{"id":"https://openalex.org/W4404317275","doi":"https://doi.org/10.1109/tac.2024.3497001","title":"A Semialgebraic Framework for Verification and Synthesis of Control Barrier Functions","display_name":"A Semialgebraic Framework for Verification and Synthesis of Control Barrier Functions","publication_year":2024,"publication_date":"2024-11-13","ids":{"openalex":"https://openalex.org/W4404317275","doi":"https://doi.org/10.1109/tac.2024.3497001"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2024.3497001","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2024.3497001","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-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/A5004774385","display_name":"Andrew Clark","orcid":"https://orcid.org/0000-0002-5868-6186"},"institutions":[{"id":"https://openalex.org/I204465549","display_name":"Washington University in St. Louis","ror":"https://ror.org/01yc7t268","country_code":"US","type":"education","lineage":["https://openalex.org/I204465549"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Andrew Clark","raw_affiliation_strings":["Department of Electrical and Systems Engineering, Washington University in St. Louis, St. Louis, MO, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Systems Engineering, Washington University in St. Louis, St. Louis, MO, USA","institution_ids":["https://openalex.org/I204465549"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5004774385"],"corresponding_institution_ids":["https://openalex.org/I204465549"],"apc_list":null,"apc_paid":null,"fwci":2.4462,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.89616601,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"70","issue":"5","first_page":"3101","last_page":"3116"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12810","display_name":"Real-time simulation and control systems","score":0.9915000200271606,"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/T12810","display_name":"Real-time simulation and control systems","score":0.9915000200271606,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9817000031471252,"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/T10933","display_name":"Real-Time Systems Scheduling","score":0.9740999937057495,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/algebraic-number","display_name":"Algebraic number","score":0.586847722530365},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5343602895736694},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.46023085713386536},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4262269139289856},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3018510043621063},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1651495099067688},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.0984722375869751},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07858964800834656}],"concepts":[{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.586847722530365},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5343602895736694},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.46023085713386536},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4262269139289856},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3018510043621063},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1651495099067688},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0984722375869751},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07858964800834656}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2024.3497001","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2024.3497001","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W59305859","https://openalex.org/W1496537269","https://openalex.org/W1515174179","https://openalex.org/W1880805667","https://openalex.org/W1967184028","https://openalex.org/W1975236902","https://openalex.org/W1980569135","https://openalex.org/W1982099023","https://openalex.org/W1999629321","https://openalex.org/W2033118636","https://openalex.org/W2035962113","https://openalex.org/W2041076275","https://openalex.org/W2140531311","https://openalex.org/W2536620281","https://openalex.org/W2560504659","https://openalex.org/W2589869525","https://openalex.org/W2963530480","https://openalex.org/W2968945909","https://openalex.org/W3011609080","https://openalex.org/W3021643916","https://openalex.org/W3045947256","https://openalex.org/W3046160353","https://openalex.org/W3120023780","https://openalex.org/W3155061166","https://openalex.org/W3157346982","https://openalex.org/W3195647294","https://openalex.org/W3200805077","https://openalex.org/W3204383275","https://openalex.org/W3206495240","https://openalex.org/W4210279164","https://openalex.org/W4225672205","https://openalex.org/W4226242368","https://openalex.org/W4245376853","https://openalex.org/W4299599836","https://openalex.org/W4312847395","https://openalex.org/W4314945971","https://openalex.org/W4315606134","https://openalex.org/W4382935993","https://openalex.org/W4383172109","https://openalex.org/W4387123822","https://openalex.org/W4388479641","https://openalex.org/W4388918424","https://openalex.org/W6857462865"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027"],"abstract_inverted_index":{"Safety":[0],"is":[1],"a":[2,24,38,86,124],"critical":[3],"property":[4],"for":[5,67,88,116],"control":[6,53,93],"systems":[7,101],"in":[8],"medicine,":[9],"transportation,":[10],"manufacturing,":[11],"and":[12,15,100,105,123,138],"other":[13],"applications,":[14],"can":[16,47],"be":[17,48],"defined":[18],"as":[19,41,43],"ensuring":[20],"positive":[21,35,50,68],"invariance":[22,36,69],"of":[23,33,37,64,91,111],"predefined":[25],"safe":[26],"set.":[27],"This":[28],"article":[29],"investigates":[30],"the":[31,74,109],"problems":[32],"verifying":[34,89],"semialgebraic":[39],"set":[40],"well":[42],"synthesizing":[44],"sets":[45],"that":[46],"made":[49],"invariant":[51],"through":[52,132],"barrier":[54],"function":[55],"(CBF)-based":[56],"control.":[57],"The":[58],"key":[59],"to":[60,70],"our":[61,130],"approach":[62,122,131],"consists":[63],"mapping":[65],"conditions":[66],"sum-of-squares":[71],"constraints":[72],"via":[73],"Positivstellensatz":[75],"from":[76],"real":[77],"algebraic":[78],"geometry.":[79],"Based":[80],"on":[81,135],"these":[82],"conditions,":[83],"we":[84,113],"propose":[85,114],"framework":[87],"safety":[90],"CBF-based":[92],"including":[94],"single":[95],"CBFs,":[96,98,118],"high-order":[97],"multi-CBFs,":[99],"with":[102],"trigonometric":[103],"dynamics":[104],"actuation":[106],"constraints.":[107],"In":[108],"area":[110],"synthesis,":[112],"algorithms":[115],"constructing":[117],"namely,":[119],"an":[120],"alternating-descent":[121],"local":[125],"CBF":[126],"approach.":[127],"We":[128],"evaluate":[129],"case":[133],"studies":[134],"quadrotor":[136],"UAV":[137],"power":[139],"converter":[140],"test":[141],"systems.":[142]},"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":1}],"updated_date":"2025-12-27T23:08:20.325037","created_date":"2025-10-10T00:00:00"}
