{"id":"https://openalex.org/W4319865700","doi":"https://doi.org/10.1109/tac.2023.3241180","title":"Efficient Computation of State-Constrained Reachability Problems Using Hopf\u2013Lax Formulae","display_name":"Efficient Computation of State-Constrained Reachability Problems Using Hopf\u2013Lax Formulae","publication_year":2023,"publication_date":"2023-01-31","ids":{"openalex":"https://openalex.org/W4319865700","doi":"https://doi.org/10.1109/tac.2023.3241180"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2023.3241180","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tac.2023.3241180","pdf_url":"https://ieeexplore.ieee.org/ielx7/9/4601496/10032791.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":true,"oa_status":"hybrid","oa_url":"https://ieeexplore.ieee.org/ielx7/9/4601496/10032791.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075094704","display_name":"Donggun Lee","orcid":"https://orcid.org/0000-0003-4073-1353"},"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":"Donggun Lee","raw_affiliation_strings":["Department of Mechanical Engineering, University of California, Berkeley, CA, USA"],"raw_orcid":"https://orcid.org/0000-0003-4073-1353","affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, University of California, Berkeley, CA, 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, CA, USA"],"raw_orcid":"https://orcid.org/0000-0003-3192-3185","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA, 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":0.6543,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.66713949,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"68","issue":"11","first_page":"6481","last_page":"6495"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9976999759674072,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9976999759674072,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9717000126838684,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9587000012397766,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/reachability","display_name":"Reachability","score":0.8895301818847656},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6095981597900391},{"id":"https://openalex.org/keywords/reachability-problem","display_name":"Reachability problem","score":0.4721161127090454},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.4718974530696869},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4544714689254761},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4273463189601898},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.4268789291381836},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4265609383583069},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.12302267551422119},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10998654365539551}],"concepts":[{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.8895301818847656},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6095981597900391},{"id":"https://openalex.org/C2777669093","wikidata":"https://www.wikidata.org/wiki/Q17141570","display_name":"Reachability problem","level":3,"score":0.4721161127090454},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4718974530696869},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4544714689254761},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4273463189601898},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.4268789291381836},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4265609383583069},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.12302267551422119},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10998654365539551},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2023.3241180","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tac.2023.3241180","pdf_url":"https://ieeexplore.ieee.org/ielx7/9/4601496/10032791.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1109/tac.2023.3241180","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tac.2023.3241180","pdf_url":"https://ieeexplore.ieee.org/ielx7/9/4601496/10032791.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2228615319","display_name":null,"funder_award_id":"N00014-18-1-2214","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G4532442909","display_name":null,"funder_award_id":"FA8750-18-C-0101","funder_id":"https://openalex.org/F4320332180","funder_display_name":"Defense Advanced Research Projects Agency"},{"id":"https://openalex.org/G4713059963","display_name":null,"funder_award_id":"FA8750","funder_id":"https://openalex.org/F4320332180","funder_display_name":"Defense Advanced Research Projects Agency"},{"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/F4320306142","display_name":"John D. and Catherine T. MacArthur Foundation","ror":"https://ror.org/00dxczh48"},{"id":"https://openalex.org/F4320308331","display_name":"American