{"id":"https://openalex.org/W2807455070","doi":"https://doi.org/10.1146/annurev-control-060117-104941","title":"Hamilton\u2013Jacobi Reachability: Some Recent Theoretical Advances and Applications in Unmanned Airspace Management","display_name":"Hamilton\u2013Jacobi Reachability: Some Recent Theoretical Advances and Applications in Unmanned Airspace Management","publication_year":2018,"publication_date":"2018-05-28","ids":{"openalex":"https://openalex.org/W2807455070","doi":"https://doi.org/10.1146/annurev-control-060117-104941","mag":"2807455070"},"language":"en","primary_location":{"id":"doi:10.1146/annurev-control-060117-104941","is_oa":true,"landing_page_url":"https://doi.org/10.1146/annurev-control-060117-104941","pdf_url":"https://www.annualreviews.org/doi/pdf/10.1146/annurev-control-060117-104941","source":{"id":"https://openalex.org/S4210191328","display_name":"Annual Review of Control Robotics and Autonomous Systems","issn_l":"2573-5144","issn":["2573-5144"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320373","host_organization_name":"Annual Reviews","host_organization_lineage":["https://openalex.org/P4310320373"],"host_organization_lineage_names":["Annual Reviews"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annual Review of Control, Robotics, and Autonomous Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.annualreviews.org/doi/pdf/10.1146/annurev-control-060117-104941","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100387244","display_name":"Mo Chen","orcid":"https://orcid.org/0000-0001-8506-3665"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mo Chen","raw_affiliation_strings":["Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, California 94720, USA;,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, California 94720, USA;,","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045155646","display_name":"Claire J. Tomlin","orcid":"https://orcid.org/0000-0003-3192-3185"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Claire J. Tomlin","raw_affiliation_strings":["Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, California 94720, USA;,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, California 94720, USA;,","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I95457486"],"apc_list":null,"apc_paid":null,"fwci":8.5516,"has_fulltext":true,"cited_by_count":121,"citation_normalized_percentile":{"value":0.98207032,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"1","issue":"1","first_page":"333","last_page":"358"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9995999932289124,"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":0.9995999932289124,"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/T11424","display_name":"Security and Verification in Computing","score":0.9941999912261963,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.9851999878883362,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/reachability","display_name":"Reachability","score":0.9452799558639526},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7214824557304382},{"id":"https://openalex.org/keywords/formal-methods","display_name":"Formal methods","score":0.6297467947006226},{"id":"https://openalex.org/keywords/formal-verification","display_name":"Formal verification","score":0.5904086232185364},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.5525147318840027},{"id":"https://openalex.org/keywords/safer","display_name":"SAFER","score":0.4907923638820648},{"id":"https://openalex.org/keywords/automation","display_name":"Automation","score":0.47162961959838867},{"id":"https://openalex.org/keywords/model-checking","display_name":"Model checking","score":0.4634183943271637},{"id":"https://openalex.org/keywords/distributed-computing","display_name":"Distributed computing","score":0.4075988829135895},{"id":"https://openalex.org/keywords/systems-engineering","display_name":"Systems engineering","score":0.35754474997520447},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.27867627143859863},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.22893014550209045},{"id":"https://openalex.org/keywords/software-engineering","display_name":"Software engineering","score":0.21769610047340393},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.16382735967636108},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.10600674152374268}],"concepts":[{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.9452799558639526},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7214824557304382},{"id":"https://openalex.org/C75606506","wikidata":"https://www.wikidata.org/wiki/Q1049183","display_name":"Formal