{"id":"https://openalex.org/W4404037829","doi":"https://doi.org/10.1109/allerton63246.2024.10735269","title":"Generalized Barrier Functions: Integral Conditions &amp; Recurrent Relaxations","display_name":"Generalized Barrier Functions: Integral Conditions &amp; Recurrent Relaxations","publication_year":2024,"publication_date":"2024-09-24","ids":{"openalex":"https://openalex.org/W4404037829","doi":"https://doi.org/10.1109/allerton63246.2024.10735269"},"language":"en","primary_location":{"id":"doi:10.1109/allerton63246.2024.10735269","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/allerton63246.2024.10735269","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2024 60th Annual Allerton Conference on Communication, Control, and Computing","raw_type":"proceedings-article"},"type":"conference-paper","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/A5102010946","display_name":"Yue Shen","orcid":"https://orcid.org/0009-0007-8117-0915"},"institutions":[{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yue Shen","raw_affiliation_strings":["Johns Hopkins University,The Department of Electrical and Computer Engineering,Baltimore,MD,USA,21218"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Johns Hopkins University,The Department of Electrical and Computer Engineering,Baltimore,MD,USA,21218","institution_ids":["https://openalex.org/I145311948"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039914913","display_name":"Hussein Sibai","orcid":"https://orcid.org/0000-0002-6053-1001"},"institutions":[{"id":"https://openalex.org/I204465549","display_name":"Washington University in St. Louis","ror":"https://ror.org/01yc7t268","country_code":"US","type":"education","lineage":["https://openalex.org/I204465549"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hussein Sibai","raw_affiliation_strings":["Washington University in St. Louis,Hussein Sibai is with the Department of Computer Science and Engineering,St. Louis,MO,USA,63130"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Washington University in St. Louis,Hussein Sibai is with the Department of Computer Science and Engineering,St. Louis,MO,USA,63130","institution_ids":["https://openalex.org/I204465549"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032910355","display_name":"Enrique Mallada","orcid":"https://orcid.org/0000-0003-1568-1833"},"institutions":[{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Enrique Mallada","raw_affiliation_strings":["Johns Hopkins University,The Department of Electrical and Computer Engineering,Baltimore,MD,USA,21218"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Johns Hopkins University,The Department of Electrical and Computer Engineering,Baltimore,MD,USA,21218","institution_ids":["https://openalex.org/I145311948"]}]}],"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":0.45283019,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.12200000137090683,"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"}},"topics":[{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.12200000137090683,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.11020000278949738,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.10350000113248825,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/integral-equation","display_name":"Integral equation","score":0.45903563499450684},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38790497183799744},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38610589504241943},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3432449996471405},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29320186376571655}],"concepts":[{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.45903563499450684},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38790497183799744},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38610589504241943},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3432449996471405},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29320186376571655}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/allerton63246.2024.10735269","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/allerton63246.2024.10735269","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2024 60th Annual Allerton Conference on Communication, Control, and Computing","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4486216286","display_name":"CAREER: Control, Optimization, and Market Design for Efficient and Reliable Integration of Renewable Energy Sources in Electric Power Systems","funder_award_id":"1752362","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1563147540","https://openalex.org/W1607353007","https://openalex.org/W1972149633","https://openalex.org/W2033118636","https://openalex.org/W2041076275","https://openalex.org/W2050383062","https://openalex.org/W2099354898","https://openalex.org/W2106850246","https://openalex.org/W2129729773","https://openalex.org/W2151489480","https://openalex.org/W2171505650","https://openalex.org/W2560504659","https://openalex.org/W2789826932","https://openalex.org/W2798791976","https://openalex.org/W2968945909","https://openalex.org/W3035313359","https://openalex.org/W3120116240","https://openalex.org/W3168522732","https://openalex.org/W3195647294","https://openalex.org/W4292249799","https://openalex.org/W4315472354","https://openalex.org/W4382203285","https://openalex.org/W4386586165","https://openalex.org/W4391020211","https://openalex.org/W4396571409","https://openalex.org/W6639175102"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027"],"abstract_inverted_index":{"Barrier":[0],"functions":[1],"constitute":[2],"an":[3],"effective":[4],"tool":[5],"for":[6,49],"assessing":[7],"and":[8,163],"enforcing":[9],"safety-critical":[10],"constraints":[11],"on":[12],"dynamical":[13],"systems.":[14],"To":[15],"this":[16,66,72,87],"end,":[17],"one":[18],"is":[19,131],"required":[20],"to":[21,70,102,142,173],"find":[22],"a":[23,26,46,62,76,122,153],"function$h$that":[24,52],"satisfies":[25,53],"Lyapunov-like":[27],"differential":[28,55,104],"condition,":[29],"thereby":[30],"ensuring":[31],"the":[32,51,82,103,115,139,165,168,175],"invariance":[33,117],"of":[34,167],"its":[35],"zero":[36],"super-level":[37,169],"set$h\\geq":[38,170],"0$,":[39],"This":[40],"methodology,":[41],"however,":[42],"does":[43],"not":[44],"prescribe":[45],"general":[47],"method":[48],"finding":[50],"such":[54],"conditions,":[56,152],"which,":[57],"in":[58,88,138],"general,":[59],"can":[60,158],"be":[61],"daunting":[63],"task.":[64],"In":[65],"paper,":[67],"we":[68,92,112],"seek":[69],"overcome":[71],"limitation":[73],"by":[74],"developing":[75],"generalized":[77],"barrier":[78,95],"condition":[79,162],"that":[80,97,136,164],"makes":[81],"search":[83],"for$h$easier.":[84],"We":[85,147],"do":[86],"two":[89],"steps.":[90],"First,":[91],"develop":[93],"integral":[94],"conditions":[96],"reveal":[98],"equivalent":[99],"asymptotic":[100],"behavior":[101],"ones,":[105],"but":[106],"without":[107],"requiring":[108],"differentiability":[109],"of$h$.":[110],"Subsequently,":[111],"further":[113],"replace":[114],"stringent":[116],"requirement":[118],"on$h":[119],"\\geq":[120],"0$with":[121],"more":[123],"flexible":[124],"concept":[125],"known":[126],"as":[127],"recurrence.":[128],"A":[129],"set":[130,140],"($\\tau$-)recurrent":[132],"if":[133],"every":[134],"trajectory":[135],"starts":[137],"returns":[141],"it":[143],"(within$\\tau$seconds)":[144],"infinitely":[145],"often.":[146],"show":[148],"that,":[149],"under":[150],"mild":[151],"simple":[154],"sign":[155],"distance":[156],"function":[157],"satisfy":[159],"our":[160],"relaxed":[161],"($\\tau$-)recurrence":[166],"0$is":[171],"sufficient":[172],"guarantee":[174],"system's":[176],"safety.":[177]},"counts_by_year":[],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2025-10-10T00:00:00"}
