{"id":"https://openalex.org/W4396766460","doi":"https://doi.org/10.1109/tie.2024.3390717","title":"Deep Bilinear Koopman Model Predictive Control for Nonlinear Dynamical Systems","display_name":"Deep Bilinear Koopman Model Predictive Control for Nonlinear Dynamical Systems","publication_year":2024,"publication_date":"2024-05-09","ids":{"openalex":"https://openalex.org/W4396766460","doi":"https://doi.org/10.1109/tie.2024.3390717"},"language":"en","primary_location":{"id":"doi:10.1109/tie.2024.3390717","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tie.2024.3390717","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/A5101936848","display_name":"Dongdong Zhao","orcid":"https://orcid.org/0000-0002-5305-1616"},"institutions":[{"id":"https://openalex.org/I76214153","display_name":"Lanzhou University","ror":"https://ror.org/01mkqqe32","country_code":"CN","type":"education","lineage":["https://openalex.org/I76214153"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dongdong Zhao","raw_affiliation_strings":["School of Information Science and Engineering, Lanzhou University, Lanzhou, China"],"raw_orcid":"https://orcid.org/0000-0002-5305-1616","affiliations":[{"raw_affiliation_string":"School of Information Science and Engineering, Lanzhou University, Lanzhou, China","institution_ids":["https://openalex.org/I76214153"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103191065","display_name":"Boyu Li","orcid":"https://orcid.org/0009-0005-2671-3847"},"institutions":[{"id":"https://openalex.org/I76214153","display_name":"Lanzhou University","ror":"https://ror.org/01mkqqe32","country_code":"CN","type":"education","lineage":["https://openalex.org/I76214153"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Boyu Li","raw_affiliation_strings":["School of Information Science and Engineering, Lanzhou University, Lanzhou, China"],"raw_orcid":"https://orcid.org/0009-0005-2671-3847","affiliations":[{"raw_affiliation_string":"School of Information Science and Engineering, Lanzhou University, Lanzhou, China","institution_ids":["https://openalex.org/I76214153"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071383825","display_name":"Fuxiang Lu","orcid":"https://orcid.org/0000-0002-5810-7631"},"institutions":[{"id":"https://openalex.org/I76214153","display_name":"Lanzhou University","ror":"https://ror.org/01mkqqe32","country_code":"CN","type":"education","lineage":["https://openalex.org/I76214153"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fuxiang Lu","raw_affiliation_strings":["School of Information Science and Engineering, Lanzhou University, Lanzhou, China"],"raw_orcid":"https://orcid.org/0000-0002-5810-7631","affiliations":[{"raw_affiliation_string":"School of Information Science and Engineering, Lanzhou University, Lanzhou, China","institution_ids":["https://openalex.org/I76214153"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101916568","display_name":"Jinhua She","orcid":"https://orcid.org/0000-0003-3165-5045"},"institutions":[{"id":"https://openalex.org/I148798404","display_name":"Tokyo University of Technology","ror":"https://ror.org/021a26605","country_code":"JP","type":"education","lineage":["https://openalex.org/I148798404"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Jinhua She","raw_affiliation_strings":["School of Engineering, Tokyo University of Technology, Hachioji, Japan"],"raw_orcid":"https://orcid.org/0000-0003-3165-5045","affiliations":[{"raw_affiliation_string":"School of Engineering, Tokyo University of Technology, Hachioji, Japan","institution_ids":["https://openalex.org/I148798404"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011375249","display_name":"Shi Yan","orcid":"https://orcid.org/0000-0002-4396-0488"},"institutions":[{"id":"https://openalex.org/I76214153","display_name":"Lanzhou University","ror":"https://ror.org/01mkqqe32","country_code":"CN","type":"education","lineage":["https://openalex.org/I76214153"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shi Yan","raw_affiliation_strings":["School of Information Science and Engineering, Lanzhou University, Lanzhou, China"],"raw_orcid":"https://orcid.org/0000-0002-4396-0488","affiliations":[{"raw_affiliation_string":"School of Information Science and Engineering, Lanzhou University, Lanzhou, China","institution_ids":["https://openalex.org/I76214153"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.1214,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.96571074,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"71","issue":"12","first_page":"16077","last_page":"16086"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9866999983787537,"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":0.9866999983787537,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9746000170707703,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"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":0.720543622970581},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6312351822853088},{"id":"https://openalex.org/keywords/model-predictive-control","display_name":"Model