methods","level":2,"score":0.6297467947006226},{"id":"https://openalex.org/C111498074","wikidata":"https://www.wikidata.org/wiki/Q173326","display_name":"Formal verification","level":2,"score":0.5904086232185364},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.5525147318840027},{"id":"https://openalex.org/C2776654903","wikidata":"https://www.wikidata.org/wiki/Q2601463","display_name":"SAFER","level":2,"score":0.4907923638820648},{"id":"https://openalex.org/C115901376","wikidata":"https://www.wikidata.org/wiki/Q184199","display_name":"Automation","level":2,"score":0.47162961959838867},{"id":"https://openalex.org/C110251889","wikidata":"https://www.wikidata.org/wiki/Q1569697","display_name":"Model checking","level":2,"score":0.4634183943271637},{"id":"https://openalex.org/C120314980","wikidata":"https://www.wikidata.org/wiki/Q180634","display_name":"Distributed computing","level":1,"score":0.4075988829135895},{"id":"https://openalex.org/C201995342","wikidata":"https://www.wikidata.org/wiki/Q682496","display_name":"Systems engineering","level":1,"score":0.35754474997520447},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.27867627143859863},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.22893014550209045},{"id":"https://openalex.org/C115903868","wikidata":"https://www.wikidata.org/wiki/Q80993","display_name":"Software engineering","level":1,"score":0.21769610047340393},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.16382735967636108},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.10600674152374268},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1146/annurev-control-060117-104941","is_oa":true,"landing_page_url":"https://doi.org/10.1146/annurev-control-060117-104941","pdf_url":"https://www.annualreviews.org/doi/pdf/10.1146/annurev-control-060117-104941","source":{"id":"https://openalex.org/S4210191328","display_name":"Annual Review of Control Robotics and Autonomous Systems","issn_l":"2573-5144","issn":["2573-5144"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320373","host_organization_name":"Annual Reviews","host_organization_lineage":["https://openalex.org/P4310320373"],"host_organization_lineage_names":["Annual Reviews"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annual Review of Control, Robotics, and Autonomous Systems","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1146/annurev-control-060117-104941","is_oa":true,"landing_page_url":"https://doi.org/10.1146/annurev-control-060117-104941","pdf_url":"https://www.annualreviews.org/doi/pdf/10.1146/annurev-control-060117-104941","source":{"id":"https://openalex.org/S4210191328","display_name":"Annual Review of Control Robotics and Autonomous Systems","issn_l":"2573-5144","issn":["2573-5144"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320373","host_organization_name":"Annual Reviews","host_organization_lineage":["https://openalex.org/P4310320373"],"host_organization_lineage_names":["Annual Reviews"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annual Review of Control, Robotics, and Autonomous Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G233385737","display_name":null,"funder_award_id":"#N00014-16-1-2206","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G3331613907","display_name":null,"funder_award_id":"931843","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4183124897","display_name":"CPS: Frontier: Collaborative Research: VeHICaL: Verified Human Interfaces, Control, and Learning for Semi-Autonomous Systems","funder_award_id":"1545126","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4422603081","display_name":"DEVELOPMENT OF THE \"WHERE-TO-LAND\" DECISION FUNCTION FOR AN EXPERT PILOTING SYSTEMS (EPS) IN MAN-RATED AUTONOMOUS AIR VEHICLES. CURRENT AIRCRAFT HAVE","funder_award_id":"NNX12AR18A","funder_id":"https://openalex.org/F4320306101","funder_display_name":"National Aeronautics and Space Administration"},{"id":"https://openalex.org/G5613400488","display_name":null,"funder_award_id":"CNS-931843","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G8876996369","display_name":null,"funder_award_id":"N00014","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306101","display_name":"National Aeronautics and Space Administration","ror":"https://ror.org/027ka1x80"},{"id":"https://openalex.org/F4320333591","display_name":"Multidisciplinary University Research