{"id":"https://openalex.org/W2146504107","doi":"https://doi.org/10.1109/acc.2012.6315297","title":"Synthesis of optimal ensemble controls for linear systems using the singular value decomposition","display_name":"Synthesis of optimal ensemble controls for linear systems using the singular value decomposition","publication_year":2012,"publication_date":"2012-06-01","ids":{"openalex":"https://openalex.org/W2146504107","doi":"https://doi.org/10.1109/acc.2012.6315297","mag":"2146504107"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2012.6315297","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2012.6315297","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 American Control Conference (ACC)","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/A5024207408","display_name":"Anatoly Zlotnik","orcid":"https://orcid.org/0000-0002-2646-8264"},"institutions":[{"id":"https://openalex.org/I187476118","display_name":"Saint Louis University","ror":"https://ror.org/03fkbz285","country_code":"ES","type":"education","lineage":["https://openalex.org/I187476118"]},{"id":"https://openalex.org/I204465549","display_name":"Washington University in St. Louis","ror":"https://ror.org/01yc7t268","country_code":"US","type":"education","lineage":["https://openalex.org/I204465549"]}],"countries":["ES","US"],"is_corresponding":true,"raw_author_name":"A. Zlotnik","raw_affiliation_strings":["Electrical and Systems Engineering, Washington University of Saint Louis, Saint Louis, MO, USA","Electrical and Systems Engineering, Washington University in St. Louis, One Brookings Drive, Saint Louis, MO 63130"],"affiliations":[{"raw_affiliation_string":"Electrical and Systems Engineering, Washington University of Saint Louis, Saint Louis, MO, USA","institution_ids":["https://openalex.org/I204465549","https://openalex.org/I187476118"]},{"raw_affiliation_string":"Electrical and Systems Engineering, Washington University in St. Louis, One Brookings Drive, Saint Louis, MO 63130","institution_ids":["https://openalex.org/I204465549"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079314465","display_name":"Jr-Shin Li","orcid":"https://orcid.org/0000-0001-6693-3979"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jr-Shin Li","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5024207408"],"corresponding_institution_ids":["https://openalex.org/I187476118","https://openalex.org/I204465549"],"apc_list":null,"apc_paid":null,"fwci":2.0043,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.86323905,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"5849","last_page":"5854"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10378","display_name":"Advanced MRI Techniques and Applications","score":0.9894000291824341,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},"topics":[{"id":"https://openalex.org/T10378","display_name":"Advanced MRI Techniques and Applications","score":0.9894000291824341,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T11414","display_name":"Quantum optics and atomic interactions","score":0.9864000082015991,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T11809","display_name":"Advanced NMR Techniques and Applications","score":0.984499990940094,"subfield":{"id":"https://openalex.org/subfields/1607","display_name":"Spectroscopy"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/controllability","display_name":"Controllability","score":0.8215922117233276},{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.7864287495613098},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.6210651993751526},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.49771764874458313},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.49405887722969055},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4859970510005951},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4803296625614166},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4673994183540344},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.42515113949775696},{"id":"https://openalex.org/keywords/linear-dynamical-system","display_name":"Linear dynamical system","score":0.4112905263900757},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.37384968996047974},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3662877678871155},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35901162028312683},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.32955777645111084},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.27106305956840515},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.2168148159980774},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.1999882459640503},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1408892571926117},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13340404629707336},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13154080510139465}],"concepts":[{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.8215922117233276},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.7864287495613098},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.6210651993751526},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.49771764874458313},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.49405887722969055},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4859970510005951},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4803296625614166},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4673994183540344},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.42515113949775696},{"id":"https://openalex.org/C114275822","wikidata":"https://www.wikidata.org/wiki/Q621512","display_name":"Linear