{"id":"https://openalex.org/W7140094986","doi":"https://doi.org/10.48550/arxiv.2603.19813","title":"A Spectral Perspective on Stochastic Control Barrier Functions","display_name":"A Spectral Perspective on Stochastic Control Barrier Functions","publication_year":2026,"publication_date":"2026-03-20","ids":{"openalex":"https://openalex.org/W7140094986","doi":"https://doi.org/10.48550/arxiv.2603.19813"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.19813","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.19813","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.19813","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006359565","display_name":"Inkyu Jang","orcid":"https://orcid.org/0000-0002-5107-446X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jang, Inkyu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130389576","display_name":"Chams E. Mballo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mballo, Chams E.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130338392","display_name":"Claire J. Tomlin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tomlin, Claire J.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5130403648","display_name":"H. Jin Kim","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kim, H. Jin","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":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/T10917","display_name":"Smart Grid Security and Resilience","score":0.22110000252723694,"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/T10917","display_name":"Smart Grid Security and Resilience","score":0.22110000252723694,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.20340000092983246,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.12080000340938568,"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/bounding-overwatch","display_name":"Bounding overwatch","score":0.6639999747276306},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5508000254631042},{"id":"https://openalex.org/keywords/eigenfunction","display_name":"Eigenfunction","score":0.5385000109672546},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.483599990606308},{"id":"https://openalex.org/keywords/probability-measure","display_name":"Probability measure","score":0.4246000051498413},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.40059998631477356},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.384799987077713}],"concepts":[{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.6639999747276306},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5508000254631042},{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.5385000109672546},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48579999804496765},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.483599990606308},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.4246000051498413},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4101000130176544},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.40059998631477356},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.384799987077713},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37540000677108765},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.3747999966144562},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37130001187324524},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.35190001130104065},{"id":"https://openalex.org/C170131372","wikidata":"https://www.wikidata.org/wiki/Q7617811","display_name":"Stochastic control","level":3,"score":0.336899995803833},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.3093999922275543},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.26969999074935913},{"id":"https://openalex.org/C127491075","wikidata":"https://www.wikidata.org/wiki/Q7617825","display_name":"Stochastic modelling","level":2,"score":0.26930001378059387},{"id":"https://openalex.org/C2780945871","wikidata":"https://www.wikidata.org/wiki/Q194274","display_name":"Backup","level":2,"score":0.26930001378059387},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.26339998841285706},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.2526000142097473}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.19813","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.19813","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.19813","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.19813","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Stochastic":[0],"control":[1,8],"barrier":[2],"functions":[3],"(SCBFs)":[4],"provide":[5],"a":[6,23,28,50,59,98],"safety-critical":[7,157],"framework":[9],"for":[10],"systems":[11],"subject":[12],"to":[13],"stochastic":[14,92],"disturbances":[15],"by":[16,57],"bounding":[17],"the":[18,34,39,43,63,68,71,79,91,108,113,116,120,125,141],"probability":[19,37,127],"of":[20,38,47,70,82,90,112],"remaining":[21],"within":[22],"safe":[24],"set.":[25],"However,":[26],"synthesizing":[27],"valid":[29,101],"SCBF":[30],"that":[31,66,78,105],"explicitly":[32,106],"reflects":[33],"true":[35],"safety":[36,74,88,111,126],"system,":[40],"which":[41,124,138],"is":[42,97,133,151],"most":[44],"natural":[45,99],"measure":[46],"safety,":[48],"remains":[49],"challenge.":[51],"This":[52],"paper":[53],"addresses":[54],"this":[55,83],"issue":[56],"adopting":[58],"spectral":[60],"perspective,":[61],"utilizing":[62],"linear":[64],"operator":[65,85],"governs":[67],"evolution":[69],"closed-loop":[72],"system's":[73],"probability.":[75],"We":[76],"find":[77],"dominant":[80,95,117,142],"eigenpair":[81,143],"Koopman-like":[84],"encodes":[86],"fundamental":[87],"information":[89],"system.":[93],"The":[94,149],"eigenfunction":[96],"and":[100,144],"SCBF,":[102],"with":[103],"values":[104],"quantify":[107],"relative":[109],"long-term":[110],"state,":[114],"while":[115],"eigenvalue":[118],"indicates":[119],"global":[121],"rate":[122],"at":[123],"decays.":[128],"A":[129],"practical":[130],"synthesis":[131],"algorithm":[132],"proposed,":[134],"termed":[135],"power-policy":[136],"iteration,":[137],"jointly":[139],"computes":[140],"an":[145],"optimized":[146],"backup":[147],"policy.":[148],"method":[150],"validated":[152],"using":[153],"simulation":[154],"experiments":[155],"on":[156],"dynamics":[158],"models.":[159]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-03-24T00:00:00"}