Initiative","ror":null},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2807455070.pdf","grobid_xml":"https://content.openalex.org/works/W2807455070.grobid-xml"},"referenced_works_count":65,"referenced_works":["https://openalex.org/W7630107","https://openalex.org/W172589331","https://openalex.org/W240029891","https://openalex.org/W315739085","https://openalex.org/W618708471","https://openalex.org/W856973001","https://openalex.org/W1515569264","https://openalex.org/W1550828720","https://openalex.org/W1561445488","https://openalex.org/W1574960890","https://openalex.org/W1964345118","https://openalex.org/W1966165240","https://openalex.org/W1975236902","https://openalex.org/W1986571762","https://openalex.org/W1995408953","https://openalex.org/W1998452137","https://openalex.org/W1999016870","https://openalex.org/W1999244633","https://openalex.org/W2001331101","https://openalex.org/W2020254113","https://openalex.org/W2027664020","https://openalex.org/W2057462050","https://openalex.org/W2057789475","https://openalex.org/W2062319484","https://openalex.org/W2065798383","https://openalex.org/W2067202372","https://openalex.org/W2085744412","https://openalex.org/W2093834886","https://openalex.org/W2098073114","https://openalex.org/W2106816694","https://openalex.org/W2110073061","https://openalex.org/W2116364955","https://openalex.org/W2123357397","https://openalex.org/W2136719854","https://openalex.org/W2139132599","https://openalex.org/W2142455750","https://openalex.org/W2153012550","https://openalex.org/W2159001937","https://openalex.org/W2176215692","https://openalex.org/W2298907094","https://openalex.org/W2336607923","https://openalex.org/W2414457428","https://openalex.org/W2416561473","https://openalex.org/W2553348230","https://openalex.org/W2563550261","https://openalex.org/W2567355071","https://openalex.org/W2576277975","https://openalex.org/W2749408143","https://openalex.org/W2912107695","https://openalex.org/W2913760422","https://openalex.org/W2962888568","https://openalex.org/W2962896691","https://openalex.org/W2963118121","https://openalex.org/W2963395620","https://openalex.org/W2963530790","https://openalex.org/W2963606896","https://openalex.org/W2964187480","https://openalex.org/W2964310440","https://openalex.org/W3100051638","https://openalex.org/W3105702345","https://openalex.org/W3105818906","https://openalex.org/W3106187616","https://openalex.org/W4210875302","https://openalex.org/W4244726376","https://openalex.org/W4251258386"],"related_works":["https://openalex.org/W2884574904","https://openalex.org/W2006962382","https://openalex.org/W2149716943","https://openalex.org/W4312733571","https://openalex.org/W4315606162","https://openalex.org/W113732979","https://openalex.org/W161255303","https://openalex.org/W1544097700","https://openalex.org/W2340807904","https://openalex.org/W2037121848"],"abstract_inverted_index":{"Autonomous":[0],"systems":[1,12,130],"are":[2,13],"becoming":[3,132],"pervasive":[4,140],"in":[5,58,63],"everyday":[6],"life,":[7],"and":[8,15,24,42,54,113,141],"many":[9],"of":[10,105,124,128],"these":[11,28],"complex":[14,52],"safety-critical.":[16],"Formal":[17],"verification":[18,38,94,127],"is":[19,35,47,57,131],"important":[20],"for":[21,27,40,50,109,116,138],"providing":[22],"performance":[23],"safety":[25],"guarantees":[26],"systems.":[29],"In":[30,66],"particular,":[31],"Hamilton\u2013Jacobi":[32],"(HJ)":[33],"reachability":[34,76,93],"a":[36,60,133],"formal":[37,64],"tool":[39],"nonlinear":[41,111],"hybrid":[43],"systems;":[44],"however,":[45],"it":[46],"computationally":[48],"intractable":[49],"analyzing":[51],"systems,":[53,112],"computational":[55],"burden":[56],"general":[59,110],"difficult":[61],"challenge":[62],"verification.":[65],"this":[67],"review,":[68],"we":[69],"begin":[70],"by":[71,100],"briefly":[72],"presenting":[73],"background":[74],"on":[75,81,102],"analysis":[77],"with":[78],"an":[79],"emphasis":[80],"the":[82,122,136],"HJ":[83],"formulation.":[84],"We":[85],"then":[86],"present":[87],"recent":[88],"work":[89],"showing":[90],"how":[91],"high-dimensional":[92],"can":[95],"be":[96],"made":[97],"more":[98,139],"tractable":[99,126],"focusing":[101],"two":[103],"areas":[104],"development:":[106],"system":[107],"decomposition":[108],"traffic":[114],"protocols":[115],"unmanned":[117],"airspace":[118],"management.":[119],"By":[120],"tackling":[121],"curse":[123],"dimensionality,":[125],"practical":[129],"reality,":[134],"paving":[135],"way":[137],"safer":[142],"automation.":[143]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":25},{"year":2024,"cited_by_count":24},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":15},{"year":2021,"cited_by_count":19},{"year":2020,"cited_by_count":18},{"year":2019,"cited_by_count":8}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}