dynamical system","level":3,"score":0.4112905263900757},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37384968996047974},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3662877678871155},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35901162028312683},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.32955777645111084},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27106305956840515},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.2168148159980774},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.1999882459640503},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1408892571926117},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13340404629707336},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13154080510139465},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"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":2,"locations":[{"id":"doi:10.1109/acc.2012.6315297","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2012.6315297","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 American Control Conference (ACC)","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.766.6596","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.766.6596","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1109.5322.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W138869387","https://openalex.org/W641617372","https://openalex.org/W1534416612","https://openalex.org/W1977120413","https://openalex.org/W1989521361","https://openalex.org/W2008298717","https://openalex.org/W2011086792","https://openalex.org/W2011989099","https://openalex.org/W2016067881","https://openalex.org/W2018097850","https://openalex.org/W2059116080","https://openalex.org/W2097349975","https://openalex.org/W2103854823","https://openalex.org/W2107982977","https://openalex.org/W2114265982","https://openalex.org/W2132993835","https://openalex.org/W2134298283","https://openalex.org/W2140753922","https://openalex.org/W2141285356","https://openalex.org/W2159859241","https://openalex.org/W2161044358","https://openalex.org/W2187565700","https://openalex.org/W2951597533","https://openalex.org/W4301491118","https://openalex.org/W6674847199"],"related_works":["https://openalex.org/W4319586039","https://openalex.org/W4382583540","https://openalex.org/W1607100495","https://openalex.org/W2010100052","https://openalex.org/W2148568324","https://openalex.org/W1990844505","https://openalex.org/W4378770618","https://openalex.org/W4386721910","https://openalex.org/W2038393145","https://openalex.org/W2059545631"],"abstract_inverted_index":{"An":[0],"emerging":[1],"and":[2,60,82,94,98,146,181],"challenging":[3],"area":[4],"in":[5,54,125],"mathematical":[6],"control":[7,101,174],"theory":[8],"called":[9],"Ensemble":[10],"Control":[11],"encompasses":[12],"a":[13,35,131,143],"class":[14],"of":[15,21,26,50,73,87,112,161,172],"problems":[16,177],"that":[17,75,157],"involves":[18],"the":[19,40,48,71,77,92,109,113,116,126,152,170],"guidance":[20],"an":[22],"uncountably":[23],"infinite":[24],"collection":[25],"structurally":[27],"identical":[28],"dynamical":[29],"systems,":[30,91],"which":[31,69],"are":[32,122],"indexed":[33],"by":[34,38],"parameter":[36],"set,":[37],"applying":[39],"same":[41],"open-loop":[42],"control.":[43],"The":[44],"subject":[45],"originates":[46],"from":[47],"study":[49],"complex":[51],"spin":[52],"dynamics":[53],"Nuclear":[55],"Magnetic":[56],"Resonance":[57],"(NMR)":[58],"spectroscopy":[59],"imaging":[61],"(MRI).":[62],"A":[63],"fundamental":[64],"question":[65],"concerns":[66],"ensemble":[67,159,173],"controllability,":[68],"determines":[70],"existence":[72],"controls":[74,160],"transfer":[76],"system":[78,111,117],"between":[79],"desired":[80],"initial":[81],"target":[83],"states.":[84],"For":[85],"ensembles":[86],"finite-dimensional":[88],"time-varying":[89],"linear":[90,183],"necessary":[93],"sufficient":[95],"controllability":[96],"conditions":[97],"analytical":[99,120],"optimal":[100],"laws":[102],"have":[103],"been":[104],"shown":[105],"to":[106,133,175],"depend":[107],"on":[108,151],"singular":[110,153],"operator":[114],"characterizing":[115],"dynamics.":[118],"Because":[119],"solutions":[121],"available":[123],"only":[124],"simplest":[127],"cases,":[128],"there":[129],"is":[130],"need":[132],"develop":[134],"numerical":[135],"methods":[136],"for":[137,164],"synthesizing":[138],"these":[139],"controls.":[140],"We":[141],"introduce":[142],"direct,":[144],"accurate,":[145],"computationally":[147],"efficient":[148],"algorithm":[149],"based":[150],"value":[154],"decomposition":[155],"(SVD)":[156],"approximates":[158],"minimum":[162],"norm":[163],"such":[165],"systems.":[166,185],"This":[167],"method":[168],"enables":[169],"application":[171],"engineering":[176],"involving":[178],"complex,":[179],"time-varying,":[180],"high-dimensional":[182],"dynamic":[184]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}