{"id":"https://openalex.org/W2957957932","doi":"https://doi.org/10.1080/00207179.2019.1643910","title":"Bracketing backward reach sets of a dynamical system","display_name":"Bracketing backward reach sets of a dynamical system","publication_year":2019,"publication_date":"2019-07-15","ids":{"openalex":"https://openalex.org/W2957957932","doi":"https://doi.org/10.1080/00207179.2019.1643910","mag":"2957957932"},"language":"en","primary_location":{"id":"doi:10.1080/00207179.2019.1643910","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207179.2019.1643910","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"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 Control","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/A5006606211","display_name":"Thomas Le M\u00e9zo","orcid":"https://orcid.org/0000-0001-7165-4499"},"institutions":[{"id":"https://openalex.org/I201181511","display_name":"\u00c9cole Nationale Sup\u00e9rieure de Techniques Avanc\u00e9es","ror":"https://ror.org/0309cs235","country_code":"FR","type":"education","lineage":["https://openalex.org/I201181511","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I4210148559","display_name":"\u00c9cole nationale sup\u00e9rieure de techniques avanc\u00e9es Bretagne","ror":"https://ror.org/059n54003","country_code":"FR","type":"education","lineage":["https://openalex.org/I201181511","https://openalex.org/I4210145102","https://openalex.org/I4210148559"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Thomas Le M\u00e9zo","raw_affiliation_strings":["ENSTA-Bretagne, LabSTICC UMR CNR 6285, Brest, France","\u00c9cole Nationale Sup\u00e9rieure de Techniques Avanc\u00e9es Bretagne","Lab-STICC_ENSTAB_CID_PRASYS"],"raw_orcid":"https://orcid.org/0000-0001-7165-4499","affiliations":[{"raw_affiliation_string":"ENSTA-Bretagne, LabSTICC UMR CNR 6285, Brest, France","institution_ids":["https://openalex.org/I4210148559"]},{"raw_affiliation_string":"\u00c9cole Nationale Sup\u00e9rieure de Techniques Avanc\u00e9es Bretagne","institution_ids":["https://openalex.org/I4210148559","https://openalex.org/I201181511"]},{"raw_affiliation_string":"Lab-STICC_ENSTAB_CID_PRASYS","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053641817","display_name":"Luc Jaulin","orcid":"https://orcid.org/0000-0002-0938-0615"},"institutions":[{"id":"https://openalex.org/I201181511","display_name":"\u00c9cole Nationale Sup\u00e9rieure de Techniques Avanc\u00e9es","ror":"https://ror.org/0309cs235","country_code":"FR","type":"education","lineage":["https://openalex.org/I201181511","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I4210148559","display_name":"\u00c9cole nationale sup\u00e9rieure de techniques avanc\u00e9es Bretagne","ror":"https://ror.org/059n54003","country_code":"FR","type":"education","lineage":["https://openalex.org/I201181511","https://openalex.org/I4210145102","https://openalex.org/I4210148559"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Luc Jaulin","raw_affiliation_strings":["ENSTA-Bretagne, LabSTICC UMR CNR 6285, Brest, France","\u00c9cole Nationale Sup\u00e9rieure de Techniques Avanc\u00e9es Bretagne","Lab-STICC_ENSTAB_CID_PRASYS"],"raw_orcid":"https://orcid.org/0000-0002-0938-0615","affiliations":[{"raw_affiliation_string":"ENSTA-Bretagne, LabSTICC UMR CNR 6285, Brest, France","institution_ids":["https://openalex.org/I4210148559"]},{"raw_affiliation_string":"\u00c9cole Nationale Sup\u00e9rieure de Techniques Avanc\u00e9es Bretagne","institution_ids":["https://openalex.org/I4210148559","https://openalex.org/I201181511"]},{"raw_affiliation_string":"Lab-STICC_ENSTAB_CID_PRASYS","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027610616","display_name":"Beno\u00eet Zerr","orcid":"https://orcid.org/0000-0002-0148-1374"},"institutions":[{"id":"https://openalex.org/I201181511","display_name":"\u00c9cole Nationale Sup\u00e9rieure de Techniques Avanc\u00e9es","ror":"https://ror.org/0309cs235","country_code":"FR","type":"education","lineage":["https://openalex.org/I201181511","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I4210148559","display_name":"\u00c9cole nationale sup\u00e9rieure de techniques avanc\u00e9es Bretagne","ror":"https://ror.org/059n54003","country_code":"FR","type":"education","lineage":["https://openalex.org/I201181511","https://openalex.org/I4210145102","https://openalex.org/I4210148559"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Beno\u00eet Zerr","raw_affiliation_strings":["ENSTA-Bretagne, LabSTICC UMR CNR 6285, Brest, France","Lab-STICC_ENSTAB_CID_PRASYS","\u00c9cole Nationale Sup\u00e9rieure de Techniques Avanc\u00e9es Bretagne"],"raw_orcid":"https://orcid.org/0000-0002-0148-1374","affiliations":[{"raw_affiliation_string":"ENSTA-Bretagne, LabSTICC UMR CNR 6285, Brest, France","institution_ids":["https://openalex.org/I4210148559"]},{"raw_affiliation_string":"Lab-STICC_ENSTAB_CID_PRASYS","institution_ids":[]},{"raw_affiliation_string":"\u00c9cole Nationale Sup\u00e9rieure de Techniques Avanc\u00e9es Bretagne","institution_ids":["https://openalex.org/I4210148559","https://openalex.org/I201181511"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5006606211"],"corresponding_institution_ids":["https://openalex.org/I201181511","https://openalex.org/I4210148559"],"apc_list":null,"apc_paid":null,"fwci":0.4926,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.6435203,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"93","issue":"11","first_page":"2528","last_page":"2540"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.993399977684021,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.993399977684021,"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/T11236","display_name":"Control Systems and Identification","score":0.9732999801635742,"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9711999893188477,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bracketing","display_name":"Bracketing (phenomenology)","score":0.9398359060287476},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.6361200213432312},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5994899272918701},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.5716031193733215},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5423880219459534},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.5204346776008606},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5045367479324341},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4806886315345764},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.46679621934890747},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.46634548902511597},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4572529196739197},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4229433238506317},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.38532090187072754},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33135759830474854},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.171735018491745},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.16038620471954346},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08936390280723572},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06422543525695801}],"concepts":[{"id":"https://openalex.org/C102944935","wikidata":"https://www.wikidata.org/wiki/Q4953701","display_name":"Bracketing (phenomenology)","level":2,"score":0.9398359060287476},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6361200213432312},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5994899272918701},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.5716031193733215},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5423880219459534},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.5204346776008606},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5045367479324341},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4806886315345764},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.46679621934890747},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.46634548902511597},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4572529196739197},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4229433238506317},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38532090187072754},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33135759830474854},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.171735018491745},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.16038620471954346},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08936390280723572},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06422543525695801},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00207179.2019.1643910","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207179.2019.1643910","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"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 Control","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-02190303v1","is_oa":false,"landing_page_url":"https://hal.science/hal-02190303","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":"International Journal of Control, 2020, 93 (11), pp.2528-2540. &#x27E8;10.1080/00207179.2019.1643910&#x27E9;","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8584749347","display_name":"Intervals and Contractors for Dynamical Systems","funder_award_id":"ANR-16-CE33-0024","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":55,"referenced_works":["https://openalex.org/W86892992","https://openalex.org/W296311487","https://openalex.org/W1502028089","https://openalex.org/W1504204411","https://openalex.org/W1531018690","https://openalex.org/W1554237731","https://openalex.org/W1574960890","https://openalex.org/W1577258119","https://openalex.org/W1582464544","https://openalex.org/W1592793563","https://openalex.org/W1598855039","https://openalex.org/W1604870856","https://openalex.org/W1792923791","https://openalex.org/W1880805667","https://openalex.org/W1928417259","https://openalex.org/W1938260438","https://openalex.org/W1969306316","https://openalex.org/W1994786880","https://openalex.org/W1999497797","https://openalex.org/W2039295495","https://openalex.org/W2043100293","https://openalex.org/W2045814149","https://openalex.org/W2046497103","https://openalex.org/W2050170725","https://openalex.org/W2073733903","https://openalex.org/W2074020819","https://openalex.org/W2074498173","https://openalex.org/W2083862837","https://openalex.org/W2090967418","https://openalex.org/W2099084425","https://openalex.org/W2102158516","https://openalex.org/W2103121907","https://openalex.org/W2109569369","https://openalex.org/W2112948245","https://openalex.org/W2118341469","https://openalex.org/W2134675215","https://openalex.org/W2135432705","https://openalex.org/W2136919283","https://openalex.org/W2139132599","https://openalex.org/W2139405251","https://openalex.org/W2154679417","https://openalex.org/W2163182586","https://openalex.org/W2197995027","https://openalex.org/W2249393294","https://openalex.org/W2313274380","https://openalex.org/W2329087169","https://openalex.org/W2467485666","https://openalex.org/W2507290609","https://openalex.org/W2616158676","https://openalex.org/W2744320624","https://openalex.org/W2912589708","https://openalex.org/W2963655224","https://openalex.org/W2963669205","https://openalex.org/W4206318793","https://openalex.org/W4298290503"],"related_works":["https://openalex.org/W4250831671","https://openalex.org/W2230606337","https://openalex.org/W2089869689","https://openalex.org/W4388681848","https://openalex.org/W2078952919","https://openalex.org/W2945666329","https://openalex.org/W2617651062","https://openalex.org/W2330535098","https://openalex.org/W2377513064","https://openalex.org/W2952544653"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,79],"present":[4],"a":[5,26,41,65,77,85,90,95,104],"new":[6],"method":[7,34,86,117],"for":[8,94,113],"bracketing":[9],"(i.e.":[10],"characterising":[11],"from":[12,15],"inside":[13],"and":[14,108],"outside)":[16],"backward":[17,91],"reach":[18,92],"set":[19,66,93],"of":[20,25,32,52,67,73,98,103],"the":[21,33,38,45,48,53,74],"target":[22],"region":[23],"T":[24],"continuous-time":[27],"dynamical":[28],"system.":[29,54,115],"The":[30,55,116],"principle":[31],"is":[35,57,64],"to":[36,83,88],"formalise":[37],"problem":[39],"as":[40],"constraint":[42],"network,":[43],"where":[44],"variables":[46],"are":[47],"trajectories":[49],"(or":[50],"paths)":[51],"resolution":[56],"made":[58],"possible":[59],"by":[60],"using":[61],"mazes":[62],"which":[63],"paths":[68],"that":[69],"contain":[70],"all":[71],"solutions":[72],"problem.":[75],"As":[76],"result,":[78],"will":[80,118],"be":[81,119],"able":[82,87],"derive":[84],"compute":[89],"huge":[96],"class":[97],"systems":[99],"without":[100,109],"any":[101,111],"knowledge":[102],"parametric":[105],"Lyapunov":[106],"function":[107],"assuming":[110],"linearity":[112],"our":[114],"illustrated":[120],"in":[121],"several":[122],"examples.":[123]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}
