{"id":"https://openalex.org/W4414538485","doi":"https://doi.org/10.1109/tnnls.2025.3604566","title":"Virtual Target-Oriented Neural Learning for Robust Optimal Tracking Control of Discrete Strict-Feedback Systems","display_name":"Virtual Target-Oriented Neural Learning for Robust Optimal Tracking Control of Discrete Strict-Feedback Systems","publication_year":2025,"publication_date":"2025-09-26","ids":{"openalex":"https://openalex.org/W4414538485","doi":"https://doi.org/10.1109/tnnls.2025.3604566","pmid":"https://pubmed.ncbi.nlm.nih.gov/41004376"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2025.3604566","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2025.3604566","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 Neural Networks and Learning Systems","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/A5024996421","display_name":"Ying Yan","orcid":"https://orcid.org/0000-0002-5912-2462"},"institutions":[{"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"],"is_corresponding":true,"raw_author_name":"Ying Yan","raw_affiliation_strings":["College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning, China"],"affiliations":[{"raw_affiliation_string":"College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning, China","institution_ids":["https://openalex.org/I9224756"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100625792","display_name":"Huaguang Zhang","orcid":"https://orcid.org/0000-0002-2375-9824"},"institutions":[{"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"],"is_corresponding":false,"raw_author_name":"Huaguang Zhang","raw_affiliation_strings":["College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning, China"],"affiliations":[{"raw_affiliation_string":"College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning, China","institution_ids":["https://openalex.org/I9224756"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002903770","display_name":"Jiayue Sun","orcid":"https://orcid.org/0000-0002-7774-2606"},"institutions":[{"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"],"is_corresponding":false,"raw_author_name":"Jiayue Sun","raw_affiliation_strings":["College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning, China"],"affiliations":[{"raw_affiliation_string":"College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning, China","institution_ids":["https://openalex.org/I9224756"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010477724","display_name":"Zhongyang Ming","orcid":"https://orcid.org/0009-0001-1002-6840"},"institutions":[{"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"],"is_corresponding":false,"raw_author_name":"Zhongyang Ming","raw_affiliation_strings":["College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning, China"],"affiliations":[{"raw_affiliation_string":"College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning, China","institution_ids":["https://openalex.org/I9224756"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5024996421"],"corresponding_institution_ids":["https://openalex.org/I9224756"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.34981932,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"37","issue":"1","first_page":"261","last_page":"273"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.8245000243186951,"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"}},"topics":[{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.8245000243186951,"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/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.8144000172615051,"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/T10320","display_name":"Neural Networks and Applications","score":0.7113999724388123,"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/robustness","display_name":"Robustness (evolution)","score":0.7311999797821045},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6539000272750854},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6247000098228455},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.510699987411499},{"id":"https://openalex.org/keywords/tracking","display_name":"Tracking (education)","score":0.4894999861717224},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.44040000438690186},{"id":"https://openalex.org/keywords/robust-control","display_name":"Robust control","score":0.4049000144004822},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.40299999713897705},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.3840000033378601}],"concepts":[{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.7311999797821045},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6539000272750854},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6247000098228455},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6029999852180481},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.510699987411499},{"id":"https://openalex.org/C2775936607","wikidata":"https://www.wikidata.org/wiki/Q466845","display_name":"Tracking (education)","level":2,"score":0.4894999861717224},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.44040000438690186},{"id":"https://openalex.org/C31531917","wikidata":"https://www.wikidata.org/wiki/Q915157","display_name":"Robust control","level":3,"score":0.4049000144004822},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.40299999713897705},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.3840000033378601},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.3682999908924103},{"id":"https://openalex.org/C107464732","wikidata":"https://www.wikidata.org/wiki/Q235781","display_name":"Adaptive