{"id":"https://openalex.org/W7138200490","doi":"https://doi.org/10.48550/arxiv.2603.13509","title":"Verification and Forward Invariance of Control Barrier Functions for Differential-Algebraic Systems","display_name":"Verification and Forward Invariance of Control Barrier Functions for Differential-Algebraic Systems","publication_year":2026,"publication_date":"2026-03-13","ids":{"openalex":"https://openalex.org/W7138200490","doi":"https://doi.org/10.48550/arxiv.2603.13509"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.13509","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.13509","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.13509","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5129732337","display_name":"Hongchao Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Zhang, Hongchao","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5129662401","display_name":"Mohamad H. Kazma","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kazma, Mohamad H.","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5129652647","display_name":"Meiyi Ma","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ma, Meiyi","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067901159","display_name":"Taylor T. Johnson","orcid":"https://orcid.org/0000-0001-8021-9923"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Johnson, Taylor T.","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5129742087","display_name":"Ahmad F. Taha","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Taha, Ahmad F.","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5129732337"],"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/T10142","display_name":"Formal Methods in Verification","score":0.6657000184059143,"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"}},"topics":[{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.6657000184059143,"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"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.061400000005960464,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10917","display_name":"Smart Grid Security and Resilience","score":0.05510000139474869,"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/correctness","display_name":"Correctness","score":0.7350000143051147},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.5304999947547913},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.43299999833106995},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4327999949455261},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.40220001339912415},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.40119999647140503},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.3824000060558319},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.37529999017715454},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3677999973297119},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.3425999879837036}],"concepts":[{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.7350000143051147},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5304999947547913},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.43299999833106995},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4327999949455261},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43209999799728394},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.40220001339912415},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.40119999647140503},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3824000060558319},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.37529999017715454},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37040001153945923},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3677999973297119},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36079999804496765},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.3425999879837036},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.34040001034736633},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.33169999718666077},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.3278999924659729},{"id":"https://openalex.org/C2777798563","wikidata":"https://www.wikidata.org/wiki/Q7603916","display_name":"State vector","level":2,"score":0.3273000121116638},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.3082999885082245},{"id":"https://openalex.org/C116672817","wikidata":"https://www.wikidata.org/wiki/Q1454986","display_name":"Physical system","level":2,"score":0.30820000171661377},{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.3077000081539154},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.3034999966621399},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.3034000098705292},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.3027999997138977},{"id":"https://openalex.org/C164155591","wikidata":"https://www.wikidata.org/wiki/Q2067766","display_name":"Satisfiability modulo theories","level":2,"score":0.2985000014305115},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.2935999929904938},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2775999903678894},{"id":"https://openalex.org/C2778449969","wikidata":"https://www.wikidata.org/wiki/Q130760","display_name":"Turbine","level":2,"score":0.2766999900341034},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.27570000290870667},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2694000005722046},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.26499998569488525},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.262800008058548},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.2572999894618988},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.25600001215934753}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.13509","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.13509","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.13509","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.13509","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[{"display_name":"Life in Land","score":0.42857784032821655,"id":"https://metadata.un.org/sdg/15"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Differential-algebraic":[0],"equations":[1],"(DAEs)":[2],"arise":[3],"in":[4],"power":[5],"networks,":[6],"chemical":[7],"processes,":[8],"and":[9,71,103,118,124,139,157],"multibody":[10],"systems,":[11,131],"where":[12],"algebraic":[13,32,101],"constraints":[14,33,102],"encode":[15],"physical":[16],"conservation":[17],"laws.":[18],"The":[19,150],"safety":[20,45],"of":[21,96,126],"such":[22],"systems":[23],"is":[24,29,114,152],"critical,":[25],"yet":[26],"safe":[27,97],"control":[28],"challenging":[30],"because":[31],"restrict":[34],"allowable":[35],"state":[36],"trajectories.":[37],"Control":[38],"barrier":[39],"functions":[40],"(CBFs)":[41],"provide":[42],"computationally":[43],"efficient":[44],"filters":[46],"for":[47,121,137,148],"ordinary":[48],"differential":[49],"equation":[50],"(ODE)":[51],"systems.":[52,160],"However,":[53],"existing":[54],"CBF":[55,69],"methods":[56],"are":[57,134,146],"not":[58],"directly":[59],"applicable":[60],"to":[61,64,107],"DAEs":[62],"due":[63],"potential":[65],"conflicts":[66],"between":[67],"the":[68,72,82,105],"condition":[70],"constraint":[73],"manifold.":[74],"This":[75],"paper":[76],"introduces":[77],"DAE-aware":[78,127],"CBFs":[79],"that":[80,92],"incorporate":[81],"differential-algebraic":[83],"structure":[84],"through":[85],"projected":[86],"vector":[87],"fields.":[88],"We":[89],"derive":[90],"conditions":[91,120],"ensure":[93],"forward":[94],"invariance":[95],"sets":[98],"while":[99,136],"preserving":[100],"extend":[104],"framework":[106,113],"higher-index":[108],"DAEs.":[109],"A":[110],"systematic":[111],"verification":[112],"developed,":[115],"establishing":[116],"necessary":[117],"sufficient":[119],"geometric":[122],"correctness":[123],"feasibility":[125],"CBFs.":[128],"For":[129],"polynomial":[130],"sum-of-squares":[132],"certificates":[133],"provided,":[135],"nonpolynomial":[138],"neural":[140],"network":[141],"candidates,":[142],"satisfiability":[143],"modulo":[144],"theories":[145],"used":[147],"falsification.":[149],"approach":[151],"validated":[153],"on":[154],"wind":[155],"turbine":[156],"flexible-link":[158],"manipulator":[159]},"counts_by_year":[],"updated_date":"2026-03-18T06:31:55.123368","created_date":"2026-03-18T00:00:00"}
