{"id":"https://openalex.org/W2901363724","doi":"https://doi.org/10.1109/tie.2018.2880728","title":"Nonlinear Constrained Optimal Control of Wave Energy Converters With Adaptive Dynamic Programming","display_name":"Nonlinear Constrained Optimal Control of Wave Energy Converters With Adaptive Dynamic Programming","publication_year":2018,"publication_date":"2018-11-15","ids":{"openalex":"https://openalex.org/W2901363724","doi":"https://doi.org/10.1109/tie.2018.2880728","mag":"2901363724"},"language":"en","primary_location":{"id":"doi:10.1109/tie.2018.2880728","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tie.2018.2880728","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":true,"oa_status":"green","oa_url":"https://qmro.qmul.ac.uk/xmlui/bitstream/123456789/52503/1/Na%20et%20al.%202018.%20Nonlinear%20Constrained%20Optimal%20Control.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","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":true,"raw_author_name":"Jing Na","raw_affiliation_strings":["Faculty of Mechanical and Electrical Engineering, Kunming University of Science and Technology, Kunming, China"],"raw_orcid":"https://orcid.org/0000-0002-3067-1580","affiliations":[{"raw_affiliation_string":"Faculty of Mechanical and Electrical Engineering, Kunming University of Science and Technology, Kunming, China","institution_ids":["https://openalex.org/I10660446"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101752456","display_name":"Bin Wang","orcid":"https://orcid.org/0000-0002-5558-1610"},"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":"Bin Wang","raw_affiliation_strings":["Faculty of Mechanical and Electrical Engineering, Kunming University of Science and Technology, Kunming, China"],"raw_orcid":"https://orcid.org/0000-0002-5558-1610","affiliations":[{"raw_affiliation_string":"Faculty of Mechanical and Electrical Engineering, Kunming University of Science and Technology, Kunming, China","institution_ids":["https://openalex.org/I10660446"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108049333","display_name":"Guang Li","orcid":"https://orcid.org/0000-0001-9323-5076"},"institutions":[{"id":"https://openalex.org/I166337079","display_name":"Queen Mary University of London","ror":"https://ror.org/026zzn846","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I166337079"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Guang Li","raw_affiliation_strings":["School of Engineering and Materials Science, Queen Mary University of London, London, U.K"],"raw_orcid":"https://orcid.org/0000-0001-9323-5076","affiliations":[{"raw_affiliation_string":"School of Engineering and Materials Science, Queen Mary University of London, London, U.K","institution_ids":["https://openalex.org/I166337079"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041446314","display_name":"Siyuan Zhan","orcid":"https://orcid.org/0000-0002-0002-3427"},"institutions":[{"id":"https://openalex.org/I166337079","display_name":"Queen Mary University of London","ror":"https://ror.org/026zzn846","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I166337079"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Siyuan Zhan","raw_affiliation_strings":["School of Engineering and Materials Science, Queen Mary University of London, London, U.K"],"raw_orcid":"https://orcid.org/0000-0002-0002-3427","affiliations":[{"raw_affiliation_string":"School of Engineering and Materials Science, Queen Mary University of London, London, U.K","institution_ids":["https://openalex.org/I166337079"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022113595","display_name":"Wei He","orcid":"https://orcid.org/0000-0002-8944-9861"},"institutions":[{"id":"https://openalex.org/I92403157","display_name":"University of Science and Technology Beijing","ror":"https://ror.org/02egmk993","country_code":"CN","type":"education","lineage":["https://openalex.org/I92403157"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wei He","raw_affiliation_strings":["School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-8944-9861","affiliations":[{"raw_affiliation_string":"School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, China","institution_ids":["https://openalex.org/I92403157"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5008377523"],"corresponding_institution_ids":["https://openalex.org/I10660446"],"apc_list":null,"apc_paid":null,"fwci":9.0268,"has_fulltext":true,"cited_by_count":94,"citation_normalized_percentile":{"value":0.98333146,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"66","issue":"10","first_page":"7904","last_page":"7915"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.9988999962806702,"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":0.9988999962806702,"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/T10223","display_name":"Microgrid