{"id":"https://openalex.org/W7204277461","doi":"https://doi.org/10.48550/arxiv.2608.24598","title":"Comparison Invariants for Verifying Control Invariance","display_name":"Comparison Invariants for Verifying Control Invariance","publication_year":2026,"publication_date":"2026-08-25","ids":{"openalex":"https://openalex.org/W7204277461","doi":"https://doi.org/10.48550/arxiv.2608.24598"},"language":null,"primary_location":{"id":"pmh:oai:arXiv.org:2608.24598","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.24598","pdf_url":"https://arxiv.org/pdf/2608.24598","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.24598","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5093618438","display_name":"Promit Panja","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]},{"id":"https://openalex.org/I70886390","display_name":"Karlsruhe University of Applied Sciences","ror":"https://ror.org/01c0m1t63","country_code":"DE","type":"education","lineage":["https://openalex.org/I70886390"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Panja, Promit","raw_affiliation_strings":["Department of Informatics , Karlsruhe Institute of Technology , Karlsruhe , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Informatics , Karlsruhe Institute of Technology , Karlsruhe , Germany","institution_ids":["https://openalex.org/I102335020","https://openalex.org/I70886390"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080481427","display_name":"Andr\u00e9 Platzer","orcid":"https://orcid.org/0000-0001-7238-5710","observed_orcids":["https://orcid.org/0000-0001-7238-5710"]},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]},{"id":"https://openalex.org/I70886390","display_name":"Karlsruhe University of Applied Sciences","ror":"https://ror.org/01c0m1t63","country_code":"DE","type":"education","lineage":["https://openalex.org/I70886390"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Platzer, Andr\u00e9","raw_affiliation_strings":["Department of Informatics , Karlsruhe Institute of Technology , Karlsruhe , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Informatics , Karlsruhe Institute of Technology , Karlsruhe , Germany","institution_ids":["https://openalex.org/I102335020","https://openalex.org/I70886390"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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":0.9961000084877014,"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":0.9961000084877014,"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/T10126","display_name":"Logic, programming, and type systems","score":0.003100000089034438,"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/T10791","display_name":"Advanced Control Systems Optimization","score":9.999999747378752e-05,"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/differential-dynamic-logic","display_name":"differential dynamic logic","score":0.9210000038146973},{"id":"https://openalex.org/keywords/comparison-principle","display_name":"comparison principle","score":0.8360000252723694},{"id":"https://openalex.org/keywords/control-barrier-functions","display_name":"control barrier functions","score":0.8650000095367432},{"id":"https://openalex.org/keywords/lie-derivative","display_name":"Lie derivative","score":0.6800000071525574},{"id":"https://openalex.org/keywords/safety-verification","display_name":"safety verification","score":0.7559999823570251},{"id":"https://openalex.org/keywords/differential-invariants","display_name":"differential invariants","score":0.9959999918937683},{"id":"https://openalex.org/keywords/proof-rules","display_name":"proof rules","score":0.6959999799728394},{"id":"https://openalex.org/keywords/safety-critical-control","display_name":"safety-critical control","score":0.6970000267028809},{"id":"https://openalex.org/keywords/decidability","display_name":"decidability","score":0.5360000133514404}],"concepts":[{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.7044000029563904},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.682200014591217},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6173999905586243},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5497999787330627},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5131999850273132},{"id":"https://openalex.org/C70834904","wikidata":"https://www.wikidata.org/wiki/Q1054638","display_name":"Differential inclusion","level":2,"score":0.49709999561309814},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.47130000591278076},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.45980000495910645},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4507000148296356},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.43050000071525574},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.391400009393692},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.37700000405311584},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36059999465942383},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3278000056743622},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.31529998779296875},{"id":"https://openalex.org/C125773388","wikidata":"https://www.wikidata.org/wiki/Q792542","display_name":"Axiomatic