control","level":3,"score":0.3637000024318695},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.3589000105857849},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.34150001406669617},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.32019999623298645},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.32010000944137573},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.3197000026702881},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.3050000071525574},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.30390000343322754},{"id":"https://openalex.org/C117619785","wikidata":"https://www.wikidata.org/wiki/Q6094414","display_name":"Iterative learning control","level":3,"score":0.2987000048160553},{"id":"https://openalex.org/C154586513","wikidata":"https://www.wikidata.org/wiki/Q4420972","display_name":"Tracking system","level":3,"score":0.29649999737739563},{"id":"https://openalex.org/C183356978","wikidata":"https://www.wikidata.org/wiki/Q1779213","display_name":"Tracking error","level":3,"score":0.2851000130176544},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.28279998898506165},{"id":"https://openalex.org/C2779714256","wikidata":"https://www.wikidata.org/wiki/Q25305062","display_name":"Multiple Models","level":2,"score":0.28189998865127563},{"id":"https://openalex.org/C91581856","wikidata":"https://www.wikidata.org/wiki/Q2707001","display_name":"Nonlinear control","level":3,"score":0.2786000072956085},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.2777999937534332},{"id":"https://openalex.org/C172205157","wikidata":"https://www.wikidata.org/wiki/Q1782962","display_name":"Model predictive control","level":3,"score":0.2718000113964081}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2025.3604566","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2025.3604566","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 Neural Networks and Learning Systems","raw_type":"journal-article"},{"id":"pmid:41004376","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/41004376","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 neural networks and learning systems","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W1614417283","https://openalex.org/W1977230515","https://openalex.org/W2093831009","https://openalex.org/W2098926291","https://openalex.org/W2102057409","https://openalex.org/W2117945258","https://openalex.org/W2333120204","https://openalex.org/W2732330082","https://openalex.org/W2735449579","https://openalex.org/W2909711564","https://openalex.org/W2920850588","https://openalex.org/W3027251624","https://openalex.org/W3043186131","https://openalex.org/W3096135216","https://openalex.org/W3108326949","https://openalex.org/W3159667783","https://openalex.org/W3161510627","https://openalex.org/W3174955147","https://openalex.org/W3197005866","https://openalex.org/W3197820042","https://openalex.org/W3206104399","https://openalex.org/W4210751743","https://openalex.org/W4249919931","https://openalex.org/W4285293172","https://openalex.org/W4300439422","https://openalex.org/W4312368523","https://openalex.org/W4312809224","https://openalex.org/W4368232614","https://openalex.org/W4375928760","https://openalex.org/W4383295119","https://openalex.org/W4385819645","https://openalex.org/W4386025831","https://openalex.org/W4388052800","https://openalex.org/W4391991791","https://openalex.org/W4393948478","https://openalex.org/W4399110712","https://openalex.org/W4400905831","https://openalex.org/W4401507514","https://openalex.org/W4402208407","https://openalex.org/W4404952704","https://openalex.org/W4409057812","https://openalex.org/W4410114594"],"related_works":[],"abstract_inverted_index":{"This":[0],"article":[1],"proposes":[2],"a":[3,45,75,128],"hierarchical":[4],"neural":[5,119],"learning":[6],"(HNL)":[7],"algorithm":[8],"for":[9,71,103],"optimal":[10],"tracking":[11,129,140,153,168],"control":[12,88,149],"(OTC)":[13],"of":[14,30,48],"nonlinear":[15,46],"strict-feedback":[16],"systems":[17],"(SFSs)":[18],"with":[19,127,138],"unmatched":[20],"disturbances":[21],"(uMDs)":[22],"and":[23,52,89,151,175],"unknown":[24],"dynamics.":[25],"Leveraging":[26],"the":[27,34,49,57,86,90,101,118,123,158],"recursive":[28],"structure":[29],"SFSs,":[31],"we":[32,115],"introduce":[33],"virtual":[35],"target":[36],"(VT)":[37],"construction":[38],"scheme":[39,161],"in":[40,165],"which":[41],"each":[42,144],"VT":[43],"is":[44,94],"mapping":[47],"current":[50],"state":[51],"desired":[53],"output,":[54],"thereby":[55],"eliminating":[56],"noncausal":[58],"that":[59,143,157],"typically":[60],"plagues":[61],"discrete-time":[62],"SFS":[63],"control.":[64],"The":[65,92],"VTs":[66],"serve":[67],"as":[68],"auxiliary":[69,87],"inputs":[70],"low-order":[72],"subsystems,":[73],"while":[74],"time-varying":[76],"affine":[77],"Hamilton-Jacobi-Isaacs":[78],"(HJI)":[79],"formulation":[80],"establishes":[81],"an":[82,104,109],"explicit":[83],"relationship":[84],"between":[85],"disturbance.":[91],"controller":[93],"synthesized":[95],"directly":[96],"from":[97],"input-output":[98],"data,":[99],"removing":[100],"need":[102],"accurate":[105],"plant":[106],"model.":[107],"Within":[108],"adaptive":[110],"dynamic":[111],"programming":[112],"(ADP)":[113],"framework,":[114],"further":[116],"enhance":[117],"architecture":[120],"by":[121],"replacing":[122],"conventional":[124],"action":[125],"network":[126,130],"(T-network)":[131],"whose":[132],"energy":[133],"function":[134],"merges":[135],"gradient":[136],"information":[137],"future":[139],"errors,":[141],"ensuring":[142],"policy":[145],"update":[146],"simultaneously":[147],"reduces":[148],"effort":[150],"improves":[152],"accuracy.":[154],"Simulations":[155],"confirm":[156],"proposed":[159],"HNL":[160],"achieves":[162],"outstanding":[163],"performance":[164],"both":[166],"(optimal)":[167],"modes,":[169],"exhibiting":[170],"strong":[171],"robustness":[172],"to":[173],"uMDs":[174],"significant":[176],"model":[177],"uncertainties.":[178]},"counts_by_year":[],"updated_date":"2026-03-07T16:01:11.037858","created_date":"2025-10-10T00:00:00"}