Academy of Arts and Sciences","ror":"https://ror.org/018224621"},{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4319865700.pdf","grobid_xml":"https://content.openalex.org/works/W4319865700.grobid-xml"},"referenced_works_count":67,"referenced_works":["https://openalex.org/W204462166","https://openalex.org/W1494982173","https://openalex.org/W1562460111","https://openalex.org/W1990244934","https://openalex.org/W1999244633","https://openalex.org/W2004561989","https://openalex.org/W2011669849","https://openalex.org/W2026079951","https://openalex.org/W2026829488","https://openalex.org/W2038855137","https://openalex.org/W2050188930","https://openalex.org/W2057553555","https://openalex.org/W2083098238","https://openalex.org/W2085873703","https://openalex.org/W2087002964","https://openalex.org/W2090501324","https://openalex.org/W2090921058","https://openalex.org/W2093834886","https://openalex.org/W2106816694","https://openalex.org/W2111216640","https://openalex.org/W2111838834","https://openalex.org/W2113108728","https://openalex.org/W2116554046","https://openalex.org/W2119974577","https://openalex.org/W2123357397","https://openalex.org/W2141616022","https://openalex.org/W2142058898","https://openalex.org/W2160781031","https://openalex.org/W2165489953","https://openalex.org/W2170498251","https://openalex.org/W2229008027","https://openalex.org/W2411640870","https://openalex.org/W2529031700","https://openalex.org/W2560504659","https://openalex.org/W2588802774","https://openalex.org/W2767578104","https://openalex.org/W2767915842","https://openalex.org/W2769302154","https://openalex.org/W2797923482","https://openalex.org/W2841721725","https://openalex.org/W2887154784","https://openalex.org/W2899087494","https://openalex.org/W2920846412","https://openalex.org/W2939501205","https://openalex.org/W2963056268","https://openalex.org/W2963395620","https://openalex.org/W2964040381","https://openalex.org/W2966932052","https://openalex.org/W2968547875","https://openalex.org/W2996196387","https://openalex.org/W3047155704","https://openalex.org/W3099188500","https://openalex.org/W3106144869","https://openalex.org/W3119862069","https://openalex.org/W3120797897","https://openalex.org/W3125921861","https://openalex.org/W3143034939","https://openalex.org/W3152915553","https://openalex.org/W4226065362","https://openalex.org/W4240902880","https://openalex.org/W4250589301","https://openalex.org/W4251849361","https://openalex.org/W4287112072","https://openalex.org/W4293775970","https://openalex.org/W4312464760","https://openalex.org/W6772100842","https://openalex.org/W6797475556"],"related_works":["https://openalex.org/W2047831585","https://openalex.org/W4253760428","https://openalex.org/W2099490078","https://openalex.org/W3208672221","https://openalex.org/W3017277461","https://openalex.org/W3172202899","https://openalex.org/W4287199681","https://openalex.org/W4241289374","https://openalex.org/W1548979236","https://openalex.org/W4224983736"],"abstract_inverted_index":{"This":[0,122],"paper":[1,69,123],"considers":[2],"two":[3,36],"state-constrained":[4],"reachability":[5,76,117,129],"problems:":[6],"computing":[7],"(1)":[8],"control-invariant":[9],"and":[10,108,131],"(2)":[11],"reach-avoid":[12],"sets,":[13],"both":[14],"under":[15,119],"state":[16,59],"constraints.":[17],"Prior":[18],"research":[19],"has":[20],"developed":[21],"Hamilton-Jacobi":[22],"(HJ)":[23],"partial":[24],"differential":[25],"equations":[26],"(PDEs)":[27],"that":[28,87],"characterize":[29],"the":[30,40,57,83,95,112,116,133,136],"optimal":[31,113],"cost":[32],"functions":[33],"of":[34,82,115,135],"these":[35],"problems.":[37,97],"Unfortunately,":[38],"solving":[39],"HJ":[41,78],"PDEs":[42],"by":[43],"grid-based":[44],"methods,":[45,49],"such":[46],"as":[47],"level-set":[48],"suffers":[50],"from":[51],"exponentially":[52],"growing":[53],"computational":[54,66],"complexity":[55],"in":[56],"system":[58],"dimension.":[60],"In":[61],"order":[62],"to":[63,104],"alleviate":[64],"this":[65,68],"issue,":[67],"proposes":[70],"a":[71],"Hopf-Lax":[72,84,106,138],"formula":[73],"for":[74,127],"each":[75,128],"problem's":[77],"PDE.":[79],"The":[80],"advantage":[81],"formulae":[85,107],"is":[86],"they":[88],"have":[89],"more":[90],"favorable":[91],"convexity":[92],"conditions":[93],"than":[94],"corresponding":[96],"Thus,":[98],"direct":[99],"methods":[100],"may":[101],"be":[102],"used":[103],"solve":[105],"thus":[109],"efficiently":[110],"compute":[111],"solution":[114],"problems":[118],"specified":[120],"conditions.":[121],"provides":[124],"an":[125],"example":[126],"problem":[130],"demonstrates":[132],"performance":[134],"proposed":[137],"method.":[139]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}