{"id":"https://openalex.org/W1974327165","doi":"https://doi.org/10.1109/aucc.2013.6697246","title":"Closeness of solutions and averaging for nonlinear systems on Riemannian manifolds","display_name":"Closeness of solutions and averaging for nonlinear systems on Riemannian manifolds","publication_year":2013,"publication_date":"2013-11-01","ids":{"openalex":"https://openalex.org/W1974327165","doi":"https://doi.org/10.1109/aucc.2013.6697246","mag":"1974327165"},"language":"en","primary_location":{"id":"doi:10.1109/aucc.2013.6697246","is_oa":false,"landing_page_url":"https://doi.org/10.1109/aucc.2013.6697246","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 Australian Control Conference","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":["Department of Electrical & Electronic Engineering, University of Melbourne, Victoria, Australia","Dept. of Electr. & Electron. Eng., Univ. of Melbourne, Melbourne, VIC, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical & Electronic Engineering, University of Melbourne, Victoria, Australia","institution_ids":["https://openalex.org/I165779595"]},{"raw_affiliation_string":"Dept. of Electr. & Electron. Eng., 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":["Department of Electrical & Electronic Engineering, University of Melbourne, Victoria, Australia","Dept. of Electr. & Electron. Eng., Univ. of Melbourne, Melbourne, VIC, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical & Electronic Engineering, University of Melbourne, Victoria, Australia","institution_ids":["https://openalex.org/I165779595"]},{"raw_affiliation_string":"Dept. of Electr. & Electron. Eng., 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":["Department of Electrical & Electronic Engineering, University of Melbourne, Victoria, Australia","Dept. of Electr. & Electron. Eng., Univ. of Melbourne, Melbourne, VIC, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical & Electronic Engineering, University of Melbourne, Victoria, Australia","institution_ids":["https://openalex.org/I165779595"]},{"raw_affiliation_string":"Dept. of Electr. & Electron. Eng., 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":["Department of Electrical & Electronic Engineering, University of Melbourne, Victoria, Australia","Dept. of Electr. & Electron. Eng., Univ. of Melbourne, Melbourne, VIC, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical & Electronic Engineering, University of Melbourne, Victoria, Australia","institution_ids":["https://openalex.org/I165779595"]},{"raw_affiliation_string":"Dept. of Electr. & Electron. Eng., 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":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":null,"first_page":"47","last_page":"52"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9948999881744385,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9948999881744385,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.994700014591217,"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"}},{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.9866999983787537,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/closeness","display_name":"Closeness","score":0.6807293891906738},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.6520291566848755},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.6220912337303162},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5468657612800598},{"id":"https://openalex.org/keywords/riemannian-geometry","display_name":"Riemannian geometry","score":0.5329210758209229},{"id":"https://openalex.org/keywords/nonlinear-dynamical-systems","display_name":"Nonlinear dynamical systems","score":0.5237212777137756},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.5180209279060364},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5100191235542297},{"id":"https://openalex.org/keywords/method-of-averaging","display_name":"Method of averaging","score":0.4297448694705963},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.42014414072036743},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.354671835899353},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16177299618721008}],"concepts":[{"id":"https://openalex.org/C2779545769","wikidata":"https://www.wikidata.org/wiki/Q5135364","display_name":"Closeness","level":2,"score":0.6807293891906738},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6520291566848755},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.6220912337303162},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5468657612800598},{"id":"https://openalex.org/C181104567","wikidata":"https://www.wikidata.org/wiki/Q761383","display_name":"Riemannian geometry","level":2,"score":0.5329210758209229},{"id":"https://openalex.org/C2983030100","wikidata":"https://www.wikidata.org/wiki/Q638328","display_name":"Nonlinear dynamical systems","level":3,"score":0.5237212777137756},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.5180209279060364},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5100191235542297},{"id":"https://openalex.org/C5555538","wikidata":"https://www.wikidata.org/wiki/Q6823703","display_name":"Method of averaging","level":3,"score":0.4297448694705963},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42014414072036743},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.354671835899353},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16177299618721008},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/aucc.2013.6697246","is_oa":false,"landing_page_url":"https://doi.org/10.1109/aucc.2013.6697246","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 Australian Control Conference","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":26,"referenced_works":["https://openalex.org/W148728713","https://openalex.org/W1516803934","https://openalex.org/W1561445488","https://openalex.org/W1581443647","https://openalex.org/W1974327165","https://openalex.org/W1981870190","https://openalex.org/W1996413955","https://openalex.org/W2071355416","https://openalex.org/W2074126690","https://openalex.org/W2074257552","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/W4212819559","https://openalex.org/W4234194857","https://openalex.org/W4240542879","https://openalex.org/W4246954948","https://openalex.org/W4292402580","https://openalex.org/W4292408540","https://openalex.org/W4299143332","https://openalex.org/W4299657804","https://openalex.org/W6774339549"],"related_works":["https://openalex.org/W2156910174","https://openalex.org/W1995054232","https://openalex.org/W2011510925","https://openalex.org/W1557920161","https://openalex.org/W1556709767","https://openalex.org/W1993023208","https://openalex.org/W2077076477","https://openalex.org/W4232338310","https://openalex.org/W4234976534","https://openalex.org/W4233923526"],"abstract_inverted_index":{"An":[0],"averaging":[1,79],"result":[2,28,51,87],"for":[3,29],"periodic":[4,62],"dynamical":[5,31,63],"systems":[6,32,64],"evolving":[7,15],"on":[8,16,44,71],"Euclidean":[9],"spaces":[10],"is":[11,33,52],"extended":[12,54],"to":[13,55],"those":[14,66],"(differentiable)":[17],"Riemannian":[18],"manifolds.":[19],"Using":[20],"standard":[21],"tools":[22],"from":[23,65],"differential":[24],"geometry,":[25],"a":[26,41,45],"perturbation":[27,50],"time-varying":[30],"developed":[34],"that":[35],"measures":[36],"closeness":[37],"of":[38,61,67],"trajectories":[39,60],"via":[40],"suitable":[42],"metric":[43],"finite":[46],"time":[47,74],"horizon.":[48],"This":[49],"then":[53],"bound":[56],"excursions":[57],"in":[58],"the":[59,77],"their":[68],"respective":[69],"averages,":[70],"an":[72],"infinite":[73],"horizon,":[75],"yielding":[76],"specified":[78],"result.":[80],"Some":[81],"simple":[82],"examples":[83],"further":[84],"illustrating":[85],"this":[86],"are":[88],"also":[89],"presented.":[90]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}