{"id":"https://openalex.org/W2567764623","doi":"https://doi.org/10.1109/cdc.2016.7798642","title":"Control of ensemble systems on special orthogonal groups","display_name":"Control of ensemble systems on special orthogonal groups","publication_year":2016,"publication_date":"2016-12-01","ids":{"openalex":"https://openalex.org/W2567764623","doi":"https://doi.org/10.1109/cdc.2016.7798642","mag":"2567764623"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2016.7798642","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2016.7798642","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE 55th 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/A5090811629","display_name":"Wei Zhang","orcid":"https://orcid.org/0000-0002-3411-8694"},"institutions":[{"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":["US"],"is_corresponding":true,"raw_author_name":"Wei Zhang","raw_affiliation_strings":["Department of Electrical and Systems Engineering, Washington University, St. Louis, MO, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Systems Engineering, Washington University, St. Louis, MO, USA","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":[{"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":["US"],"is_corresponding":false,"raw_author_name":"Jr-Shin Li","raw_affiliation_strings":["Department of Electrical and Systems Engineering, Washington University, St. Louis, MO, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Systems Engineering, Washington University, St. Louis, MO, USA","institution_ids":["https://openalex.org/I204465549"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5090811629"],"corresponding_institution_ids":["https://openalex.org/I204465549"],"apc_list":null,"apc_paid":null,"fwci":0.4461,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.7009812,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"12","issue":null,"first_page":"2529","last_page":"2534"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12748","display_name":"Molecular spectroscopy and chirality","score":0.9890000224113464,"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"}},"topics":[{"id":"https://openalex.org/T12748","display_name":"Molecular spectroscopy and chirality","score":0.9890000224113464,"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"}},{"id":"https://openalex.org/T11414","display_name":"Quantum optics and atomic interactions","score":0.9828000068664551,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9797999858856201,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/controllability","display_name":"Controllability","score":0.9320338368415833},{"id":"https://openalex.org/keywords/lie-group","display_name":"Lie group","score":0.5729615092277527},{"id":"https://openalex.org/keywords/terminology","display_name":"Terminology","score":0.4999125003814697},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.49962663650512695},{"id":"https://openalex.org/keywords/lie-algebra","display_name":"Lie algebra","score":0.49054139852523804},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.48883217573165894},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44893983006477356},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4414409101009369},{"id":"https://openalex.org/keywords/orthogonal-group","display_name":"Orthogonal group","score":0.4168875217437744},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3972625136375427},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3843157887458801},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3704800605773926},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3258730471134186},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.28351184725761414},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.24238717555999756},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.19114035367965698},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12689119577407837}],"concepts":[{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.9320338368415833},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.5729615092277527},{"id":"https://openalex.org/C547195049","wikidata":"https://www.wikidata.org/wiki/Q1725664","display_name":"Terminology","level":2,"score":0.4999125003814697},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.49962663650512695},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.49054139852523804},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.48883217573165894},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44893983006477356},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4414409101009369},{"id":"https://openalex.org/C146561895","wikidata":"https://www.wikidata.org/wiki/Q1783179","display_name":"Orthogonal group","level":2,"score":0.4168875217437744},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3972625136375427},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3843157887458801},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3704800605773926},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3258730471134186},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.28351184725761414},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.24238717555999756},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.19114035367965698},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12689119577407837},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2016.7798642","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2016.7798642","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE 55th Conference on Decision and Control (CDC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.6399999856948853}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1540059687","https://openalex.org/W1557324374","https://openalex.org/W1561445488","https://openalex.org/W1582706191","https://openalex.org/W1981449324","https://openalex.org/W1989521361","https://openalex.org/W2000438926","https://openalex.org/W2011989099","https://openalex.org/W2023285936","https://openalex.org/W2033102642","https://openalex.org/W2041277461","https://openalex.org/W2057285417","https://openalex.org/W2079951449","https://openalex.org/W2114265982","https://openalex.org/W2149129194","https://openalex.org/W3102355313","https://openalex.org/W4252614677","https://openalex.org/W4293203252"],"related_works":["https://openalex.org/W2036697162","https://openalex.org/W2332386680","https://openalex.org/W2561315646","https://openalex.org/W2248621902","https://openalex.org/W2963288691","https://openalex.org/W4298401637","https://openalex.org/W2940979654","https://openalex.org/W2625783959","https://openalex.org/W2394160247","https://openalex.org/W2154642391"],"abstract_inverted_index":{"In":[0,86],"this":[1],"paper,":[2],"we":[3,88],"study":[4],"the":[5,16,34,59,67,70,82,90],"control":[6,25],"of":[7,10,23,36,46,61,72,97],"an":[8,50],"ensemble":[9,24,95,100],"time-invariant":[11],"bilinear":[12],"systems":[13,26,62,104],"defined":[14],"on":[15,63,106],"special":[17],"orthogonal":[18],"group":[19],"SO(n).":[20,107],"This":[21],"type":[22],"appears":[27],"in":[28],"various":[29],"application":[30],"domains,":[31],"such":[32],"as":[33],"manipulation":[35],"quantum":[37],"spin":[38],"ensembles":[39],"and":[40,54,94,99],"motion":[41],"planning":[42],"for":[43,103],"a":[44,77],"population":[45],"robots.":[47],"We":[48],"establish":[49],"explicit":[51],"algebraic":[52],"necessary":[53],"sufficient":[55],"condition":[56],"to":[57,80],"examine":[58],"controllability":[60,93,96],"SO(n)":[64],"by":[65],"using":[66],"terminology":[68],"from":[69],"theory":[71],"symmetric":[73],"groups,":[74],"which":[75],"provides":[76],"transparent":[78],"means":[79],"analyze":[81],"underlying":[83],"Lie":[84],"algebras.":[85],"addition,":[87],"show":[89],"equivalence":[91],"between":[92],"individual":[98],"systems,":[101],"respectively,":[102],"evolving":[105]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}