system","level":3,"score":0.31380000710487366},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.3125999867916107},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.31209999322891235},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.30379998683929443},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.30000001192092896},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2946000099182129},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.2879999876022339},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.2856000065803528},{"id":"https://openalex.org/C39920170","wikidata":"https://www.wikidata.org/wiki/Q693083","display_name":"Soundness","level":2,"score":0.28459998965263367},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.2718000113964081},{"id":"https://openalex.org/C65880906","wikidata":"https://www.wikidata.org/wiki/Q1771121","display_name":"Sequent calculus","level":3,"score":0.2669000029563904},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26159998774528503},{"id":"https://openalex.org/C111498074","wikidata":"https://www.wikidata.org/wiki/Q173326","display_name":"Formal verification","level":2,"score":0.25780001282691956},{"id":"https://openalex.org/C14158598","wikidata":"https://www.wikidata.org/wiki/Q853831","display_name":"Lebesgue integration","level":2,"score":0.2524000108242035}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.24598","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.24598","pdf_url":"https://arxiv.org/pdf/2608.24598","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.2608.24598","doi":"https://doi.org/10.48550/arxiv.2608.24598","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.24598","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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.24598","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.24598","pdf_url":"https://arxiv.org/pdf/2608.24598","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":[],"sustainable_development_goals_aurora":[{"score":0.4429100751876831,"display_name":"Peace, justice, and strong institutions","id":"https://metadata.un.org/sdg/16"}],"study_designs":[],"awards":[{"id":"https://openalex.org/G2423332075","display_name":null,"funder_award_id":"SFB1608","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G7230842961","display_name":"SFB 1608: Konsistenz in der sichtenbasierten Entwicklung CyberPhysikalischer Systeme","funder_award_id":"501798263","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204277461.pdf","grobid_xml":"https://content.openalex.org/works/W7204277461.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Control":[0],"invariance":[1,59,111],"validates":[2],"that":[3,10,34,58,165],"dynamical":[4],"systems":[5],"have":[6],"a":[7,12,21,48,54,113,121,153,168],"control":[8,38,110,141,148],"input":[9],"preserves":[11],"given":[13],"property":[14],"at":[15],"all":[16],"times.":[17],"This":[18,70,159],"paper":[19],"introduces":[20],"set":[22,170],"of":[23,37,50,80,109,124,130,156,163,171,180],"sound":[24,97],"axioms":[25,98],"and":[26,43,96,99,207],"proof":[27,100,172],"rules":[28,101,175],"in":[29,68,134,146],"differential":[30,51,74,208],"dynamic":[31],"logic":[32],"(dL)":[33],"enable":[35],"verification":[36,179,202],"invariance.":[39],"First,":[40],"the":[41,85,90,107,127,138,178],"scalar":[42],"vector":[44],"comparison":[45,55,81,86,92,157,193],"principles,":[46],"relating":[47],"system":[49,56],"equations":[52],"to":[53,112,151,167,197],"such":[57],"properties":[60],"can":[61,132],"be":[62,152],"established":[63],"more":[64],"easily,":[65],"are":[66,77,94,102,149,183,195],"axiomatized":[67],"dL.":[69],"axiomatization":[71,162],"primarily":[72],"utilizes":[73],"ghosts,":[75],"which":[76,182],"proof-theoretic":[78],"generalizations":[79],"systems.":[82],"Next,":[83],"with":[84],"principles":[87],"serving":[88],"as":[89],"basis,":[91],"invariants":[93,105,194,206],"introduced,":[95],"derived.":[103],"Comparison":[104],"reduce":[106],"question":[108],"functional":[114],"inequality":[115],"on":[116],"its":[117],"Lie":[118],"derivative":[119],"for":[120,177,186],"suitable":[122],"class":[123],"functions,":[125],"moreover,":[126],"right":[128],"choice":[129],"function":[131],"result":[133],"decidable":[135],"arithmetic.":[136],"Furthermore,":[137],"perennially":[139],"popular":[140],"barrier":[142],"functions":[143],"(CBFs)":[144],"used":[145,185],"safety-critical":[147],"shown":[150,196],"special":[154],"instance":[155],"invariants.":[158],"yields":[160],"an":[161],"CBFs":[164],"leads":[166],"dedicated":[169],"rules.":[173],"The":[174],"allow":[176],"CBFs,":[181],"traditionally":[184],"synthesizing":[187],"safe":[188],"controllers":[189],"without":[190],"verification.":[191],"Lastly,":[192],"unify":[198],"several":[199],"other":[200],"safety":[201],"techniques,":[203],"including":[204],"Darboux":[205],"invariants,":[209],"further":[210],"cementing":[211],"their":[212],"versatility.":[213]},"counts_by_year":[],"updated_date":"2026-09-30T09:27:27.532063","created_date":"2026-08-27T00:00:00"}