{"id":"https://openalex.org/W4409640862","doi":"https://doi.org/10.1109/tcyb.2025.3559235","title":"A Constructive Approach for Neural Network Approximation Sets in Adaptive Control of Strict-Feedback Systems","display_name":"A Constructive Approach for Neural Network Approximation Sets in Adaptive Control of Strict-Feedback Systems","publication_year":2025,"publication_date":"2025-04-21","ids":{"openalex":"https://openalex.org/W4409640862","doi":"https://doi.org/10.1109/tcyb.2025.3559235","pmid":"https://pubmed.ncbi.nlm.nih.gov/40257885"},"language":"en","primary_location":{"id":"doi:10.1109/tcyb.2025.3559235","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2025.3559235","pdf_url":null,"source":{"id":"https://openalex.org/S4210191041","display_name":"IEEE Transactions on Cybernetics","issn_l":"2168-2267","issn":["2168-2267","2168-2275"],"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 Cybernetics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5054878549","display_name":"Yufa Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I139024713","display_name":"Guangdong University of Technology","ror":"https://ror.org/04azbjn80","country_code":"CN","type":"education","lineage":["https://openalex.org/I139024713"]},{"id":"https://openalex.org/I4210142539","display_name":"Guangdong Institute of Intelligent Manufacturing","ror":"https://ror.org/049jpjz09","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210142539"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yu-Fa Liu","raw_affiliation_strings":["School of Automation, Guangdong-Hong Kong Joint Laboratory of Intelligent Decision and Cooperative Control, Guangdong Province Key Laboratory of Intelligent Decision and Cooperative Control, Guangdong University of Technology, Guangzhou, China","Guangdong-Hong Kong Joint Laboratory of Intelligent Decision and Cooperative Control, Guangdong Province Key Laboratory of Intelligent Decision and Cooperative Control, School of Automation, Guangdong University of Technology, Guangzhou, China"],"affiliations":[{"raw_affiliation_string":"School of Automation, Guangdong-Hong Kong Joint Laboratory of Intelligent Decision and Cooperative Control, Guangdong Province Key Laboratory of Intelligent Decision and Cooperative Control, Guangdong University of Technology, Guangzhou, China","institution_ids":["https://openalex.org/I4210142539"]},{"raw_affiliation_string":"Guangdong-Hong Kong Joint Laboratory of Intelligent Decision and Cooperative Control, Guangdong Province Key Laboratory of Intelligent Decision and Cooperative Control, School of Automation, Guangdong University of Technology, Guangzhou, China","institution_ids":["https://openalex.org/I139024713"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086722817","display_name":"Yonghua Liu","orcid":"https://orcid.org/0000-0001-7137-7591"},"institutions":[{"id":"https://openalex.org/I139024713","display_name":"Guangdong University of Technology","ror":"https://ror.org/04azbjn80","country_code":"CN","type":"education","lineage":["https://openalex.org/I139024713"]},{"id":"https://openalex.org/I4210142539","display_name":"Guangdong Institute of Intelligent Manufacturing","ror":"https://ror.org/049jpjz09","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210142539"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yong-Hua Liu","raw_affiliation_strings":["School of Automation, Guangdong-Hong Kong Joint Laboratory of Intelligent Decision and Cooperative Control, Guangdong Province Key Laboratory of Intelligent Decision and Cooperative Control, Guangdong University of Technology, Guangzhou, China","Guangdong-Hong Kong Joint Laboratory of Intelligent Decision and Cooperative Control, Guangdong Province Key Laboratory of Intelligent Decision and Cooperative Control, School of Automation, Guangdong University of Technology, Guangzhou, China"],"affiliations":[{"raw_affiliation_string":"School of Automation, Guangdong-Hong Kong Joint Laboratory of Intelligent Decision and Cooperative Control, Guangdong Province Key Laboratory of Intelligent Decision and Cooperative Control, Guangdong University of Technology, Guangzhou, China","institution_ids":["https://openalex.org/I4210142539"]},{"raw_affiliation_string":"Guangdong-Hong Kong Joint Laboratory of Intelligent Decision and Cooperative Control, Guangdong Province Key Laboratory of Intelligent Decision and Cooperative Control, School of Automation, Guangdong University of Technology, Guangzhou, China","institution_ids":["https://openalex.org/I139024713"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032169797","display_name":"Jiaxin Wu","orcid":"https://orcid.org/0000-0001-7523-7780"},"institutions":[{"id":"https://openalex.org/I139024713","display_name":"Guangdong University of Technology","ror":"https://ror.org/04azbjn80","country_code":"CN","type":"education","lineage":["https://openalex.org/I139024713"]},{"id":"https://openalex.org/I4210142539","display_name":"Guangdong Institute of Intelligent Manufacturing","ror":"https://ror.org/049jpjz09","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210142539"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jin-Wa Wu","raw_affiliation_strings":["School of Automation, Guangdong-Hong Kong Joint Laboratory of Intelligent Decision and Cooperative Control, Guangdong Province Key Laboratory of Intelligent Decision and Cooperative Control, Guangdong University of Technology, Guangzhou, China","Guangdong-Hong Kong Joint Laboratory of Intelligent Decision and Cooperative Control, Guangdong Province Key Laboratory of Intelligent Decision and Cooperative Control, School of Automation, Guangdong