{"id":"https://openalex.org/W2575090965","doi":"https://doi.org/10.1109/jas.2017.7510322","title":"Observer-based adaptive optimal control for unknown singularly perturbed nonlinear systems with input constraints","display_name":"Observer-based adaptive optimal control for unknown singularly perturbed nonlinear systems with input constraints","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2575090965","doi":"https://doi.org/10.1109/jas.2017.7510322","mag":"2575090965"},"language":"en","primary_location":{"id":"doi:10.1109/jas.2017.7510322","is_oa":false,"landing_page_url":"https://doi.org/10.1109/jas.2017.7510322","pdf_url":null,"source":{"id":"https://openalex.org/S2484288132","display_name":"IEEE/CAA Journal of Automatica Sinica","issn_l":"2329-9266","issn":["2329-9266","2329-9274"],"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/CAA Journal of Automatica Sinica","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/A5031096367","display_name":"Zhi\u2010Jun Fu","orcid":"https://orcid.org/0000-0002-9147-3676"},"institutions":[{"id":"https://openalex.org/I55712492","display_name":"Zhejiang University of Technology","ror":"https://ror.org/02djqfd08","country_code":"CN","type":"education","lineage":["https://openalex.org/I55712492"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhijun Fu","raw_affiliation_strings":["College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou, 310014, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou, 310014, China","institution_ids":["https://openalex.org/I55712492"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085378824","display_name":"Wenfang Xie","orcid":"https://orcid.org/0000-0003-2449-6306"},"institutions":[{"id":"https://openalex.org/I60158472","display_name":"Concordia University","ror":"https://ror.org/0420zvk78","country_code":"CA","type":"education","lineage":["https://openalex.org/I60158472"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Wenfang Xie","raw_affiliation_strings":["Department of Mechanical and Industrial Engineering, Concordia University, Montreal H3G ZW1, Quebec, CAN"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Industrial Engineering, Concordia University, Montreal H3G ZW1, Quebec, CAN","institution_ids":["https://openalex.org/I60158472"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056771244","display_name":"Subhash Rakheja","orcid":"https://orcid.org/0000-0002-6586-266X"},"institutions":[{"id":"https://openalex.org/I60158472","display_name":"Concordia University","ror":"https://ror.org/0420zvk78","country_code":"CA","type":"education","lineage":["https://openalex.org/I60158472"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Subhash Rakheja","raw_affiliation_strings":["Department of Mechanical and Industrial Engineering, Concordia University, Montreal H3G ZW1, Quebec, CAN"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Industrial Engineering, Concordia University, Montreal H3G ZW1, Quebec, CAN","institution_ids":["https://openalex.org/I60158472"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008377523","display_name":"Jing Na","orcid":"https://orcid.org/0000-0002-3067-1580"},"institutions":[{"id":"https://openalex.org/I10660446","display_name":"Kunming University of Science and Technology","ror":"https://ror.org/00xyeez13","country_code":"CN","type":"education","lineage":["https://openalex.org/I10660446"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jing Na","raw_affiliation_strings":["Faculty of Mechanical and Electrical Engineering, Kunming University of Science and Technology, Kunming 650500, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mechanical and Electrical Engineering, Kunming University of Science and Technology, Kunming 650500, China","institution_ids":["https://openalex.org/I10660446"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.0412,"has_fulltext":false,"cited_by_count":40,"citation_normalized_percentile":{"value":0.95894501,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"4","issue":"1","first_page":"48","last_page":"57"},"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":0.9825999736785889,"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/T14413","display_name":"Advanced Technologies in Various Fields","score":0.9251000285148621,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.8273886442184448},{"id":"https://openalex.org/keywords/hamilton\u2013jacobi\u2013bellman-equation","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","score":0.7932605743408203},{"id":"https://openalex.org/keywords/observer","display_name":"Observer (physics)","score":0.6750046014785767},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.6674968004226685},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5433365702629089},{"id":"https://openalex.org/keywords/separation-principle","display_name":"Separation principle","score":0.5302279591560364},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4718755781650543},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4692615866661072},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.46430352330207825},{"id":"https://openalex.org/keywords/adaptive-control","display_name":"Adaptive control","score":0.432089626789093},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4208712875843048},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4100174009799957},{"id":"https://openalex.org/keywords/state-observer","display_name":"State observer","score":0.34818530082702637},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33777564764022827},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.2061520218849182},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08938312530517578}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.8273886442184448},{"id":"https://openalex.org/C196978813","wikidata":"https://www.wikidata.org/wiki/Q3302775","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","level":3,"score":0.7932605743408203},{"id":"https://openalex.org/C2780704645","wikidata":"https://www.wikidata.org/wiki/Q9251458","display_name":"Observer (physics)","level":2,"score":0.6750046014785767},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6674968004226685},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5433365702629089},{"id":"https://openalex.org/C62431964","wikidata":"https://www.wikidata.org/wiki/Q2271572","display_name":"Separation principle","level":4,"score":0.5302279591560364},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4718755781650543},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4692615866661072},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.46430352330207825},{"id":"https://openalex.org/C107464732","wikidata":"https://www.wikidata.org/wiki/Q235781","display_name":"Adaptive control","level":3,"score":0.432089626789093},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4208712875843048},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4100174009799957},{"id":"https://openalex.org/C3031470","wikidata":"https://www.wikidata.org/wiki/Q818544","display_name":"State observer","level":3,"score":0.34818530082702637},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33777564764022827},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.2061520218849182},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08938312530517578},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"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/jas.2017.7510322","is_oa":false,"landing_page_url":"https://doi.org/10.1109/jas.2017.7510322","pdf_url":null,"source":{"id":"https://openalex.org/S2484288132","display_name":"IEEE/CAA Journal of Automatica Sinica","issn_l":"2329-9266","issn":["2329-9266","2329-9274"],"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/CAA Journal of Automatica Sinica","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.7400000095367432}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W560518094","https://openalex.org/W575905749","https://openalex.org/W630356209","https://openalex.org/W1461376240","https://openalex.org/W1487127700","https://openalex.org/W1527736490","https://openalex.org/W1576452626","https://openalex.org/W1581808154","https://openalex.org/W1599132769","https://openalex.org/W1968481561","https://openalex.org/W1972116103","https://openalex.org/W1976368387","https://openalex.org/W1977237536","https://openalex.org/W1980092392","https://openalex.org/W1980545841","https://openalex.org/W1980724591","https://openalex.org/W1984961549","https://openalex.org/W2016469624","https://openalex.org/W2021013459","https://openalex.org/W2024303516","https://openalex.org/W2027029581","https://openalex.org/W2029907110","https://openalex.org/W2031186120","https://openalex.org/W2035003264","https://openalex.org/W2035832954","https://openalex.org/W2037131823","https://openalex.org/W2037880761","https://openalex.org/W2042034944","https://openalex.org/W2060605484","https://openalex.org/W2078977470","https://openalex.org/W2095199089","https://openalex.org/W2098701074","https://openalex.org/W2103496339","https://openalex.org/W2104843094","https://openalex.org/W2108286682","https://openalex.org/W2124829859","https://openalex.org/W2136375205","https://openalex.org/W2137092694","https://openalex.org/W2145830976","https://openalex.org/W2153890087","https://openalex.org/W2164825665","https://openalex.org/W2166302960","https://openalex.org/W2245501338","https://openalex.org/W2273116766","https://openalex.org/W2545612814","https://openalex.org/W3213472335","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1934622834","https://openalex.org/W2015036175","https://openalex.org/W2385251419","https://openalex.org/W3013416265","https://openalex.org/W2040366764","https://openalex.org/W1990647881","https://openalex.org/W2098504625","https://openalex.org/W2394201814","https://openalex.org/W2322405588","https://openalex.org/W2353206064"],"abstract_inverted_index":{"This":[0],"paper":[1],"introduces":[2],"an":[3,49,128],"observer-based":[4,123],"adaptive":[5,50],"optimal":[6,72,77,116,124,153],"control":[7,78,117,125,154],"method":[8],"for":[9,62,138],"unknown":[10],"singularly":[11],"perturbed":[12],"nonlinear":[13],"systems":[14],"with":[15,29,92],"input":[16,144,158],"constraints.":[17],"First,":[18],"a":[19,30,36],"multi-time":[20],"scales":[21],"dynamic":[22],"neural":[23],"network":[24],"U+0028":[25,87],"MTSDNN":[26,94,109],"U+0029":[27,89],"observer":[28,95],"novel":[31],"updating":[32],"law":[33],"derived":[34],"from":[35],"properly":[37],"designed":[38],"Lyapunov":[39],"function":[40],"is":[41,60,67,80,119,148],"proposed":[42,122,152],"to":[43,69,175],"estimate":[44],"the":[45,55,63,71,76,85,93,102,108,111,115,132,142,151,157,166,177,180],"system":[46,105,133],"states.":[47],"Then,":[48],"learning":[51],"rule":[52],"driven":[53],"by":[54,82],"critic":[56,64,97,112],"NN":[57,113],"weight":[58],"error":[59],"presented":[61,174],"NN,":[65],"which":[66],"used":[68],"approximate":[70],"cost":[73],"function.":[74],"Finally,":[75],"action":[79,118],"calculated":[81],"online":[83],"solving":[84],"Hamilton-Jacobi-Bellman":[86],"HJB":[88],"equation":[90],"associated":[91],"and":[96,114,140,162],"NN.":[98],"The":[99,121],"stability":[100],"of":[101,107,168,179],"overall":[103],"closed-loop":[104],"consisting":[106],"observer,":[110],"proved.":[120],"approach":[126],"has":[127],"essential":[129],"advantage":[130],"that":[131],"dynamics":[134],"are":[135,173],"not":[136],"needed":[137],"implementation,":[139],"only":[141],"measured":[143],"U+002F":[145],"output":[146],"data":[147],"needed.":[149],"Moreover,":[150],"design":[155],"takes":[156],"constraints":[159],"into":[160],"consideration":[161],"thus":[163],"can":[164],"overcome":[165],"restriction":[167],"actuator":[169],"saturation.":[170],"Simulation":[171],"results":[172],"confirm":[176],"validity":[178],"investigated":[181],"approach.":[182]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
