{"id":"https://openalex.org/W2039710193","doi":"https://doi.org/10.1109/tie.2014.2316250","title":"Convergence Analysis and Digital Implementation of a Discrete-Time Neural Network for Model Predictive Control","display_name":"Convergence Analysis and Digital Implementation of a Discrete-Time Neural Network for Model Predictive Control","publication_year":2014,"publication_date":"2014-04-09","ids":{"openalex":"https://openalex.org/W2039710193","doi":"https://doi.org/10.1109/tie.2014.2316250","mag":"2039710193"},"language":"en","primary_location":{"id":"doi:10.1109/tie.2014.2316250","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tie.2014.2316250","pdf_url":null,"source":{"id":"https://openalex.org/S58031724","display_name":"IEEE Transactions on Industrial Electronics","issn_l":"0278-0046","issn":["0278-0046","1557-9948"],"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 Industrial Electronics","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/A5103265093","display_name":"Yang Lu","orcid":"https://orcid.org/0000-0001-8981-098X"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yang Lu","raw_affiliation_strings":["Department of Automation, Key Laboratory of System Control and Information Processing, Ministry of Education, Shanghai Jiao Tong University, Shanghai, China","[Department of Automation, Shanghai Jiao Tong University, Shanghai, China.]"],"affiliations":[{"raw_affiliation_string":"Department of Automation, Key Laboratory of System Control and Information Processing, Ministry of Education, Shanghai Jiao Tong University, Shanghai, China","institution_ids":["https://openalex.org/I183067930"]},{"raw_affiliation_string":"[Department of Automation, Shanghai Jiao Tong University, Shanghai, China.]","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100650327","display_name":"Dewei Li","orcid":"https://orcid.org/0000-0002-0604-7518"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dewei Li","raw_affiliation_strings":["Department of Automation, Key Laboratory of System Control and Information Processing, Ministry of Education, Shanghai Jiao Tong University, Shanghai, China","[Department of Automation, Shanghai Jiao Tong University, Shanghai, China.]"],"affiliations":[{"raw_affiliation_string":"Department of Automation, Key Laboratory of System Control and Information Processing, Ministry of Education, Shanghai Jiao Tong University, Shanghai, China","institution_ids":["https://openalex.org/I183067930"]},{"raw_affiliation_string":"[Department of Automation, Shanghai Jiao Tong University, Shanghai, China.]","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020120796","display_name":"Zuhua Xu","orcid":"https://orcid.org/0000-0002-7873-9521"},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zuhua Xu","raw_affiliation_strings":["Department of Control Science and Engineering, Zhejiang University, Hangzhou, China","Department of Control Science & Engineering, Zhejiang University, Hangzhou, CHINA"],"affiliations":[{"raw_affiliation_string":"Department of Control Science and Engineering, Zhejiang University, Hangzhou, China","institution_ids":["https://openalex.org/I76130692"]},{"raw_affiliation_string":"Department of Control Science & Engineering, Zhejiang University, Hangzhou, CHINA","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038377162","display_name":"Yugeng Xi","orcid":"https://orcid.org/0000-0001-8869-5676"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yugeng Xi","raw_affiliation_strings":["Department of Automation, Key Laboratory of System Control and Information Processing, Ministry of Education, Shanghai Jiao Tong University, Shanghai, China","[Department of Automation, Shanghai Jiao Tong University, Shanghai, China.]"],"affiliations":[{"raw_affiliation_string":"Department of Automation, Key Laboratory of System Control and Information Processing, Ministry of Education, Shanghai Jiao Tong University, Shanghai, China","institution_ids":["https://openalex.org/I183067930"]},{"raw_affiliation_string":"[Department of Automation, Shanghai Jiao Tong University, Shanghai, China.]","institution_ids":["https://openalex.org/I183067930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5103265093"],"corresponding_institution_ids":["https://openalex.org/I183067930"],"apc_list":null,"apc_paid":null,"fwci":6.5633,"has_fulltext":false,"cited_by_count":40,"citation_normalized_percentile":{"value":0.96573681,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"61","issue":"12","first_page":"7035","last_page":"7045"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9998999834060669,"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":0.9998999834060669,"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/T10876","display_name":"Fault Detection and Control Systems","score":0.9902999997138977,"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/T11749","display_name":"Iterative Learning Control Systems","score":0.9900000095367432,"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/solver","display_name":"Solver","score":0.7239322066307068},{"id":"https://openalex.org/keywords/digital-signal-processing","display_name":"Digital signal processing","score":0.714687705039978},{"id":"https://openalex.org/keywords/model-predictive-control","display_name":"Model predictive control","score":0.6938802599906921},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6217515468597412},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6201070547103882},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6195987462997437},{"id":"https://openalex.org/keywords/digital-signal-processor","display_name":"Digital signal processor","score":0.5467289090156555},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.5465351343154907},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.43611353635787964},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.43149691820144653},{"id":"https://openalex.org/keywords/control-engineering","display_name":"Control engineering","score":0.4152626097202301},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.40002748370170593},{"id":"https://openalex.org/keywords/computer-hardware","display_name":"Computer hardware","score":0.2984897792339325},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.29663771390914917},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.19705486297607422},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.17830172181129456},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.12725839018821716},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1071162223815918}],"concepts":[{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.7239322066307068},{"id":"https://openalex.org/C84462506","wikidata":"https://www.wikidata.org/wiki/Q173142","display_name":"Digital