{"id":"https://openalex.org/W7225013010","doi":"https://doi.org/10.5281/zenodo.23847218","title":"Branching feedback at an uncontrollable linearisation with applications to stabilisation, the Brockett integrator, control of frequency and Hopf bifurcation","display_name":"Branching feedback at an uncontrollable linearisation with applications to stabilisation, the Brockett integrator, control of frequency and Hopf bifurcation","publication_year":2026,"publication_date":"2026-10-31","ids":{"openalex":"https://openalex.org/W7225013010","doi":"https://doi.org/10.5281/zenodo.23847218"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23847218","doi":"https://doi.org/10.5281/zenodo.23847218","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23847218","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.23847218","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5149314931","display_name":"Alex Shoshitaishvili","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Shoshitaishvili, Alex","raw_affiliation_strings":["Independent Researcher"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Independent Researcher","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5149314931"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9883000254631042,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9883000254631042,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.004699999932199717,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.0017999999690800905,"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/invariant-manifolds","display_name":"invariant manifolds","score":0.6959999799728394},{"id":"https://openalex.org/keywords/caustics","display_name":"caustics","score":0.7440000176429749},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.9539999961853027},{"id":"https://openalex.org/keywords/frequency-regulation","display_name":"frequency regulation","score":0.828000009059906},{"id":"https://openalex.org/keywords/geometric-control-theory","display_name":"geometric control","score":0.7680000066757202}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.644599974155426},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.517799973487854},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4893999993801117},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.45899999141693115},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.44269999861717224},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.41990000009536743},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4163999855518341},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.38600000739097595},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.3799000084400177},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.37439998984336853},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.35740000009536743},{"id":"https://openalex.org/C206175624","wikidata":"https://www.wikidata.org/wiki/Q595731","display_name":"Branching (polymer chemistry)","level":2,"score":0.35679998993873596},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.35600000619888306},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.3522999882698059},{"id":"https://openalex.org/C20483540","wikidata":"https://www.wikidata.org/wiki/Q4200516","display_name":"Invariant manifold","level":2,"score":0.3463999927043915},{"id":"https://openalex.org/C74774103","wikidata":"https://www.wikidata.org/wiki/Q4504202","display_name":"Center manifold","level":5,"score":0.33869999647140503},{"id":"https://openalex.org/C200917960","wikidata":"https://www.wikidata.org/wiki/Q3847057","display_name":"Singular point of a curve","level":2,"score":0.33820000290870667},{"id":"https://openalex.org/C73586568","wikidata":"https://www.wikidata.org/wiki/Q2600211","display_name":"Parameter space","level":2,"score":0.3172999918460846},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.3124000132083893},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.30720001459121704},{"id":"https://openalex.org/C138632511","wikidata":"https://www.wikidata.org/wiki/Q2478109","display_name":"Nonholonomic system","level":4,"score":0.3001999855041504},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2955000102519989},{"id":"https://openalex.org/C42357961","wikidata":"https://www.wikidata.org/wiki/Q213363","display_name":"Open