Control and Optimization","score":0.9921000003814697,"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/T10305","display_name":"Power System Optimization and Stability","score":0.982200026512146,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/optimal-control","display_name":"Optimal control","score":0.7600448131561279},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6498748660087585},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"Dynamic programming","score":0.6022950410842896},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.5690174102783203},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5460848212242126},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5432731509208679},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5042999982833862},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.48470187187194824},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.4779796004295349},{"id":"https://openalex.org/keywords/adaptive-control","display_name":"Adaptive control","score":0.4309226870536804},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.3652426600456238},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.23048141598701477},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07667958736419678}],"concepts":[{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.7600448131561279},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6498748660087585},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.6022950410842896},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.5690174102783203},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5460848212242126},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5432731509208679},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5042999982833862},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.48470187187194824},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.4779796004295349},{"id":"https://openalex.org/C107464732","wikidata":"https://www.wikidata.org/wiki/Q235781","display_name":"Adaptive control","level":3,"score":0.4309226870536804},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.3652426600456238},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.23048141598701477},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07667958736419678},{"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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":3,"locations":[{"id":"doi:10.1109/tie.2018.2880728","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tie.2018.2880728","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:pure.atira.dk:openaire_cris_publications/19c354c8-e186-4541-92d2-9fdc88b3cf86","is_oa":false,"landing_page_url":"https://research.manchester.ac.uk/en/publications/19c354c8-e186-4541-92d2-9fdc88b3cf86","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Na, J, Wang, B, Li, G, Zhan, S & He, W 2019, 'Nonlinear constrained optimal control of wave energy converters with adaptive dynamic programming', IEEE Transactions on Industrial Electronics. https://doi.org/10.1109/TIE.2018.2880728","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:qmro.qmul.ac.uk:123456789/52503","is_oa":true,"landing_page_url":"http://qmro.qmul.ac.uk/xmlui/handle/123456789/52503","pdf_url":"https://qmro.qmul.ac.uk/xmlui/bitstream/123456789/52503/1/Na%20et%20al.%202018.%20Nonlinear%20Constrained%20Optimal%20Control.pdf","source":{"id":"https://openalex.org/S4306400530","display_name":"Queen Mary Research Online (Queen Mary University of London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I166337079","host_organization_name":"Queen Mary University of London","host_organization_lineage":["https://openalex.org/I166337079"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:qmro.qmul.ac.uk:123456789/52503","is_oa":true,"landing_page_url":"http://qmro.qmul.ac.uk/xmlui/handle/123456789/52503","pdf_url":"https://qmro.qmul.ac.uk/xmlui/bitstream/123456789/52503/1/Na%20et%20al.%202018.