University of Technology, Guangzhou, China"],"affiliations":[{"raw_affiliation_string":"School of Automation, Guangdong-Hong Kong Joint Laboratory of Intelligent Decision and Cooperative Control, Guangdong Province Key Laboratory of Intelligent Decision and Cooperative Control, Guangdong University of Technology, Guangzhou, China","institution_ids":["https://openalex.org/I4210142539"]},{"raw_affiliation_string":"Guangdong-Hong Kong Joint Laboratory of Intelligent Decision and Cooperative Control, Guangdong Province Key Laboratory of Intelligent Decision and Cooperative Control, School of Automation, Guangdong University of Technology, Guangzhou, China","institution_ids":["https://openalex.org/I139024713"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5115596655","display_name":"Ante Su","orcid":null},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ante Su","raw_affiliation_strings":["School of Mechanical Engineering, Shandong University, Jinan, China"],"affiliations":[{"raw_affiliation_string":"School of Mechanical Engineering, Shandong University, Jinan, China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076212272","display_name":"Chun\u2010Yi Su","orcid":"https://orcid.org/0000-0002-1869-5563"},"institutions":[{"id":"https://openalex.org/I139024713","display_name":"Guangdong University of Technology","ror":"https://ror.org/04azbjn80","country_code":"CN","type":"education","lineage":["https://openalex.org/I139024713"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chun-Yi Su","raw_affiliation_strings":["School of Automation, Guangdong Province Key Laboratory of Intelligent Decision and Cooperative Control, Guangdong University of Technology, Guangzhou, China","Guangdong Province Key Laboratory of Intelligent Decision and Cooperative Control, School of Automation, Guangdong University of Technology, Guangzhou, China"],"affiliations":[{"raw_affiliation_string":"School of Automation, Guangdong Province Key Laboratory of Intelligent Decision and Cooperative Control, Guangdong University of Technology, Guangzhou, China","institution_ids":["https://openalex.org/I139024713"]},{"raw_affiliation_string":"Guangdong Province Key Laboratory of Intelligent Decision and Cooperative Control, School of Automation, Guangdong University of Technology, Guangzhou, China","institution_ids":["https://openalex.org/I139024713"]}]},{"author_position":"last","author":{"id":null,"display_name":"Renquan Lu","orcid":"https://orcid.org/0000-0003-1084-8243"},"institutions":[{"id":"https://openalex.org/I139024713","display_name":"Guangdong University of Technology","ror":"https://ror.org/04azbjn80","country_code":"CN","type":"education","lineage":["https://openalex.org/I139024713"]},{"id":"https://openalex.org/I4210142539","display_name":"Guangdong Institute of Intelligent Manufacturing","ror":"https://ror.org/049jpjz09","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210142539"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Renquan Lu","raw_affiliation_strings":["School of Automation, Guangdong-Hong Kong Joint Laboratory of Intelligent Decision and Cooperative Control, Guangdong Province Key Laboratory of Intelligent Decision and Cooperative Control, Guangdong University of Technology, Guangzhou, China","Guangdong-Hong Kong Joint Laboratory of Intelligent Decision and Cooperative Control, Guangdong Province Key Laboratory of Intelligent Decision and Cooperative Control, School of Automation, Guangdong University of Technology, Guangzhou, China"],"affiliations":[{"raw_affiliation_string":"School of Automation, Guangdong-Hong Kong Joint Laboratory of Intelligent Decision and Cooperative Control, Guangdong Province Key Laboratory of Intelligent Decision and Cooperative Control, Guangdong University of Technology, Guangzhou, China","institution_ids":["https://openalex.org/I4210142539"]},{"raw_affiliation_string":"Guangdong-Hong Kong Joint Laboratory of Intelligent Decision and Cooperative Control, Guangdong Province Key Laboratory of Intelligent Decision and Cooperative Control, School of Automation, Guangdong University of Technology, Guangzhou, China","institution_ids":["https://openalex.org/I139024713"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5054878549"],"corresponding_institution_ids":["https://openalex.org/I139024713","https://openalex.org/I4210142539"],"apc_list":null,"apc_paid":null,"fwci":9.9395,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.9758055,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"55","issue":"8","first_page":"4015","last_page":"4025"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9169999957084656,"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"}},"topics":[{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9169999957084656,"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/constructive","display_name":"Constructive","score":0.860135555267334},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6814680695533752},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5636573433876038},{"id":"https://openalex.org/keywords/feedback-control","display_name":"Feedback control","score":0.5160550475120544},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.4773143231868744},{"id":"https://openalex.org/keywords/adaptive-control","display_name":"Adaptive control","score":0.45290571451187134},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.42609071731567383},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3462297320365906},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.34153467416763306},{"id":"https://openalex.org/keywords/control-engineering","display_name":"Control