{"id":"https://openalex.org/W7214116205","doi":"https://doi.org/10.48550/arxiv.2609.25747","title":"On the optimal control of entry-exit phenomena in planar fast-slow dynamical systems","display_name":"On the optimal control of entry-exit phenomena in planar fast-slow dynamical systems","publication_year":2026,"publication_date":"2026-09-22","ids":{"openalex":"https://openalex.org/W7214116205","doi":"https://doi.org/10.48550/arxiv.2609.25747"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.25747","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.25747","pdf_url":"https://arxiv.org/pdf/2609.25747","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,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.25747","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5119241538","display_name":"Jacopo Borsotti","orcid":"https://orcid.org/0009-0006-3872-5818","observed_orcids":["https://orcid.org/0009-0006-3872-5818"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Borsotti, Jacopo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5148276649","display_name":"Christian Kuehn","orcid":"https://orcid.org/0000-0002-7063-6173","observed_orcids":["https://orcid.org/0000-0002-7063-6173"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kuehn, Christian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5055476133","display_name":"Mattia Sensi","orcid":"https://orcid.org/0000-0002-6631-0242","observed_orcids":["https://orcid.org/0000-0002-6631-0242"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sensi, Mattia","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Singular Perturbation, Asymptotics and Difference Schemes","score":0.9667999744415283,"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"}},"topics":[{"id":"https://openalex.org/T12727","display_name":"Singular Perturbation, Asymptotics and Difference Schemes","score":0.9667999744415283,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.0052999998442828655,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.004399999976158142,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/optimal-control","display_name":"optimal control","score":0.949999988079071},{"id":"https://openalex.org/keywords/geometric-singular-perturbation-theory","display_name":"geometric singular perturbation theory","score":0.9039999842643738},{"id":"https://openalex.org/keywords/time-optimal-control","display_name":"time-optimal control","score":0.9850000143051147},{"id":"https://openalex.org/keywords/planar-systems","display_name":"planar systems","score":0.7319999933242798},{"id":"https://openalex.org/keywords/non-autonomous-dynamics","display_name":"non-autonomous dynamics","score":0.6610000133514404},{"id":"https://openalex.org/keywords/limit-cycles","display_name":"limit cycles","score":0.6430000066757202},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.8510000109672546},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"dynamic programming","score":0.9580000042915344}],"concepts":[{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.7660999894142151},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6503000259399414},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.6333000063896179},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.6014999747276306},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.58160001039505},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.5232999920845032},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5113000273704529},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.4300000071525574},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.42419999837875366},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.36899998784065247},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35499998927116394},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.35280001163482666},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.31279999017715454},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.3125},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.3109000027179718},{"id":"https://openalex.org/C114275822","wikidata":"https://www.wikidata.org/wiki/Q621512","display_name":"Linear dynamical system","level":3,"score":0.30799999833106995},{"id":"https://openalex.org/C77405623","wikidata":"https://www.wikidata.org/wiki/Q598451","display_name":"System dynamics","level":2,"score":0.3028999865055084},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.30250000953674316},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2896000146865845},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.2849000096321106},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.26109999418258667},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2549000084400177}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.25747","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.25747","pdf_url":"https://arxiv.org/pdf/2609.25747","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,"listed_in":[],"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":"doi:10.48550/arxiv.2609.25747","doi":"https://doi.org/10.48550/arxiv.2609.25747","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.25747","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,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.25747","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.25747","pdf_url":"https://arxiv.org/pdf/2609.25747","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,"listed_in":[],"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":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320334080","display_name":"Gruppo