%20Nonlinear%20Constrained%20Optimal%20Control.pdf","source":{"id":"https://openalex.org/S4306400530","display_name":"Queen Mary Research Online (Queen Mary University of London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I166337079","host_organization_name":"Queen Mary University of London","host_organization_lineage":["https://openalex.org/I166337079"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},"sustainable_development_goals":[{"score":0.9100000262260437,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G3358819595","display_name":null,"funder_award_id":"EP/P023002/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6458044528","display_name":null,"funder_award_id":"61573174","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7198406823","display_name":null,"funder_award_id":"61873115","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G859794079","display_name":null,"funder_award_id":"NA160436","funder_id":"https://openalex.org/F4320320006","funder_display_name":"Royal Society"}],"funders":[{"id":"https://openalex.org/F4320315173","display_name":"Wave Energy Scotland","ror":null},{"id":"https://openalex.org/F4320320006","display_name":"Royal Society","ror":"https://ror.org/03wnrjx87"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2901363724.pdf"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W15764369","https://openalex.org/W92805021","https://openalex.org/W1570071546","https://openalex.org/W1597554859","https://openalex.org/W1599132769","https://openalex.org/W1904486563","https://openalex.org/W1964375638","https://openalex.org/W1965291863","https://openalex.org/W1983523797","https://openalex.org/W1988876996","https://openalex.org/W1989684253","https://openalex.org/W1992984181","https://openalex.org/W2014046054","https://openalex.org/W2017316460","https://openalex.org/W2019015670","https://openalex.org/W2048877249","https://openalex.org/W2052305027","https://openalex.org/W2061045238","https://openalex.org/W2074689895","https://openalex.org/W2080182938","https://openalex.org/W2108286682","https://openalex.org/W2110361814","https://openalex.org/W2121863487","https://openalex.org/W2132858840","https://openalex.org/W2138131694","https://openalex.org/W2145830976","https://openalex.org/W2154868061","https://openalex.org/W2326828262","https://openalex.org/W2381073747","https://openalex.org/W2464180915","https://openalex.org/W2554601184","https://openalex.org/W2596126472","https://openalex.org/W2732790960","https://openalex.org/W2736406891","https://openalex.org/W2757619290","https://openalex.org/W2758621768","https://openalex.org/W2781216998","https://openalex.org/W2789282887","https://openalex.org/W2883690282","https://openalex.org/W3010562861","https://openalex.org/W4214717370","https://openalex.org/W6600629665","https://openalex.org/W6603762378"],"related_works":["https://openalex.org/W1932159282","https://openalex.org/W4285537323","https://openalex.org/W2379312070","https://openalex.org/W2136173754","https://openalex.org/W2110050003","https://openalex.org/W2953025626","https://openalex.org/W2499081552","https://openalex.org/W2366053282","https://openalex.org/W1653644965","https://openalex.org/W2128788708"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"address":[4],"the":[5,28,37,43,59,67,87,98,125,152,155],"energy":[6,11,118],"maximization":[7],"problem":[8],"of":[9,30,97,117,127,154],"wave":[10],"converters":[12],"(WEC)":[13],"subject":[14],"to":[15,57,80,111,134,150],"nonlinearities":[16,143],"and":[17,19,64,132,144],"constraints,":[18],"present":[20],"an":[21],"efficient":[22],"online":[23],"control":[24,48,71,77,100,157],"strategy":[25,78],"based":[26],"on":[27,108],"principle":[29],"adaptive":[31],"dynamic":[32],"programming":[33],"(ADP)":[34],"for":[35,104],"solving":[36],"associated":[38],"Hamilton-Jacobi-Bellman":[39],"equation.":[40],"To":[41],"solve":[42],"derived":[44],"constrained":[45],"nonlinear":[46],"optimal":[47,61],"problem,":[49],"a":[50,81,109,113,128,139],"critic":[51],"neural":[52],"network":[53],"(NN)":[54],"is":[55,121],"used":[56,89],"approximate":[58],"time-dependant":[60],"cost":[62,116],"value":[63],"then":[65],"calculate":[66],"practical":[68,106],"suboptimal":[69],"causal":[70],"action.":[72],"The":[73,92],"proposed":[74,99,156],"novel":[75],"WEC":[76,110,129],"leads":[79],"simplified":[82],"ADP":[83],"framework":[84],"without":[85],"involving":[86],"widely":[88],"actor":[90],"NN.":[91],"significantly":[93],"improved":[94],"computational":[95],"efficacy":[96,153],"makes":[101],"it":[102],"attractive":[103],"its":[105],"implementation":[107],"achieve":[112],"reduced":[114],"unit":[115],"output,":[119],"which":[120],"especially":[122],"important":[123],"when":[124],"dynamics":[126],"are":[130,148],"complicated":[131],"need":[133],"be":[135],"described":[136],"accurately":[137],"by":[138],"high-order":[140],"model":[141],"with":[142],"constraints.":[145],"Simulation":[146],"results":[147],"provided":[149],"show":[151],"method.":[158]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":15},{"year":2023,"cited_by_count":18},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":28},{"year":2019,"cited_by_count":6}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}