{"id":"https://openalex.org/W2077076477","doi":"https://doi.org/10.1109/cdc.2013.6759956","title":"Averaging for nonlinear systems on Riemannian manifolds","display_name":"Averaging for nonlinear systems on Riemannian manifolds","publication_year":2013,"publication_date":"2013-12-01","ids":{"openalex":"https://openalex.org/W2077076477","doi":"https://doi.org/10.1109/cdc.2013.6759956","mag":"2077076477"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2013.6759956","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2013.6759956","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"52nd IEEE Conference on Decision and Control","raw_type":"proceedings-article"},"type":"conference-paper","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/A5045638418","display_name":"Farzin Taringoo","orcid":null},"institutions":[{"id":"https://openalex.org/I165779595","display_name":"The University of Melbourne","ror":"https://ror.org/01ej9dk98","country_code":"AU","type":"education","lineage":["https://openalex.org/I165779595"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Farzin Taringoo","raw_affiliation_strings":["Electrical and Electronic Engineering Department, University of Melbourne, Victoria, Australia","Electr. & Electron. Eng. Dept., Univ. of Melbourne, Melbourne, VIC, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical and Electronic Engineering Department, University of Melbourne, Victoria, Australia","institution_ids":["https://openalex.org/I165779595"]},{"raw_affiliation_string":"Electr. & Electron. Eng. Dept., Univ. of Melbourne, Melbourne, VIC, Australia","institution_ids":["https://openalex.org/I165779595"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035230630","display_name":"Dragan Ne\u0161i\u0107","orcid":"https://orcid.org/0000-0001-7944-0241"},"institutions":[{"id":"https://openalex.org/I165779595","display_name":"The University of Melbourne","ror":"https://ror.org/01ej9dk98","country_code":"AU","type":"education","lineage":["https://openalex.org/I165779595"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Dragan Nesic","raw_affiliation_strings":["Electrical and Electronic Engineering Department, University of Melbourne, Victoria, Australia","Electr. & Electron. Eng. Dept., Univ. of Melbourne, Melbourne, VIC, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical and Electronic Engineering Department, University of Melbourne, Victoria, Australia","institution_ids":["https://openalex.org/I165779595"]},{"raw_affiliation_string":"Electr. & Electron. Eng. Dept., Univ. of Melbourne, Melbourne, VIC, Australia","institution_ids":["https://openalex.org/I165779595"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078570390","display_name":"Ying Tan","orcid":"https://orcid.org/0000-0001-8495-0246"},"institutions":[{"id":"https://openalex.org/I165779595","display_name":"The University of Melbourne","ror":"https://ror.org/01ej9dk98","country_code":"AU","type":"education","lineage":["https://openalex.org/I165779595"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Ying Tan","raw_affiliation_strings":["Electrical and Electronic Engineering Department, University of Melbourne, Victoria, Australia","Electr. & Electron. Eng. Dept., Univ. of Melbourne, Melbourne, VIC, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical and Electronic Engineering Department, University of Melbourne, Victoria, Australia","institution_ids":["https://openalex.org/I165779595"]},{"raw_affiliation_string":"Electr. & Electron. Eng. Dept., Univ. of Melbourne, Melbourne, VIC, Australia","institution_ids":["https://openalex.org/I165779595"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004101031","display_name":"Peter M. Dower","orcid":"https://orcid.org/0000-0002-9791-7776"},"institutions":[{"id":"https://openalex.org/I165779595","display_name":"The University of Melbourne","ror":"https://ror.org/01ej9dk98","country_code":"AU","type":"education","lineage":["https://openalex.org/I165779595"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Peter M. Dower","raw_affiliation_strings":["Electrical and Electronic Engineering Department, University of Melbourne, Victoria, Australia","Electr. & Electron. Eng. Dept., Univ. of Melbourne, Melbourne, VIC, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical and Electronic Engineering Department, University of Melbourne, Victoria, Australia","institution_ids":["https://openalex.org/I165779595"]},{"raw_affiliation_string":"Electr. & Electron. Eng. Dept., Univ. of Melbourne, Melbourne, VIC, Australia","institution_ids":["https://openalex.org/I165779595"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I165779595"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"654","last_page":"659"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9990000128746033,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9990000128746033,"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":0.9847999811172485,"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/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9818000197410583,"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/riemannian-geometry","display_name":"Riemannian geometry","score":0.7565743923187256},{"id":"https://openalex.org/keywords/differential-geometry","display_name":"Differential geometry","score":0.6754468679428101},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6294071674346924},{"id":"https://openalex.org/keywords/nonlinear-dynamical-systems","display_name":"Nonlinear dynamical