{"id":"https://openalex.org/W2772867050","doi":"https://doi.org/10.1137/15m1037755","title":"Expressing an Observer in Preferred Coordinates by Transforming an Injective Immersion into a Surjective Diffeomorphism","display_name":"Expressing an Observer in Preferred Coordinates by Transforming an Injective Immersion into a Surjective Diffeomorphism","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2772867050","doi":"https://doi.org/10.1137/15m1037755","mag":"2772867050"},"language":"en","primary_location":{"id":"doi:10.1137/15m1037755","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1037755","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1509.04865","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052117463","display_name":"Pauline Bernard","orcid":"https://orcid.org/0000-0002-7710-0136"},"institutions":[{"id":"https://openalex.org/I4210116740","display_name":"Laboratoire d'Informatique et d'Automatique pour les Syst\u00e8mes","ror":"https://ror.org/02b5vq778","country_code":"FR","type":"facility","lineage":["https://openalex.org/I32881790","https://openalex.org/I4210116740"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"P. Bernard","raw_affiliation_strings":["Centre Automatique et Syst\u00e8mes"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre Automatique et Syst\u00e8mes","institution_ids":["https://openalex.org/I4210116740"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082790000","display_name":"Vincent Andrieu","orcid":"https://orcid.org/0000-0003-1877-6205"},"institutions":[{"id":"https://openalex.org/I4210143168","display_name":"Laboratoire d'Automatique, de G\u00e9nie des Proc\u00e9d\u00e9s et de G\u00e9nie Pharmaceutique","ror":"https://ror.org/03kfjwy31","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I203339264","https://openalex.org/I4210095849","https://openalex.org/I4210143168","https://openalex.org/I59692284"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"V. Andrieu","raw_affiliation_strings":["LAGEP"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LAGEP","institution_ids":["https://openalex.org/I4210143168"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101466166","display_name":"Laurent Praly","orcid":"https://orcid.org/0000-0003-4380-7616"},"institutions":[{"id":"https://openalex.org/I4210116740","display_name":"Laboratoire d'Informatique et d'Automatique pour les Syst\u00e8mes","ror":"https://ror.org/02b5vq778","country_code":"FR","type":"facility","lineage":["https://openalex.org/I32881790","https://openalex.org/I4210116740"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"L. Praly","raw_affiliation_strings":["Centre Automatique et Syst\u00e8mes"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre Automatique et Syst\u00e8mes","institution_ids":["https://openalex.org/I4210116740"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01405686,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"56","issue":"3","first_page":"2327","last_page":"2352"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9835000038146973,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9835000038146973,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9796000123023987,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9789000153541565,"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/injective-function","display_name":"Injective function","score":0.8984767198562622},{"id":"https://openalex.org/keywords/surjective-function","display_name":"Surjective function","score":0.6581830382347107},{"id":"https://openalex.org/keywords/observer","display_name":"Observer (physics)","score":0.5929914116859436},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5864455699920654},{"id":"https://openalex.org/keywords/diffeomorphism","display_name":"Diffeomorphism","score":0.5410517454147339},{"id":"https://openalex.org/keywords/immersion","display_name":"Immersion (mathematics)","score":0.5199295878410339},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5037893652915955},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4575374126434326},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3930794298648834},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.36385682225227356},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07019999623298645}],"concepts":[{"id":"https://openalex.org/C128107574","wikidata":"https://www.wikidata.org/wiki/Q182003","display_name":"Injective function","level":2,"score":0.8984767198562622},{"id":"https://openalex.org/C119238805","wikidata":"https://www.wikidata.org/wiki/Q229102","display_name":"Surjective function","level":2,"score":0.6581830382347107},{"id":"https://openalex.org/C2780704645","wikidata":"https://www.wikidata.org/wiki/Q9251458","display_name":"Observer (physics)","level":2,"score":0.5929914116859436},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5864455699920654},{"id":"https://openalex.org/C47556283","wikidata":"https://www.wikidata.org/wiki/Q1058314","display_name":"Diffeomorphism","level":2,"score":0.5410517454147339},{"id":"https://openalex.org/C199068039","wikidata":"https://www.wikidata.org/wiki/Q574523","display_name":"Immersion (mathematics)","level":2,"score":0.5199295878410339},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5037893652915955},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4575374126434326},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3930794298648834},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36385682225227356},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07019999623298645},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1137/15m1037755","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1037755","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1509.04865","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1509.04865","pdf_url":"https://arxiv.org/pdf/1509.04865","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2772867050","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1509.04865","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:HAL:hal-01199791v4","is_oa":true,"landing_page_url":"https://hal.archives-ouvertes.fr/hal-01199791","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://hal.archives-ouvertes.fr/hal-01199791","raw_type":"info:eu-repo/semantics/preprint"},{"id":"pmh:oai:HAL:hal-01199791v6","is_oa":false,"landing_page_url":"https://hal.science/hal-01199791","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Control and Optimization, 2018, 56 (3), pp.2327-2352. &#x27E8;10.1137/15M1037755&#x27E9;","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:HAL:hal-01886153v1","is_oa":false,"landing_page_url":"https://hal-mines-paristech.archives-ouvertes.fr/hal-01886153","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 0363-0129","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1509.04865","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1509.04865","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1509.04865","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1509.04865","pdf_url":"https://arxiv.org/pdf/1509.04865","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1967530463","https://openalex.org/W1968153361","https://openalex.org/W1975670275","https://openalex.org/W2023596262","https://openalex.org/W2027277168","https://openalex.org/W2063157339","https://openalex.org/W2085148945","https://openalex.org/W2115852080","https://openalex.org/W2125336652","https://openalex.org/W2127894883","https://openalex.org/W2173487526","https://openalex.org/W3196167895"],"related_works":["https://openalex.org/W2618987468","https://openalex.org/W2962868712","https://openalex.org/W2493195292","https://openalex.org/W2460431811","https://openalex.org/W3088932472","https://openalex.org/W2521715257","https://openalex.org/W1793834480","https://openalex.org/W2103178091","https://openalex.org/W23619336","https://openalex.org/W1203392064","https://openalex.org/W2232924255","https://openalex.org/W127055403","https://openalex.org/W188770420","https://openalex.org/W2770327267","https://openalex.org/W2948103149","https://openalex.org/W3165527564","https://openalex.org/W151631643","https://openalex.org/W2106762190","https://openalex.org/W2777723974","https://openalex.org/W2152261259"],"abstract_inverted_index":{"When":[0],"designing":[1],"observers":[2],"for":[3],"nonlinear":[4],"systems,":[5],"the":[6,9,14,22,35,50,70,74,75,79,104,107,110,124,143,154,157,160,175],"dynamics":[7,72,177],"of":[8,13,49,109,135,139,156],"given":[10,80],"system":[11],"and":[12,56,141,168],"designed":[15],"observer":[16,71,176],"are":[17],"usually":[18],"not":[19,53],"expressed":[20],"in":[21,30,47,73],"same":[23,76],"coordinates":[24,77],"or":[25,106,113],"even":[26],"have":[27],"states":[28],"evolving":[29],"different":[31],"spaces.":[32],"In":[33],"general,":[34],"function,":[36],"denoted":[37,42],"$\\tau$":[38,112],"(or":[39],"its":[40],"inverse,":[41],"$\\tau^*$)":[43],"giving":[44],"one":[45],"state":[46],"terms":[48],"other":[51],"is":[52],"explicitly":[54],"known":[55],"this":[57,66,83],"creates":[58],"implementation":[59],"issues.":[60],"We":[61,121,163],"propose":[62],"to":[63,87,102],"get":[64],"around":[65],"problem":[67,92,116,126,145],"by":[68,131,149],"expressing":[69],"as":[78],"system.":[81],"But":[82],"may":[84,98],"force":[85,100],"us":[86,101],"add":[88],"extra":[89],"coordinates,":[90],"a":[91,115,132,136,150],"that":[93,117,123,142],"we":[94,118],"call":[95,119],"augmentation.":[96],"This":[97],"also":[99,164],"modify":[103],"domain":[105],"range":[108],"\u201caugmented\u201d":[111],"$\\tau^*$,":[114],"extension.":[120],"show":[122,165],"augmentation":[125,167],"can":[127,146,170],"be":[128,147,171],"solved":[129,148],"partly":[130],"continuous":[133],"completion":[134],"free":[137],"family":[138],"vectors":[140],"extension":[144,152,169],"function":[151,159],"making":[153],"image":[155],"extended":[158],"whole":[161],"space.":[162],"how":[166],"done":[172],"without":[173],"modifying":[174],"and,":[178],"therefore,":[179],"with":[180],"maintaining":[181],"convergence.":[182],"Several":[183],"examples":[184],"illustrate":[185],"our":[186],"results.":[187]},"counts_by_year":[],"updated_date":"2026-07-30T17:31:21.811387","created_date":"2025-10-10T00:00:00"}
