{"id":"https://openalex.org/W7148404055","doi":"https://doi.org/10.48550/arxiv.2604.00286","title":"Certified Set Convergence for Piecewise Affine Systems via Neural Lyapunov Functions","display_name":"Certified Set Convergence for Piecewise Affine Systems via Neural Lyapunov Functions","publication_year":2026,"publication_date":"2026-03-31","ids":{"openalex":"https://openalex.org/W7148404055","doi":"https://doi.org/10.48550/arxiv.2604.00286"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.00286","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.00286","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":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.00286","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5132790900","display_name":"Yanliang Huang","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Huang, Yanliang","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5132822684","display_name":"Peng Xie","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xie, Peng","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5132804771","display_name":"Zhen Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Zhen","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5132807414","display_name":"Wenyuan Wu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wu, Wenyuan","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5132799474","display_name":"Zhuoqi Zeng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zeng, Zhuoqi","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5122620783","display_name":"Amr Alanwar","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alanwar, Amr","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5132790900"],"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.40540000796318054,"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"}},"topics":[{"id":"https://openalex.org/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.40540000796318054,"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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.17970000207424164,"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/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.12809999287128448,"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/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.651199996471405},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5055000185966492},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.4821999967098236},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.42170000076293945},{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.40610000491142273},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.4025999903678894},{"id":"https://openalex.org/keywords/set-operations","display_name":"Set operations","score":0.3896999955177307},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.3806999921798706}],"concepts":[{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.651199996471405},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5788999795913696},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5055000185966492},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.4821999967098236},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.42170000076293945},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.40610000491142273},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.4025999903678894},{"id":"https://openalex.org/C2777168461","wikidata":"https://www.wikidata.org/wiki/Q42196253","display_name":"Set operations","level":3,"score":0.3896999955177307},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3806999921798706},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3727000057697296},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.364300012588501},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3626999855041504},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.358599990606308},{"id":"https://openalex.org/C774472","wikidata":"https://www.wikidata.org/wiki/Q6760393","display_name":"Margin (machine learning)","level":2,"score":0.3303999900817871},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.32030001282691956},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31619998812675476},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.29980000853538513},{"id":"https://openalex.org/C195975749","wikidata":"https://www.wikidata.org/wiki/Q1475705","display_name":"Fuzzy control system","level":3,"score":0.2946999967098236},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.2800999879837036},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.27880001068115234},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.2782000005245209},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.27070000767707825},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.25099998712539673}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.00286","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.00286","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":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.00286","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.00286","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":"article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.6874897480010986}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Safety-critical":[0],"control":[1,25],"of":[2,62,80],"piecewise":[3],"affine":[4,48],"(PWA)":[5],"systems":[6,156],"under":[7,46],"bounded":[8],"additive":[9],"disturbances":[10],"requires":[11],"guarantees":[12],"not":[13],"for":[14,18,72],"individual":[15],"states":[16],"but":[17],"entire":[19,140],"state":[20,30],"sets":[21,39,141],"simultaneously:":[22],"a":[23,35,83,90,124],"single":[24],"action":[26],"must":[27],"steer":[28],"every":[29,172],"in":[31],"the":[32,59,63,67,97,111,131,144,163,180,184,187],"set":[33,52,166,195],"toward":[34],"target,":[36],"even":[37],"as":[38],"crossing":[40],"mode":[41],"boundaries":[42],"split":[43],"and":[44,66,183],"evolve":[45],"distinct":[47],"dynamics.":[49],"Certifying":[50],"such":[51],"convergence":[53,167],"via":[54,107,120],"neural":[55],"Lyapunov":[56,112,136],"functions":[57],"couples":[58],"Lipschitz":[60,146],"constants":[61],"value":[64,100,132],"function":[65,101],"policy,":[68],"yet":[69],"certified":[70],"bounds":[71,138],"expressive":[73],"networks":[74],"exceed":[75],"true":[76],"values":[77],"by":[78],"orders":[79],"magnitude,":[81],"creating":[82],"certification":[84],"barrier.":[85],"We":[86],"resolve":[87],"this":[88],"through":[89,130],"three-stage":[91],"pipeline":[92],"that":[93],"decouples":[94],"verification":[95],"from":[96,102],"policy.":[98],"A":[99,114,174],"Hamilton-Jacobi":[103],"backward":[104],"reachability,":[105],"trained":[106],"reinforcement":[108],"learning,":[109],"is":[110,186],"candidate.":[113],"permutation-invariant":[115],"Deep":[116],"Sets":[117],"controller,":[118],"distilled":[119],"regret":[121],"minimization,":[122],"produces":[123],"common":[125],"action.":[126],"Verification":[127],"propagates":[128],"zonotopes":[129],"network,":[133],"yielding":[134],"verified":[135],"upper":[137],"over":[139],"without":[142],"bounding":[143],"policy":[145],"constant.":[147],"On":[148],"four":[149],"benchmarks":[150],"up":[151],"to":[152,191],"dimension":[153],"six,":[154],"including":[155],"with":[157,168],"per-mode":[158],"operator":[159],"norms":[160],"exceeding":[161],"unity,":[162],"framework":[164],"certifies":[165],"positive":[169],"margin":[170],"on":[171],"system.":[173],"spectrally":[175],"constrained":[176],"local":[177],"certificate":[178],"completes":[179],"terminal":[181],"guarantee,":[182],"set-actor":[185],"only":[188],"tested":[189],"method":[190],"achieve":[192],"full":[193],"strict":[194],"containment,":[196],"at":[197],"constant-time":[198],"online":[199],"cost.":[200]},"counts_by_year":[],"updated_date":"2026-04-03T16:44:17.987007","created_date":"2026-04-03T00:00:00"}