systems","score":0.5504817962646484},{"id":"https://openalex.org/keywords/differential-topology","display_name":"Differential topology","score":0.5079091191291809},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.5073825716972351},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4620119631290436},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4399280548095703},{"id":"https://openalex.org/keywords/curvature-of-riemannian-manifolds","display_name":"Curvature of Riemannian manifolds","score":0.429610013961792},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4221600592136383},{"id":"https://openalex.org/keywords/global-analysis","display_name":"Global analysis","score":0.4194623827934265},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3946382999420166},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.344698041677475},{"id":"https://openalex.org/keywords/ricci-flat-manifold","display_name":"Ricci-flat manifold","score":0.34076493978500366},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.21025264263153076},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1832849085330963},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17835357785224915},{"id":"https://openalex.org/keywords/sectional-curvature","display_name":"Sectional curvature","score":0.06315374374389648}],"concepts":[{"id":"https://openalex.org/C181104567","wikidata":"https://www.wikidata.org/wiki/Q761383","display_name":"Riemannian geometry","level":2,"score":0.7565743923187256},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.6754468679428101},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6294071674346924},{"id":"https://openalex.org/C2983030100","wikidata":"https://www.wikidata.org/wiki/Q638328","display_name":"Nonlinear dynamical systems","level":3,"score":0.5504817962646484},{"id":"https://openalex.org/C516171914","wikidata":"https://www.wikidata.org/wiki/Q1224402","display_name":"Differential topology","level":5,"score":0.5079091191291809},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.5073825716972351},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4620119631290436},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4399280548095703},{"id":"https://openalex.org/C146674193","wikidata":"https://www.wikidata.org/wiki/Q40139","display_name":"Curvature of Riemannian manifolds","level":5,"score":0.429610013961792},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4221600592136383},{"id":"https://openalex.org/C191174866","wikidata":"https://www.wikidata.org/wiki/Q17017346","display_name":"Global analysis","level":5,"score":0.4194623827934265},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3946382999420166},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.344698041677475},{"id":"https://openalex.org/C203934109","wikidata":"https://www.wikidata.org/wiki/Q7322952","display_name":"Ricci-flat manifold","level":4,"score":0.34076493978500366},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.21025264263153076},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1832849085330963},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17835357785224915},{"id":"https://openalex.org/C42448751","wikidata":"https://www.wikidata.org/wiki/Q855622","display_name":"Sectional curvature","level":4,"score":0.06315374374389648},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.0},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2013.6759956","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2013.6759956","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"52nd IEEE Conference on Decision and Control","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":24,"referenced_works":["https://openalex.org/W148728713","https://openalex.org/W1516803934","https://openalex.org/W1561445488","https://openalex.org/W1581443647","https://openalex.org/W1595765050","https://openalex.org/W1981870190","https://openalex.org/W1993300073","https://openalex.org/W1996413955","https://openalex.org/W2074126690","https://openalex.org/W2123155941","https://openalex.org/W2126479355","https://openalex.org/W2138003739","https://openalex.org/W2166454748","https://openalex.org/W3008682858","https://openalex.org/W3041070869","https://openalex.org/W4205424143","https://openalex.org/W4206669586","https://openalex.org/W4212819559","https://openalex.org/W4234194857","https://openalex.org/W4240542879","https://openalex.org/W4246954948","https://openalex.org/W4292402580","https://openalex.org/W6634595696","https://openalex.org/W6774339549"],"related_works":["https://openalex.org/W310341204","https://openalex.org/W3002848047","https://openalex.org/W2389192522","https://openalex.org/W4289143699","https://openalex.org/W1563480566","https://openalex.org/W2902235857","https://openalex.org/W3139064207","https://openalex.org/W2756998410","https://openalex.org/W1595217145","https://openalex.org/W1592746561"],"abstract_inverted_index":{"This":[0],"paper":[1],"provides":[2],"a":[3],"derivation":[4],"of":[5,34],"the":[6,20,32],"averaging":[7],"methods":[8],"for":[9],"nonlinear":[10],"time-varying":[11],"dynamical":[12],"systems":[13],"defined":[14],"on":[15,22],"Riemannian":[16,28],"manifolds.":[17],"We":[18],"extend":[19],"results":[21],"\u211d":[23],"<sup":[24],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[25],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</sup>":[26],"to":[27],"manifolds":[29],"by":[30],"employing":[31],"language":[33],"differential":[35],"geometry.":[36]},"counts_by_year":[{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}