{"id":"https://openalex.org/W4315488650","doi":"https://doi.org/10.1109/cdc51059.2022.9993265","title":"Spectral Analysis of Koopman Operator and Nonlinear Optimal Control","display_name":"Spectral Analysis of Koopman Operator and Nonlinear Optimal Control","publication_year":2022,"publication_date":"2022-12-06","ids":{"openalex":"https://openalex.org/W4315488650","doi":"https://doi.org/10.1109/cdc51059.2022.9993265"},"language":"en","primary_location":{"id":"doi:10.1109/cdc51059.2022.9993265","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc51059.2022.9993265","pdf_url":null,"source":{"id":"https://openalex.org/S4363607710","display_name":"2022 IEEE 61st Conference on Decision and Control (CDC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2022 IEEE 61st Conference on Decision and Control (CDC)","raw_type":"proceedings-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/A5050749492","display_name":"Umesh Vaidya","orcid":"https://orcid.org/0000-0002-0483-4921"},"institutions":[{"id":"https://openalex.org/I8078737","display_name":"Clemson University","ror":"https://ror.org/037s24f05","country_code":"US","type":"education","lineage":["https://openalex.org/I8078737"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Umesh Vaidya","raw_affiliation_strings":["Clemson University,Department of Mechanical Engineering,Clemson,SC,29631"],"affiliations":[{"raw_affiliation_string":"Clemson University,Department of Mechanical Engineering,Clemson,SC,29631","institution_ids":["https://openalex.org/I8078737"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5050749492"],"corresponding_institution_ids":["https://openalex.org/I8078737"],"apc_list":null,"apc_paid":null,"fwci":3.4945,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.9380863,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"3853","last_page":"3858"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.9753000140190125,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9564999938011169,"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/submanifold","display_name":"Submanifold","score":0.8722876906394958},{"id":"https://openalex.org/keywords/eigenfunction","display_name":"Eigenfunction","score":0.7505515217781067},{"id":"https://openalex.org/keywords/hamilton\u2013jacobi-equation","display_name":"Hamilton\u2013Jacobi equation","score":0.7414484620094299},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.7389702796936035},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6062100529670715},{"id":"https://openalex.org/keywords/lagrangian","display_name":"Lagrangian","score":0.5883610248565674},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5825647711753845},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.538234531879425},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5291505455970764},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.51605623960495},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.492064893245697},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4536513686180115},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.44502073526382446},{"id":"https://openalex.org/keywords/hamiltonian-mechanics","display_name":"Hamiltonian mechanics","score":0.4445207417011261},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4219130277633667},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1739005744457245},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.16160324215888977},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06658440828323364}],"concepts":[{"id":"https://openalex.org/C151300846","wikidata":"https://www.wikidata.org/wiki/Q125539","display_name":"Submanifold","level":2,"score":0.8722876906394958},{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.7505515217781067},{"id":"https://openalex.org/C2778860007","wikidata":"https://www.wikidata.org/wiki/Q1060137","display_name":"Hamilton\u2013Jacobi equation","level":2,"score":0.7414484620094299},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.7389702796936035},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6062100529670715},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.5883610248565674},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5825647711753845},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.538234531879425},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5291505455970764},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.51605623960495},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.492064893245697},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4536513686180115},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44502073526382446},{"id":"https://openalex.org/C136864674","wikidata":"https://www.wikidata.org/wiki/Q477921","display_name":"Hamiltonian mechanics","level":3,"score":0.4445207417011261},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4219130277633667},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1739005744457245},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.16160324215888977},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06658440828323364},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc51059.2022.9993265","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc51059.2022.9993265","pdf_url":null,"source":{"id":"https://openalex.org/S4363607710","display_name":"2022 IEEE 61st Conference on Decision and Control (CDC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2022 IEEE 61st Conference on Decision and Control (CDC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W5108103","https://openalex.org/W85133216","https://openalex.org/W1529558080","https://openalex.org/W2047090868","https://openalex.org/W2112507254","https://openalex.org/W2135957782","https://openalex.org/W2172945660","https://openalex.org/W2482944896","https://openalex.org/W2488089998","https://openalex.org/W2561027863","https://openalex.org/W2736746078","https://openalex.org/W2766388929","https://openalex.org/W2963895143","https://openalex.org/W2991844785","https://openalex.org/W3089929324","https://openalex.org/W3092417881","https://openalex.org/W3126331428","https://openalex.org/W3136945292","https://openalex.org/W3184301789","https://openalex.org/W3186374574","https://openalex.org/W4206409588","https://openalex.org/W4214690803","https://openalex.org/W4214717370"],"related_works":["https://openalex.org/W2774729628","https://openalex.org/W3103060505","https://openalex.org/W3082140557","https://openalex.org/W1978642242","https://openalex.org/W1987982369","https://openalex.org/W114740072","https://openalex.org/W2485657727","https://openalex.org/W2563936163","https://openalex.org/W2038026589","https://openalex.org/W2042058386"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"present":[4,102],"an":[5],"approach":[6],"based":[7],"on":[8],"the":[9,13,17,21,29,45,50,54,64,71,75,80,89,94,97,107,111],"spectral":[10],"analysis":[11],"of":[12,20,53,74,96,110],"Koopman":[14,76],"operator":[15,77],"for":[16],"approximate":[18],"solution":[19,95],"Hamilton":[22,46,65,98],"Jacobi":[23,47,66,99],"equation":[24],"that":[25,36,70],"arises":[26],"while":[27],"solving":[28,63],"optimal":[30],"control":[31],"problem.":[32],"It":[33],"is":[34],"well-known":[35],"one":[37],"can":[38,84],"associate":[39],"a":[40,59],"Hamiltonian":[41,55,81],"dynamical":[42,56,82],"system":[43,57,83],"with":[44,79],"equation.":[48,67,100],"Furthermore,":[49],"Lagrangian":[51,90],"submanifold":[52],"play":[58],"fundamental":[60],"role":[61],"in":[62,87],"We":[68,101],"show":[69],"principal":[72],"eigenfunctions":[73],"associated":[78],"be":[85],"used":[86],"constructing":[88],"submanifold,":[91],"thereby":[92],"approximating":[93],"simulation":[103],"results":[104],"to":[105],"verify":[106],"main":[108],"findings":[109],"paper.":[112]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":7}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
