{"id":"https://openalex.org/W1985632828","doi":"https://doi.org/10.1080/00207720118462","title":"The Lie algebra of a nonlinear dynamical system and its application to control","display_name":"The Lie algebra of a nonlinear dynamical system and its application to control","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W1985632828","doi":"https://doi.org/10.1080/00207720118462","mag":"1985632828"},"language":"en","primary_location":{"id":"doi:10.1080/00207720118462","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207720118462","pdf_url":null,"source":{"id":"https://openalex.org/S129640837","display_name":"International Journal of Systems Science","issn_l":"0020-7721","issn":["0020-7721","1464-5319"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Systems Science","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/A5007611202","display_name":"S. P. Banks","orcid":null},"institutions":[{"id":"https://openalex.org/I91136226","display_name":"University of Sheffield","ror":"https://ror.org/05krs5044","country_code":"GB","type":"education","lineage":["https://openalex.org/I91136226"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"S. P. Banks","raw_affiliation_strings":["Department of Automatic Control and Systems Engineering , University of Sheffield , Mappin Street, Sheffield, S1 3JD, UK"],"affiliations":[{"raw_affiliation_string":"Department of Automatic Control and Systems Engineering , University of Sheffield , Mappin Street, Sheffield, S1 3JD, UK","institution_ids":["https://openalex.org/I91136226"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5007611202"],"corresponding_institution_ids":["https://openalex.org/I91136226"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.08642466,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"32","issue":"2","first_page":"157","last_page":"174"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9887999892234802,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9887999892234802,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.9391000270843506,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9211000204086304,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/lie-algebra","display_name":"Lie algebra","score":0.6910809278488159},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6586092114448547},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5996422171592712},{"id":"https://openalex.org/keywords/lie-group","display_name":"Lie group","score":0.5564334392547607},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5526184439659119},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5375781655311584},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5348151326179504},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5231752991676331},{"id":"https://openalex.org/keywords/lie-conformal-algebra","display_name":"Lie conformal algebra","score":0.4295384883880615},{"id":"https://openalex.org/keywords/nonlinear-control","display_name":"Nonlinear control","score":0.421270489692688},{"id":"https://openalex.org/keywords/adjoint-representation","display_name":"Adjoint representation","score":0.4174971282482147},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3980883061885834},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.36126551032066345},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2321200668811798},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18452399969100952},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08368593454360962},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06115558743476868}],"concepts":[{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.6910809278488159},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6586092114448547},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5996422171592712},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.5564334392547607},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5526184439659119},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5375781655311584},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5348151326179504},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5231752991676331},{"id":"https://openalex.org/C73648015","wikidata":"https://www.wikidata.org/wiki/Q6543817","display_name":"Lie conformal algebra","level":3,"score":0.4295384883880615},{"id":"https://openalex.org/C91581856","wikidata":"https://www.wikidata.org/wiki/Q2707001","display_name":"Nonlinear control","level":3,"score":0.421270489692688},{"id":"https://openalex.org/C58910974","wikidata":"https://www.wikidata.org/wiki/Q1017106","display_name":"Adjoint representation","level":3,"score":0.4174971282482147},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3980883061885834},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.36126551032066345},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2321200668811798},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18452399969100952},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08368593454360962},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06115558743476868},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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":3,"locations":[{"id":"doi:10.1080/00207720118462","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207720118462","pdf_url":null,"source":{"id":"https://openalex.org/S129640837","display_name":"International Journal of Systems Science","issn_l":"0020-7721","issn":["0020-7721","1464-5319"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Systems Science","raw_type":"journal-article"},{"id":"pmh:oai:eprints.whiterose.ac.uk:83851","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400854","display_name":"White Rose Research Online (University of Leeds, The University of Sheffield, University of York)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2800616092","host_organization_name":"White Rose University Consortium","host_organization_lineage":["https://openalex.org/I2800616092"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Monograph"},{"id":"pmh:hdl:10068/653917","is_oa":false,"landing_page_url":"http://hdl.handle.net/10068/653917","pdf_url":null,"source":{"id":"https://openalex.org/S4377196900","display_name":"OpenGrey (Institut de l'Information Scientifique et Technique)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1295345811","host_organization_name":"Institut de l'Information Scientifique et Technique","host_organization_lineage":["https://openalex.org/I1295345811"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"R - Report"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2521760353","https://openalex.org/W3108652777","https://openalex.org/W2373470437","https://openalex.org/W2009463956","https://openalex.org/W4298401637","https://openalex.org/W2940979654","https://openalex.org/W2037832882","https://openalex.org/W2460513362","https://openalex.org/W2135746360","https://openalex.org/W1569557269"],"abstract_inverted_index":{"Using":[0],"a":[1,8,47],"recently":[2],"introduced":[3],"Lie":[4,35],"algebra":[5],"associated":[6,34],"with":[7],"nonlinear":[9],"system,":[10],"several":[11],"new":[12],"results":[13,43],"in":[14],"dynamical":[15],"systems":[16],"and":[17,41,46],"control":[18,52],"theory":[19],"are":[20,44],"obtained.":[21],"In":[22],"particular,":[23],"we":[24],"show":[25],"that":[26],"the":[27,30,33],"solutions":[28],"carry":[29],"structure":[31],"of":[32,39,49],"group.":[36],"A":[37],"number":[38],"stability":[40],"boundedness":[42],"given":[45],"generalization":[48],"classical":[50],"modal":[51],"is":[53],"developed.":[54]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2013,"cited_by_count":4}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
