{"id":"https://openalex.org/W1974664394","doi":"https://doi.org/10.1137/060675988","title":"Limit Time Optimal Synthesis for a Control-Affine System on $S^2$","display_name":"Limit Time Optimal Synthesis for a Control-Affine System on $S^2$","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W1974664394","doi":"https://doi.org/10.1137/060675988","mag":"1974664394"},"language":"en","primary_location":{"id":"doi:10.1137/060675988","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060675988","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":["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/A5053579534","display_name":"Paolo Mason","orcid":"https://orcid.org/0000-0002-2583-9991"},"institutions":[{"id":"https://openalex.org/I3017839442","display_name":"Institut \u00c9lie Cartan de Lorraine","ror":"https://ror.org/04rvw8791","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I3017839442","https://openalex.org/I4210141950","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"P. Mason","raw_affiliation_strings":["Institut Elie Cartan de Nancy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut Elie Cartan de Nancy","institution_ids":["https://openalex.org/I3017839442","https://openalex.org/I90183372"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073564675","display_name":"Rebecca Salmoni","orcid":null},"institutions":[{"id":"https://openalex.org/I4210097418","display_name":"Laboratoire des signaux et syst\u00e8mes","ror":"https://ror.org/00skw9v43","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I277688954","https://openalex.org/I4210097418","https://openalex.org/I4210107720"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"R. Salmoni","raw_affiliation_strings":["Laboratoire des signaux et syst\u00e8mes"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire des signaux et syst\u00e8mes","institution_ids":["https://openalex.org/I4210097418"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012657462","display_name":"Ugo Boscain","orcid":"https://orcid.org/0000-0001-5450-275X"},"institutions":[{"id":"https://openalex.org/I138549579","display_name":"Scuola Internazionale Superiore di Studi Avanzati","ror":"https://ror.org/004fze387","country_code":"IT","type":"education","lineage":["https://openalex.org/I138549579"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"U. Boscain","raw_affiliation_strings":["SISSA MathLab [Trieste]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"SISSA MathLab [Trieste]","institution_ids":["https://openalex.org/I138549579"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000279658","display_name":"Yacine Chitour","orcid":"https://orcid.org/0000-0002-3214-5824"},"institutions":[{"id":"https://openalex.org/I102197404","display_name":"Universit\u00e9 Paris-Sud","ror":"https://ror.org/028rypz17","country_code":"FR","type":"education","lineage":["https://openalex.org/I102197404"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Y. Chitour","raw_affiliation_strings":["Laboratoire des signaux et syst\u00e8mes, Universit\u00e9 Paris-Sud, CNRS, Sup\u00e9lec, 91192 Gif-Sur-Yvette, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire des signaux et syst\u00e8mes, Universit\u00e9 Paris-Sud, CNRS, Sup\u00e9lec, 91192 Gif-Sur-Yvette, France","institution_ids":["https://openalex.org/I102197404","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2815,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.57005931,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"47","issue":"1","first_page":"111","last_page":"143"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9993000030517578,"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":0.9993000030517578,"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/T11414","display_name":"Quantum optics and atomic interactions","score":0.9991999864578247,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/combinatorics","display_name":"Combinatorics","score":0.5969979166984558},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.5618219971656799},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5406256914138794},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.537590503692627},{"id":"https://openalex.org/keywords/alpha","display_name":"Alpha (finance)","score":0.5347676873207092},{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.5325599908828735},{"id":"https://openalex.org/keywords/sigma","display_name":"Sigma","score":0.4610859751701355},{"id":"https://openalex.org/keywords/bar","display_name":"Bar (unit)","score":0.4218546450138092},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.4034527838230133},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.348807156085968},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24232029914855957},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.15742266178131104},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09118485450744629}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5969979166984558},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5618219971656799},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5406256914138794},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.537590503692627},{"id":"https://openalex.org/C64943373","wikidata":"https://www.wikidata.org/wiki/Q2651003","display_name":"Alpha (finance)","level":4,"score":0.5347676873207092},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.5325599908828735},{"id":"https://openalex.org/C2778049214","wikidata":"https://www.wikidata.org/wiki/Q7512234","display_name":"Sigma","level":2,"score":0.4610859751701355},{"id":"https://openalex.org/C188721877","wikidata":"https://www.wikidata.org/wiki/Q103510","display_name":"Bar (unit)","level":2,"score":0.4218546450138092},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.4034527838230133},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.348807156085968},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24232029914855957},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.15742266178131104},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09118485450744629},{"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},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C49453240","wikidata":"https://www.wikidata.org/wiki/Q1592163","display_name":"Construct validity","level":3,"score":0.0},{"id":"https://openalex.org/C171606756","wikidata":"https://www.wikidata.org/wiki/Q506132","display_name":"Psychometrics","level":2,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/060675988","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060675988","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:CiteSeerX.psu:10.1.1.240.95","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.240.95","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0611823v1.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-02320804v1","is_oa":false,"landing_page_url":"https://hal.science/hal-02320804","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, 2008, 47 (1), pp.111-143. &#x27E8;10.1137/060675988&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.47999998927116394,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1560583427","https://openalex.org/W1970654756","https://openalex.org/W2004953010","https://openalex.org/W2015683881","https://openalex.org/W2023024274","https://openalex.org/W2034793951","https://openalex.org/W2049723320","https://openalex.org/W2056700074","https://openalex.org/W2085768952","https://openalex.org/W2103176549"],"related_works":["https://openalex.org/W2288263127","https://openalex.org/W2029404707","https://openalex.org/W2293067204","https://openalex.org/W2091508249","https://openalex.org/W4285325679","https://openalex.org/W1928239295","https://openalex.org/W2293163042","https://openalex.org/W4282982070","https://openalex.org/W4391212601","https://openalex.org/W136513132"],"abstract_inverted_index":{"For":[0],"$\\alpha":[1],"\\in":[2],"]0,\\pi/2[$,":[3],"let":[4],"$(\\Sigma)_\\alpha$":[5],"be":[6],"the":[7,15,45,51,59,73,82,91,100,116,120,156,164,173],"control":[8,74],"system":[9],"$\\dot{x}=(F+uG)x$,":[10],"where":[11,146],"x":[12],"belongs":[13],"to":[14,56,63,170],"two-dimensional":[16],"unit":[17],"sphere":[18],"$S^2$,":[19,93],"$u\\in":[20],"[-1,1]$,":[21],"and":[22,33,38,124,143,149,158],"$F,G$":[23],"are":[24],"$3\\times3$":[25],"skew-symmetric":[26],"matrices":[27],"generating":[28],"rotations":[29],"with":[30],"perpendicular":[31],"axes":[32],"of":[34,75,99,104,172],"respective":[35],"norms":[36],"$\\cos(\\alpha)$":[37],"$\\sin(\\alpha)$.":[39],"In":[40,151],"this":[41,65],"paper,":[42],"we":[43,128,154],"study":[44],"time":[46],"optimal":[47],"synthesis":[48],"(TOS)":[49],"from":[50],"north":[52],"pole":[53,102],"$(0,0,1)^T$":[54],"associated":[55],"$(\\Sigma)_\\alpha$,":[57],"as":[58,167],"parameter":[60],"$\\alpha$":[61,168],"tends":[62,169],"zero;":[64],"problem":[66],"is":[67,84],"motivated":[68],"by":[69,86,133],"specific":[70],"issues":[71],"in":[72],"quantum":[76],"systems.":[77],"We":[78,110],"first":[79],"prove":[80],"that":[81],"TOS":[83,117,157,175],"characterized":[85],"a":[87,96,161],"\u201ctwo-snakes\u201d":[88],"configuration":[89],"on":[90,119],"whole":[92],"except":[94],"for":[95],"neighborhood":[97],"$U_\\alpha$":[98],"south":[101],"$(0,0,-1)^T$":[103],"diameter":[105],"at":[106],"most":[107],"${\\cal":[108],"O}(\\alpha)$.":[109],"next":[111],"show":[112],"that,":[113],"inside":[114,176],"$U_\\alpha$,":[115],"depends":[118],"relationship":[121],"between":[122],"$r(\\alpha):=\\pi/2\\alpha-[\\pi/2\\alpha]$":[123],"$\\alpha$.":[125],"More":[126],"precisely,":[127],"characterize":[129],"three":[130],"main":[131],"relationships":[132],"considering":[134],"sequences":[135],"$(\\alpha_k)_{k\\geq":[136],"0}$":[137],"satisfying":[138],"(a)":[139],"$r(\\alpha_k)=\\bar{r}$,":[140],"(b)":[141],"$r(\\alpha_k)=C\\alpha_k$,":[142],"(c)":[144],"$r(\\alpha_k)=0$,":[145],"$\\bar{r}\\in":[147],"(0,1)$":[148],"$C>0$.":[150],"each":[152],"case,":[153],"describe":[155],"provide,":[159],"after":[160],"suitable":[162],"rescaling,":[163],"limiting":[165],"behavior,":[166],"zero,":[171],"corresponding":[174],"$U_\\alpha$.":[177]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