engineering","score":0.22637119889259338},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.10591199994087219}],"concepts":[{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.860135555267334},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6814680695533752},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5636573433876038},{"id":"https://openalex.org/C3018651601","wikidata":"https://www.wikidata.org/wiki/Q183635","display_name":"Feedback control","level":2,"score":0.5160550475120544},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.4773143231868744},{"id":"https://openalex.org/C107464732","wikidata":"https://www.wikidata.org/wiki/Q235781","display_name":"Adaptive control","level":3,"score":0.45290571451187134},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.42609071731567383},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3462297320365906},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.34153467416763306},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.22637119889259338},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.10591199994087219},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tcyb.2025.3559235","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2025.3559235","pdf_url":null,"source":{"id":"https://openalex.org/S4210191041","display_name":"IEEE Transactions on Cybernetics","issn_l":"2168-2267","issn":["2168-2267","2168-2275"],"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 Cybernetics","raw_type":"journal-article"},{"id":"pmid:40257885","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/40257885","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on cybernetics","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1877470619","display_name":null,"funder_award_id":"62173097","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3530360010","display_name":null,"funder_award_id":"61875040","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6104967667","display_name":null,"funder_award_id":"U2013601","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7037757187","display_name":null,"funder_award_id":"62121004","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8773436184","display_name":null,"funder_award_id":"2022A515011239","funder_id":"https://openalex.org/F4320337111","funder_display_name":"Basic and Applied Basic Research Foundation of Guangdong Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320337111","display_name":"Basic and Applied Basic Research Foundation of Guangdong Province","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W1613039631","https://openalex.org/W1966746027","https://openalex.org/W1969540296","https://openalex.org/W1982214011","https://openalex.org/W2065184457","https://openalex.org/W2065905935","https://openalex.org/W2117484613","https://openalex.org/W2142572589","https://openalex.org/W2150535417","https://openalex.org/W2156174311","https://openalex.org/W2921478325","https://openalex.org/W2925898180","https://openalex.org/W2971754508","https://openalex.org/W2999045630","https://openalex.org/W3017203298","https://openalex.org/W3027251624","https://openalex.org/W3033144026","https://openalex.org/W3045566279","https://openalex.org/W3104471247","https://openalex.org/W3105732827","https://openalex.org/W4200492172","https://openalex.org/W4239216443","https://openalex.org/W4282920582","https://openalex.org/W4300439422","https://openalex.org/W4308421644","https://openalex.org/W4310588780","https://openalex.org/W4313229953","https://openalex.org/W4384664190","https://openalex.org/W4385696570","https://openalex.org/W4386554079","https://openalex.org/W4386634492","https://openalex.org/W4387010628","https://openalex.org/W4387682224","https://openalex.org/W4387744325","https://openalex.org/W4388505110","https://openalex.org/W4389799578","https://openalex.org/W4403278140","https://openalex.org/W4404563099","https://openalex.org/W4407827474"],"related_works":["https://openalex.org/W2377770720","https://openalex.org/W94411513","https://openalex.org/W4311883357","https://openalex.org/W2113626999","https://openalex.org/W160889949","https://openalex.org/W2197168648","https://openalex.org/W2364696089","https://openalex.org/W4300816516","https://openalex.org/W309910862","https://openalex.org/W2052682608"],"abstract_inverted_index":{"Determining":[0],"the":[1,40,54,69,75,81,88,91,104,107],"neural":[2],"network":[3],"(NN)":[4],"approximation":[5,55,92],"sets":[6,93],"for":[7,68,80],"adaptive":[8],"control":[9],"of":[10,56,64,71,77,90,94,106],"strict-feedback":[11],"uncertain":[12],"systems":[13],"has":[14],"posed":[15],"a":[16,22],"persistent":[17],"challenge.":[18],"This":[19,85],"article":[20],"proposes":[21],"novel":[23],"and":[24,35],"constructive":[25],"solution":[26],"that":[27],"incorporates":[28],"signal":[29,41],"substitution":[30,42],"technique,":[31,43],"barrier":[32],"functions":[33,59],"(BFs),":[34],"backstepping":[36],"approach.":[37,109],"By":[38],"applying":[39],"all":[44],"system":[45,58],"states":[46],"are":[47,100],"transformed":[48],"into":[49],"state":[50,72],"error":[51],"variables,":[52],"facilitating":[53],"unknown":[57],"through":[60],"NNs.":[61],"The":[62],"use":[63],"BFs":[65],"subsequently":[66],"allows":[67],"restriction":[70],"errors,":[73],"enabling":[74],"calculation":[76],"exact":[78],"bounds":[79],"NN":[82,95],"weight":[83],"estimators.":[84],"process":[86],"reveals":[87],"determination":[89],"in":[96],"advance.":[97],"Illustrative":[98],"examples":[99],"conducted":[101],"to":[102],"validate":[103],"effectiveness":[105],"proposed":[108]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}