set","level":2,"score":0.29260000586509705},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.29249998927116394},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.2913999855518341},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.27469998598098755},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.2646999955177307},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.25679999589920044}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23847218","doi":"https://doi.org/10.5281/zenodo.23847218","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23847218","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.23847219","doi":"https://doi.org/10.5281/zenodo.23847219","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23847219","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.23847218","doi":"https://doi.org/10.5281/zenodo.23847218","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23847218","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7225007229","https://openalex.org/W2028640318","https://openalex.org/W3142610010","https://openalex.org/W2021556551","https://openalex.org/W2077413072","https://openalex.org/W2656858829","https://openalex.org/W1487218681","https://openalex.org/W2025839351","https://openalex.org/W2147211724","https://openalex.org/W2105054131"],"abstract_inverted_index":{"At":[0],"a":[1,8,28,53,57,91,119,162,209,214,232,244,248,260,265,288],"working":[2,88],"point":[3,254],"where":[4,278],"the":[5,16,24,62,77,87,94,109,129,137,141,168,171,181,184,194,206,221,239,252,258,271,291,298],"linearisation":[6],"of":[7,64,76,128,136,143,146,165,183,196,208,220,236,251,267],"plant":[9,49],"is":[10,50,102,140,180,276,287],"uncontrollable,":[11,277],"no":[12,176,279],"smooth":[13,177,280],"feedback":[14,281],"solves":[15],"qualitative-behaviour":[17],"control":[18],"(QBC)":[19],"problem,":[20],"that":[21],"is,":[22],"makes":[23],"closed":[25],"loop":[26],"reproduce":[27],"prescribed":[29,268],"qualitative":[30],"behaviour":[31],"if":[32],"its":[33,237],"spectrum":[34],"does":[35],"not":[36,106],"contain":[37],"some":[38],"uncontrollable":[39],"eigenvalue.":[40],"We":[41],"show":[42],"what":[43],"can":[44,282],"be":[45,84],"done":[46],"instead.":[47],"The":[48,156],"coupled":[51],"to":[52,83],"reference":[54,95,158],"system":[55],"by":[56,154,256],"coupling":[58,110,160],"law":[59,111],"depending":[60],"on":[61,115,126],"states":[63],"both,":[65],"and":[66,108,148,159,205,235,264,293],"one":[67,113],"looks":[68],"for":[69,226],"an":[70],"invariant":[71],"manifold":[72],"x":[73,93,101],"=":[74,100,224],"F(z)":[75,99],"combined":[78],"system.":[79],"Uncontrollability":[80],"forces":[81],"F":[82],"singular":[85],"at":[86,213],"point.":[89],"Over":[90],"state":[92,96,130],"z":[97],"with":[98,231,243,247],"then":[103],"in":[104,193,297],"general":[105],"unique,":[107],"gives":[112],"value":[114],"each":[116],"such":[117],"z:":[118],"branching":[120],"feedback,":[121],"whose":[122],"branches":[123],"are":[124,296],"defined":[125],"regions":[127],"space":[131],"glued":[132],"together":[133],"along":[134,150],"strata":[135],"caustic,":[138],"which":[139,174],"set":[142],"critical":[144,272],"values":[145],"F,":[147],"possibly":[149],"other":[151],"submanifolds":[152],"chosen":[153],"design.":[155],"same":[157],"serve":[161],"whole":[163],"family":[164],"plants":[166],"crossing":[167],"degeneracy,":[169],"including":[170],"degenerate":[172],"plant,":[173],"has":[175],"stabiliser.":[178],"This":[179,285],"method":[182],"author's":[185],"1990":[186],"paper":[187],"(Adv.":[188],"Soviet":[189],"Math.":[190],"1),":[191],"restated":[192],"language":[195],"geometric":[197],"control.":[198],"From":[199],"it":[200],"we":[201],"recall":[202],"asymptotic":[203],"stabilisation":[204,219],"synthesis":[207,246],"stable":[210],"Andronov-Hopf":[211],"bifurcation":[212],"corank-one":[215],"degeneracy.":[216],"New":[217],"are:":[218],"model":[222],"x'":[223],"u^n":[225],"every":[227],"n":[228],">=":[229],"2":[230],"rotating":[233,257],"reference,":[234],"deformations;":[238],"nonholonomic":[240],"(Brockett)":[241],"integrator,":[242],"closed-form":[245],"rate":[249],"independent":[250],"initial":[253],"and,":[255],"branch,":[259],"continuous":[261],"time-periodic":[262],"stabiliser;":[263],"cycle":[266],"frequency":[269],"when":[270],"pair":[273],"+-i":[274],"omega_0":[275],"change":[283],"omega_0.":[284],"preprint":[286],"short":[289],"version;":[290],"proofs":[292],"further":[294],"results":[295],"companion":[299],"preprint.":[300]},"counts_by_year":[],"updated_date":"2026-11-02T09:45:03.842371","created_date":"2026-11-01T00:00:00"}