{"id":"https://openalex.org/W4315488781","doi":"https://doi.org/10.1109/cdc51059.2022.9992655","title":"Safety Verification of Neural Feedback Systems Based on Constrained Zonotopes","display_name":"Safety Verification of Neural Feedback Systems Based on Constrained Zonotopes","publication_year":2022,"publication_date":"2022-12-06","ids":{"openalex":"https://openalex.org/W4315488781","doi":"https://doi.org/10.1109/cdc51059.2022.9992655"},"language":"en","primary_location":{"id":"doi:10.1109/cdc51059.2022.9992655","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc51059.2022.9992655","pdf_url":null,"source":{"id":"https://openalex.org/S4363607710","display_name":"2022 IEEE 61st Conference on Decision and Control (CDC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2022 IEEE 61st Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},"type":"article","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/A5100349346","display_name":"Yuhao Zhang","orcid":"https://orcid.org/0000-0002-2814-7317"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Yuhao Zhang","raw_affiliation_strings":["University of Wisconsin-Madison,Department of Mechanical Engineering,Madison,WI,USA,53706"],"affiliations":[{"raw_affiliation_string":"University of Wisconsin-Madison,Department of Mechanical Engineering,Madison,WI,USA,53706","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033195779","display_name":"Xiangru Xu","orcid":"https://orcid.org/0000-0003-1367-6790"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xiangru Xu","raw_affiliation_strings":["University of Wisconsin-Madison,Department of Mechanical Engineering,Madison,WI,USA,53706"],"affiliations":[{"raw_affiliation_string":"University of Wisconsin-Madison,Department of Mechanical Engineering,Madison,WI,USA,53706","institution_ids":["https://openalex.org/I135310074"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100349346"],"corresponding_institution_ids":["https://openalex.org/I135310074"],"apc_list":null,"apc_paid":null,"fwci":1.767,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.87238742,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"2737","last_page":"2744"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.9995999932289124,"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":0.9995999932289124,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9922999739646912,"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/T10876","display_name":"Fault Detection and Control Systems","score":0.9909999966621399,"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/artificial-neural-network","display_name":"Artificial neural network","score":0.7084354162216187},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6968011856079102},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5977087616920471},{"id":"https://openalex.org/keywords/feedforward-neural-network","display_name":"Feedforward neural network","score":0.5859574675559998},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5695052146911621},{"id":"https://openalex.org/keywords/feed-forward","display_name":"Feed forward","score":0.541839063167572},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5076063871383667},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.4671916961669922},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.44382405281066895},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.41207006573677063},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.32729363441467285},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.31524890661239624},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3081827461719513},{"id":"https://openalex.org/keywords/control-engineering","display_name":"Control engineering","score":0.2801407277584076},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.19720852375030518},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.09223508834838867}],"concepts":[{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.7084354162216187},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6968011856079102},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5977087616920471},{"id":"https://openalex.org/C47702885","wikidata":"https://www.wikidata.org/wiki/Q5441227","display_name":"Feedforward neural network","level":3,"score":0.5859574675559998},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5695052146911621},{"id":"https://openalex.org/C38858127","wikidata":"https://www.wikidata.org/wiki/Q5441228","display_name":"Feed forward","level":2,"score":0.541839063167572},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5076063871383667},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.4671916961669922},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.44382405281066895},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.41207006573677063},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.32729363441467285},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.31524890661239624},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3081827461719513},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.2801407277584076},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.19720852375030518},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.09223508834838867},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc51059.2022.9992655","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc51059.2022.9992655","pdf_url":null,"source":{"id":"https://openalex.org/S4363607710","display_name":"2022 IEEE 61st Conference on Decision and Control (CDC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2022 IEEE 61st Conference on Decision and Control (CDC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1507872748","https://openalex.org/W1596877211","https://openalex.org/W1945616565","https://openalex.org/W1972544340","https://openalex.org/W1982029046","https://openalex.org/W2160815625","https://openalex.org/W2183898569","https://openalex.org/W2300621294","https://openalex.org/W2594877703","https://openalex.org/W2791251367","https://openalex.org/W2890472662","https://openalex.org/W2900153411","https://openalex.org/W2938701611","https://openalex.org/W2955364893","https://openalex.org/W2964130946","https://openalex.org/W2974147052","https://openalex.org/W2977767629","https://openalex.org/W2980176926","https://openalex.org/W3024917158","https://openalex.org/W3044216288","https://openalex.org/W3045590379","https://openalex.org/W3086849158","https://openalex.org/W3107034996","https://openalex.org/W3111646504","https://openalex.org/W3120409696","https://openalex.org/W3159334459","https://openalex.org/W3185128647","https://openalex.org/W3205832376","https://openalex.org/W4206101760","https://openalex.org/W4237969418","https://openalex.org/W4313679833","https://openalex.org/W6640425456","https://openalex.org/W6685820758","https://openalex.org/W6754619240","https://openalex.org/W6798979448","https://openalex.org/W6800464454"],"related_works":["https://openalex.org/W2115072676","https://openalex.org/W2357447513","https://openalex.org/W2045727192","https://openalex.org/W4311212821","https://openalex.org/W1529660427","https://openalex.org/W2378845890","https://openalex.org/W2102065768","https://openalex.org/W4390752998","https://openalex.org/W2158578859","https://openalex.org/W2358123629"],"abstract_inverted_index":{"Artificial":[0],"neural":[1,37,64,100],"networks":[2],"have":[3],"recently":[4],"been":[5],"utilized":[6],"in":[7],"many":[8],"feedback":[9,41,65,101],"control":[10],"systems":[11,66,102],"and":[12,59,70,109],"introduced":[13],"new":[14],"challenges":[15],"regarding":[16],"the":[17,25,40,80,112],"safety":[18],"of":[19,82,111],"such":[20,83],"systems.":[21],"This":[22],"paper":[23],"considers":[24],"safe":[26],"verification":[27],"problem":[28],"for":[29,63],"a":[30,34,45,84,122],"dynamical":[31],"system":[32,85],"with":[33,67,103,124],"given":[35],"feedforward":[36],"network":[38],"as":[39,91],"controller":[42],"by":[43,117],"using":[44],"constrained":[46,92],"zonotope-based":[47],"approach.":[48],"A":[49],"novel":[50],"set-based":[51],"method":[52,114],"is":[53,127],"proposed":[54,113],"to":[55,77,99],"compute":[56],"both":[57],"exact":[58],"over-approximated":[60],"reachable":[61],"sets":[62],"linear":[68,71],"models,":[69],"program-based":[72],"sufficient":[73],"conditions":[74],"are":[75,96,115],"presented":[76],"verify":[78],"whether":[79],"trajectories":[81],"can":[86],"avoid":[87],"unsafe":[88],"regions":[89],"represented":[90],"zonotopes.":[93],"The":[94,106],"results":[95],"also":[97,128],"extended":[98],"nonlinear":[104],"models.":[105],"computational":[107],"efficiency":[108],"accuracy":[110],"demonstrated":[116],"two":[118],"numerical":[119],"examples":[120],"where":[121],"comparison":[123],"state-of-the-art":[125],"methods":[126],"provided.":[129]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":10}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}