_string":"State Key Lab. of Alternate Electr. Power Syst. with Renewable Energy Sources, North China Electr. Power Univ., Beijing, China","institution_ids":["https://openalex.org/I153473198"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068121401","display_name":"Jianhua Zhang","orcid":"https://orcid.org/0000-0003-2528-6132"},"institutions":[{"id":"https://openalex.org/I153473198","display_name":"North China Electric Power University","ror":"https://ror.org/04qr5t414","country_code":"CN","type":"education","lineage":["https://openalex.org/I153473198"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianhua Zhang","raw_affiliation_strings":["State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources and School of Control and Computer Engineering, North China Electric Power University, Beijing, China","State Key Lab. of Alternate Electr. Power Syst. with Renewable Energy Sources, North China Electr. Power Univ., Beijing, China"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources and School of Control and Computer Engineering, North China Electric Power University, Beijing, China","institution_ids":["https://openalex.org/I153473198"]},{"raw_affiliation_string":"State Key Lab. of Alternate Electr. Power Syst. with Renewable Energy Sources, North China Electr. Power Univ., Beijing, China","institution_ids":["https://openalex.org/I153473198"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100369619","display_name":"Hong Wang","orcid":"https://orcid.org/0000-0002-9876-0176"},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]},{"id":"https://openalex.org/I9224756","display_name":"Northeastern University","ror":"https://ror.org/03awzbc87","country_code":"CN","type":"education","lineage":["https://openalex.org/I9224756"]}],"countries":["CN","GB"],"is_corresponding":false,"raw_author_name":"Hong Wang","raw_affiliation_strings":["Control System Centre, School of Electrical and Electronics Engineering, Northeastern University, Shenyang, China","Sch. of Electr. & Electron. Eng., Univ. of Manchester, Manchester, UK#TAB#"],"affiliations":[{"raw_affiliation_string":"Control System Centre, School of Electrical and Electronics Engineering, Northeastern University, Shenyang, China","institution_ids":["https://openalex.org/I9224756"]},{"raw_affiliation_string":"Sch. of Electr. & Electron. Eng., Univ. of Manchester, Manchester, UK#TAB#","institution_ids":["https://openalex.org/I28407311"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101897479"],"corresponding_institution_ids":["https://openalex.org/I153473198"],"apc_list":null,"apc_paid":null,"fwci":4.00681401,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.94685195,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"59","issue":"9","first_page":"2486","last_page":"2490"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.9891999959945679,"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":0.9891999959945679,"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9858999848365784,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9829999804496765,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/mathematics","display_name":"Mathematics","score":0.6589567065238953},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.5889480113983154},{"id":"https://openalex.org/keywords/tracking-error","display_name":"Tracking error","score":0.5566085577011108},{"id":"https://openalex.org/keywords/randomness","display_name":"Randomness","score":0.509507954120636},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.493962824344635},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.48497653007507324},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.4642065167427063},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4636894762516022},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.4620581865310669},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45309972763061523},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4315371513366699},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25191164016723633},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.12492665648460388},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11645650863647461}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6589567065238953},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.5889480113983154},{"id":"https://openalex.org/C183356978","wikidata":"https://www.wikidata.org/wiki/Q1779213","display_name":"Tracking error","level":3,"score":0.5566085577011108},{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.509507954120636},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.493962824344635},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.48497653007507324},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4642065167427063},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4636894762516022},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.4620581865310669},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45309972763061523},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4315371513366699},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25191164016723633},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.12492665648460388},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11645650863647461},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/tac.2014.2305932","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2014.2305932","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":[{"score":0.8299999833106995,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G4713210665","display_name":null,"funder_award_id":"973","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G4782804432","display_name":null,"funder_award_id":"2011CB710706","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"}],"funders":[{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W54793854","https://openalex.org/W1525883337","https://openalex.org/W1589395967","https://openalex.org/W1975204614","https://openalex.org/W1976350890","https://openalex.org/W1986092330","https://openalex.org/W2023196389","https://openalex.org/W2043779031","https://openalex.org/W2060867552","https://openalex.org/W2083450299","https://openalex.org/W2091992558","https://openalex.org/W2093324180","https://openalex.org/W2097521973","https://openalex.org/W2103518782","https://openalex.org/W2106147350","https://openalex.org/W2117312103","https://openalex.org/W2120313575","https://openalex.org/W2129311259","https://openalex.org/W2133293139","https://openalex.org/W2135878731","https://openalex.org/W2142951803","https://openalex.org/W2145117626","https://openalex.org/W2158764551","https://openalex.org/W2168817745","https://openalex.org/W2354015221","https://openalex.org/W2489768403","https://openalex.org/W2491398393","https://openalex.org/W2498425058","https://openalex.org/W3144496105","https://openalex.org/W6679837025"],"related_works":["https://openalex.org/W3034924094","https://openalex.org/W1488708774","https://openalex.org/W3094954546","https://openalex.org/W2981906196","https://openalex.org/W4327779705","https://openalex.org/W1513698804","https://openalex.org/W4310560702","https://openalex.org/W2029712093","https://openalex.org/W1982811510","https://openalex.org/W4255503743"],"abstract_inverted_index":{"In":[0],"this":[1,60],"technical":[2],"note,":[3],"a":[4,91],"new":[5],"stochastic":[6,61,133],"control":[7,48,62,83,94,135],"algorithm":[8,95],"is":[9,27,37,56,96,108,122],"presented":[10],"for":[11,59],"nonlinear":[12],"and":[13,50,79,128],"non-Gaussian":[14],"continuous-time":[15],"systems.":[16],"Based":[17],"on":[18,81],"the":[19,31,35,40,70,82,88,99,104,112,116,126,131],"recently":[20],"developed":[21],"generalized":[22],"density":[23,42],"evolution":[24],"equation,":[25,34],"which":[26,64],"more":[28],"tractable":[29],"than":[30],"classical":[32],"Liouville":[33],"relationship":[36],"established":[38],"among":[39],"probability":[41],"function":[43],"(PDF)":[44],"of":[45,69,75,115,130],"tracking":[46,71,77],"error,":[47,72],"input":[49,84],"disturbances.":[51],"An":[52,119],"improved":[53],"performance":[54,89],"index":[55],"then":[57],"constructed":[58],"strategy,":[63],"includes":[65],"quadratic":[66],"information":[67],"potential":[68],"mean":[73],"value":[74],"squared":[76],"error":[78],"constraints":[80],"energy.":[85],"By":[86],"minimizing":[87],"index,":[90],"recursive":[92],"optimal":[93,134],"obtained":[97],"using":[98],"gradient":[100],"descent":[101],"method.":[102],"Moreover,":[103],"statistical":[105],"linearization":[106],"technique":[107],"adopted":[109],"to":[110,124],"formulate":[111],"boundedness":[113],"condition":[114],"closed-loop":[117],"system.":[118],"illustrative":[120],"example":[121],"given":[123],"demonstrate":[125],"validity":[127],"efficiency":[129],"proposed":[132],"methodology.":[136]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}