predictive control","score":0.6212252378463745},{"id":"https://openalex.org/keywords/nonlinear-dynamical-systems","display_name":"Nonlinear dynamical systems","score":0.6030374765396118},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.5616252422332764},{"id":"https://openalex.org/keywords/nonlinear-model","display_name":"Nonlinear model","score":0.5059213042259216},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4749612510204315},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3707538843154907},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3587961196899414},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.3402274250984192},{"id":"https://openalex.org/keywords/control-engineering","display_name":"Control engineering","score":0.3269575238227844},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.24461349844932556},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.22339510917663574},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2043187916278839}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.720543622970581},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6312351822853088},{"id":"https://openalex.org/C172205157","wikidata":"https://www.wikidata.org/wiki/Q1782962","display_name":"Model predictive control","level":3,"score":0.6212252378463745},{"id":"https://openalex.org/C2983030100","wikidata":"https://www.wikidata.org/wiki/Q638328","display_name":"Nonlinear dynamical systems","level":3,"score":0.6030374765396118},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.5616252422332764},{"id":"https://openalex.org/C2984755018","wikidata":"https://www.wikidata.org/wiki/Q17118374","display_name":"Nonlinear model","level":3,"score":0.5059213042259216},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4749612510204315},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3707538843154907},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3587961196899414},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.3402274250984192},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.3269575238227844},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.24461349844932556},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.22339510917663574},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2043187916278839},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tie.2024.3390717","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tie.2024.3390717","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6853238636","display_name":null,"funder_award_id":"U22B2040","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"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1631623342","https://openalex.org/W1779399219","https://openalex.org/W648378158","https://openalex.org/W3083517787","https://openalex.org/W1839440842","https://openalex.org/W4251946813","https://openalex.org/W2885820669","https://openalex.org/W2368407738","https://openalex.org/W2143511391","https://openalex.org/W4312206415"],"abstract_inverted_index":{"This":[0],"article":[1],"presents":[2],"a":[3,29,37,43,53,105,132],"deep":[4,57],"bilinear":[5,21,54,67,82,100],"Koopman":[6,55,68],"model":[7,31,83,89],"predictive":[8,34,90],"control":[9,15,91,142,166],"(DBKMPC)":[10],"approach":[11],"for":[12],"modelling":[13],"and":[14,32,48,117,141,165],"of":[16,28,36,46,98,113,120,139,143,163],"unknown":[17],"nonlinear":[18,38,144],"systems.":[19,51,146],"The":[20,147],"model,":[22,39],"which":[23],"has":[24],"the":[25,33,65,71,81,87,96,99,107,111,125,137,152,157],"computational":[26],"speed":[27],"linear":[30],"accuracy":[35],"can":[40],"accurately":[41],"characterize":[42],"large":[44],"class":[45],"airborne":[47],"ground-based":[49],"robotic":[50,145],"Specifically,":[52],"dynamic":[56],"neural":[58],"network":[59],"(BKDDNN)":[60],"is":[61,84],"developed":[62],"to":[63,136],"learn":[64],"finite-dimensional":[66],"operator":[69],"in":[70,161],"lifting":[72],"space":[73],"without":[74],"prior":[75],"knowledge":[76],"or":[77],"system":[78],"parameters.":[79],"Moreover,":[80],"integrated":[85],"into":[86],"standard":[88],"(MPC)":[92],"optimization":[93,101],"problem,":[94],"facilitating":[95],"solution":[97,135],"problem.":[102],"In":[103],"such":[104],"way,":[106],"proposed":[108,153],"DBKMPC":[109,154],"avoids":[110],"problems":[112],"excessive":[114],"inductive":[115],"bias":[116],"selection":[118],"difficulty":[119],"dictionary":[121],"functions":[122],"encountered":[123],"by":[124],"existing":[126,158],"methods,":[127],"so":[128],"that":[129,151],"it":[130],"enables":[131],"more":[133],"effective":[134],"problem":[138],"modeling":[140],"experimental":[148],"results":[149],"show":[150],"method":[155],"surpasses":[156],"representative":[159],"methods":[160],"terms":[162],"prediction":[164],"performance.":[167]},"counts_by_year":[{"year":2026,"cited_by_count":10},{"year":2025,"cited_by_count":16},{"year":2024,"cited_by_count":1}],"updated_date":"2026-07-19T07:52:34.831488","created_date":"2025-10-10T00:00:00"}