Nazionale per la Fisica Matematica","ror":"https://ror.org/01d6bq278"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214116205.pdf","grobid_xml":"https://content.openalex.org/works/W7214116205.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W420509224","https://openalex.org/W1515224583","https://openalex.org/W1548148540","https://openalex.org/W1971039616","https://openalex.org/W1980516134","https://openalex.org/W2014157641","https://openalex.org/W2016767879","https://openalex.org/W2062272038","https://openalex.org/W2093803812","https://openalex.org/W2131599387","https://openalex.org/W2251815740","https://openalex.org/W2253503060","https://openalex.org/W2336126067","https://openalex.org/W2626466676","https://openalex.org/W2967677276","https://openalex.org/W2989795695","https://openalex.org/W2994097525","https://openalex.org/W3004297054","https://openalex.org/W3008606610","https://openalex.org/W3046188513","https://openalex.org/W3095708272","https://openalex.org/W3176541892","https://openalex.org/W4318069124","https://openalex.org/W4383263843","https://openalex.org/W4385753505","https://openalex.org/W4385920262","https://openalex.org/W4394612431","https://openalex.org/W4399376522","https://openalex.org/W4400660670","https://openalex.org/W4401481062","https://openalex.org/W4402601496","https://openalex.org/W4405840465","https://openalex.org/W4406473328","https://openalex.org/W4407011739","https://openalex.org/W4413040361","https://openalex.org/W4415160688","https://openalex.org/W7164004156","https://openalex.org/W7165379020","https://openalex.org/W7204820654"],"related_works":["https://openalex.org/W1993859730","https://openalex.org/W2006351578","https://openalex.org/W2019426461","https://openalex.org/W1970679191","https://openalex.org/W1639699","https://openalex.org/W2797767579","https://openalex.org/W2024402984","https://openalex.org/W2101019468","https://openalex.org/W2591905591","https://openalex.org/W2165717547"],"abstract_inverted_index":{"We":[0,56],"study":[1],"a":[2,53,61,68,74,112,167,204],"geometric":[3],"singular":[4],"perturbation":[5],"theory":[6],"(GSPT)":[7],"approach":[8,148,214],"to":[9,23,51,60,85,105,124,215],"optimal":[10,41,103,145,194],"control":[11,30,42,80,106,195],"problems":[12,43],"involving":[13],"entry-exit":[14,71,96,135],"phenomena":[15],"in":[16,166,176,203],"planar":[17,218],"fast-slow":[18,63,219],"dynamical":[19,220],"systems.":[20,221],"In":[21,191],"contrast":[22],"previous":[24],"work,":[25],"we":[26,38,45,92,100,116,132,139,158,210],"assume":[27],"that":[28,160,201],"the":[29,34,49,79,87,102,126,141,170,193],"acts":[31],"only":[32],"on":[33,183],"slow":[35],"dynamics":[36,81],"and":[37,82,99,138,154],"consider":[39],"minimum-time":[40],"(i.e.,":[44],"aim":[46],"at":[47],"minimizing":[48],"time":[50],"reach":[52,125],"certain":[54],"target).":[55],"apply":[57],"this":[58,212],"method":[59],"simplified":[62],"toy":[64],"model,":[65],"characterized":[66],"by":[67,109],"repetition":[69],"of":[70,78,143,152,207],"processes,":[72],"enabling":[73],"transparent":[75],"analytical":[76,189],"exploration":[77],"allowing":[83],"us":[84],"derive":[86,101],"key":[88],"results":[89],"explicitly.":[90],"First,":[91],"analyze":[93],"each":[94],"non-autonomous":[95],"phenomenon":[97],"separately,":[98],"way":[104,168],"them.":[107],"Second,":[108],"artificially":[110],"generating":[111],"stable":[113],"limit":[114],"cycle,":[115],"determine":[117],"under":[118,129],"which":[119],"conditions":[120],"it":[121],"is":[122,196],"possible":[123],"target.":[127],"Finally,":[128],"such":[130,184],"conditions,":[131],"combine":[133],"all":[134],"processes":[136],"together":[137],"demonstrate":[140],"existence":[142],"an":[144,199],"control.":[146],"Our":[147],"mainly":[149],"exploits":[150],"techniques":[151],"GSPT":[153],"dynamic":[155],"programming.":[156],"Indeed,":[157],"show":[159],"our":[161,188],"problem":[162],"can":[163],"be":[164],"formulated":[165],"resembling":[169],"Bellman":[171],"equation,":[172],"even":[173],"though":[174],"not":[175],"its":[177],"standard":[178],"setting.":[179],"Numerical":[180],"simulations,":[181],"built":[182],"Bellman-like":[185],"formulation,":[186],"illustrate":[187],"results.":[190],"particular,":[192],"derived":[197],"with":[198],"algorithm":[200],"converges":[202],"finite":[205],"number":[206],"steps.":[208],"Lastly,":[209],"extend":[211],"novel":[213],"more":[216],"complex":[217]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-24T00:00:00"}