signal processing","level":2,"score":0.714687705039978},{"id":"https://openalex.org/C172205157","wikidata":"https://www.wikidata.org/wiki/Q1782962","display_name":"Model predictive control","level":3,"score":0.6938802599906921},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6217515468597412},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6201070547103882},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6195987462997437},{"id":"https://openalex.org/C161611012","wikidata":"https://www.wikidata.org/wiki/Q106370","display_name":"Digital signal processor","level":3,"score":0.5467289090156555},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.5465351343154907},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.43611353635787964},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.43149691820144653},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.4152626097202301},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.40002748370170593},{"id":"https://openalex.org/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.2984897792339325},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.29663771390914917},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.19705486297607422},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.17830172181129456},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.12725839018821716},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1071162223815918},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tie.2014.2316250","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tie.2014.2316250","pdf_url":null,"source":{"id":"https://openalex.org/S58031724","display_name":"IEEE Transactions on Industrial Electronics","issn_l":"0278-0046","issn":["0278-0046","1557-9948"],"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 Industrial Electronics","raw_type":"journal-article"},{"id":"pmh:oai:eprints.lancs.ac.uk:172569","is_oa":false,"landing_page_url":"https://eprints.lancs.ac.uk/id/eprint/172569/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401916","display_name":"Lancaster EPrints (Lancaster University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67415387","host_organization_name":"Lancaster University","host_organization_lineage":["https://openalex.org/I67415387"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2526985831","display_name":null,"funder_award_id":"20120073110017","funder_id":"https://openalex.org/F4320336024","funder_display_name":"Specialized Research Fund for the Doctoral Program of Higher Education of China"},{"id":"https://openalex.org/G4954122135","display_name":null,"funder_award_id":"71361130012","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4956378139","display_name":null,"funder_award_id":"61221003","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5104435456","display_name":null,"funder_award_id":"61333009","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8737213476","display_name":null,"funder_award_id":"61374110","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335661","display_name":"State Key Laboratory of Synthetical Automation for Process Industries","ror":null},{"id":"https://openalex.org/F4320336024","display_name":"Specialized Research Fund for the Doctoral Program of Higher Education of China","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1516681311","https://openalex.org/W1519818083","https://openalex.org/W1977323979","https://openalex.org/W1977564650","https://openalex.org/W1978956894","https://openalex.org/W1982157348","https://openalex.org/W1988918758","https://openalex.org/W1989167860","https://openalex.org/W2027158167","https://openalex.org/W2043724067","https://openalex.org/W2046559377","https://openalex.org/W2056625347","https://openalex.org/W2058804598","https://openalex.org/W2066400947","https://openalex.org/W2091940053","https://openalex.org/W2104140733","https://openalex.org/W2107492200","https://openalex.org/W2108903668","https://openalex.org/W2112169395","https://openalex.org/W2128483128","https://openalex.org/W2137743180","https://openalex.org/W2158810475","https://openalex.org/W2159047711","https://openalex.org/W6631064487"],"related_works":["https://openalex.org/W2319687164","https://openalex.org/W1556297113","https://openalex.org/W2080896647","https://openalex.org/W2025587901","https://openalex.org/W2572037897","https://openalex.org/W2028217664","https://openalex.org/W2077289773","https://openalex.org/W2352569066","https://openalex.org/W2158000646","https://openalex.org/W2379636925"],"abstract_inverted_index":{"In":[0],"this":[1,87],"paper,":[2],"a":[3,26,60,64,102,106,124,137],"discrete-time":[4,52],"neural":[5,53,72,99],"network":[6,54,73,100],"for":[7,43],"solving":[8],"convex":[9],"quadratic":[10],"programming":[11],"(QP)":[12],"problems":[13],"in":[14,121],"constrained":[15],"model":[16],"predictive":[17],"control":[18,42,153],"(MPC)":[19],"technology":[20,39],"is":[21,55,67,82,110,129,134,143],"investigated":[22],"and":[23,92,150],"implemented":[24],"on":[25,101,136],"digital":[27],"signal":[28],"processor":[29],"(DSP)":[30],"device.":[31],"This":[32,81,155],"makes":[33],"it":[34],"possible":[35],"to":[36,40,75,96,146],"apply":[37],"MPC":[38,122,127],"local":[41],"high-dimensional":[44],"multiple-input-multiple-output":[45],"systems.":[46],"The":[47],"convergence":[48],"issue":[49],"of":[50,86,159],"the":[51,71,76,83,98,114,118,157,160],"first":[56],"studied.":[57],"By":[58],"choosing":[59],"proper":[61],"error":[62],"function,":[63],"sufficient":[65],"condition":[66],"obtained":[68],"under":[69],"which":[70],"converges":[74],"exact":[77],"optimal":[78],"solution":[79],"globally.":[80],"theoretical":[84],"basis":[85],"paper.":[88],"An":[89],"integrated":[90],"hardware":[91],"software":[93],"design":[94],"method":[95],"implement":[97],"DSP":[103,139],"chip":[104],"as":[105],"universal":[107],"QP":[108,115],"solver":[109,116],"then":[111,144],"developed.":[112],"With":[113],"handling":[117],"computational":[119],"tasks":[120],"problems,":[123],"general":[125],"DSP-based":[126],"controller":[128],"achieved.":[130],"A":[131],"prototype":[132],"system":[133,149],"built":[135],"TMDSEVM6678L":[138],"development":[140],"board.":[141],"It":[142],"applied":[145],"an":[147],"air-separation-unit":[148],"achieves":[151],"satisfactory":[152],"performance.":[154],"verifies":[156],"effectiveness":[158],"whole":[161],"design.":[162]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}