{"id":"https://openalex.org/W1975236902","doi":"https://doi.org/10.1145/2728606.2728612","title":"Reach-avoid problems with time-varying dynamics, targets and constraints","display_name":"Reach-avoid problems with time-varying dynamics, targets and constraints","publication_year":2015,"publication_date":"2015-04-14","ids":{"openalex":"https://openalex.org/W1975236902","doi":"https://doi.org/10.1145/2728606.2728612","mag":"1975236902"},"language":"en","primary_location":{"id":"doi:10.1145/2728606.2728612","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2728606.2728612","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 18th International Conference on Hybrid Systems: Computation and Control","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/A5050710435","display_name":"Jaime F. Fisac","orcid":"https://orcid.org/0000-0002-2676-5090"},"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":true,"raw_author_name":"Jaime F. Fisac","raw_affiliation_strings":["University of California, Berkeley, CA","University of California: Berkeley, CA#TAB#"],"affiliations":[{"raw_affiliation_string":"University of California, Berkeley, CA","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"University of California: Berkeley, CA#TAB#","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"middle","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":["University of California, Berkeley, CA","University of California: Berkeley, CA#TAB#"],"affiliations":[{"raw_affiliation_string":"University of California, Berkeley, CA","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"University of California: Berkeley, CA#TAB#","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"middle","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":["University of California, Berkeley, CA","University of California: Berkeley, CA#TAB#"],"affiliations":[{"raw_affiliation_string":"University of California, Berkeley, CA","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"University of California: Berkeley, CA#TAB#","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103101043","display_name":"S. Shankar Sastry","orcid":null},"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":"S. Shankar Sastry","raw_affiliation_strings":["University of California, Berkeley, CA","University of California: Berkeley, CA#TAB#"],"affiliations":[{"raw_affiliation_string":"University of California, Berkeley, CA","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"University of California: Berkeley, CA#TAB#","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5050710435"],"corresponding_institution_ids":["https://openalex.org/I95457486"],"apc_list":null,"apc_paid":null,"fwci":309.7924,"has_fulltext":false,"cited_by_count":214,"citation_normalized_percentile":{"value":0.99982439,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"11","last_page":"20"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11082","display_name":"Spacecraft Dynamics and Control","score":0.6072999835014343,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T11082","display_name":"Spacecraft Dynamics and Control","score":0.6072999835014343,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T10545","display_name":"Optimization and Variational Analysis","score":0.16740000247955322,"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/T10586","display_name":"Robotic Path Planning Algorithms","score":0.06030000001192093,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/computer-science","display_name":"Computer science","score":0.6191879510879517},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5587137937545776},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5409859418869019},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5365296602249146},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.5203320980072021},{"id":"https://openalex.org/keywords/obstacle","display_name":"Obstacle","score":0.4544033706188202},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4382885694503784},{"id":"https://openalex.org/keywords/differential-game","display_name":"Differential game","score":0.4150926470756531},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.38740038871765137},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.27283135056495667},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.22897258400917053},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.14616069197654724},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1254260241985321}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6191879510879517},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5587137937545776},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5409859418869019},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5365296602249146},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5203320980072021},{"id":"https://openalex.org/C2776650193","wikidata":"https://www.wikidata.org/wiki/Q264661","display_name":"Obstacle","level":2,"score":0.4544033706188202},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4382885694503784},{"id":"https://openalex.org/C2779006483","wikidata":"https://www.wikidata.org/wiki/Q1973196","display_name":"Differential game","level":2,"score":0.4150926470756531},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.38740038871765137},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.27283135056495667},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.22897258400917053},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.14616069197654724},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1254260241985321},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"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:10.1145/2728606.2728612","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2728606.2728612","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 18th International Conference on Hybrid Systems: Computation and Control","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2102899048","display_name":null,"funder_award_id":"N0014-08-0696","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G4466780832","display_name":null,"funder_award_id":"CNS-931843","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W149761250","https://openalex.org/W153353184","https://openalex.org/W168874853","https://openalex.org/W240029891","https://openalex.org/W1550828720","https://openalex.org/W1964345118","https://openalex.org/W1966660110","https://openalex.org/W1973481688","https://openalex.org/W1986571762","https://openalex.org/W1998452137","https://openalex.org/W1999244633","https://openalex.org/W2000111160","https://openalex.org/W2027664020","https://openalex.org/W2038855137","https://openalex.org/W2041587439","https://openalex.org/W2053572490","https://openalex.org/W2093834886","https://openalex.org/W2101560656","https://openalex.org/W2116364955","https://openalex.org/W2554493256","https://openalex.org/W2962794004","https://openalex.org/W2962896691","https://openalex.org/W3010292040","https://openalex.org/W4244726376","https://openalex.org/W6606935068","https://openalex.org/W6704298589","https://openalex.org/W7024974029"],"related_works":["https://openalex.org/W2794103424","https://openalex.org/W1996530509","https://openalex.org/W3028317537","https://openalex.org/W2389515972","https://openalex.org/W4245435724","https://openalex.org/W2055301889","https://openalex.org/W4400979532","https://openalex.org/W2376554934","https://openalex.org/W2077790809","https://openalex.org/W1505959757"],"abstract_inverted_index":{"We":[0,189],"consider":[1],"a":[2,18,23,128,136,206,211],"reach-avoid":[3],"differential":[4],"game,":[5],"in":[6,60,132,214],"which":[7,215],"one":[8],"of":[9,25,53,135,147,193],"the":[10,15,29,35,39,75,89,121,133,143,152,156,159,169,186,220],"players":[11],"aims":[12],"to":[13,33,92,99,185],"steer":[14],"system":[16,40],"into":[17],"target":[19,42,157],"set":[20,24,146],"without":[21,120],"violating":[22],"state":[26,45,90,104,124,160,221],"constraints,":[27],"while":[28],"other":[30,69],"player":[31,84],"tries":[32],"prevent":[34],"first":[36],"from":[37],"succeeding;":[38],"dynamics,":[41,116],"set,":[43],"and":[44,65,80,111,118,140,172,201],"constraints":[46,105,110,119],"may":[47],"all":[48],"be":[49],"time-varying.":[50],"The":[51],"analysis":[52],"this":[54,163,194],"problem":[55],"plays":[56],"an":[57,191],"important":[58],"role":[59],"collision":[61],"avoidance,":[62],"motion":[63],"planning":[64],"aircraft":[66],"control,":[67],"among":[68],"applications.":[70],"Previous":[71],"methods":[72],"for":[73,82,123,155,175],"computing":[74],"guaranteed":[76],"winning":[77,173],"initial":[78],"conditions":[79],"strategies":[81,174],"each":[83],"have":[85,96],"either":[86,102],"required":[87],"augmenting":[88],"vector":[91],"include":[93,210],"time,":[94],"or":[95,106],"been":[97],"limited":[98],"problems":[100],"with":[101],"no":[103,180],"entirely":[107],"static":[108],"targets,":[109],"dynamics.":[112],"To":[113],"incorporate":[114],"time-varying":[115,176],"targets":[117],"need":[122],"augmentation,":[125],"we":[126,209],"propose":[127],"modified":[129],"Hamilton-Jacobi-Isaacs":[130],"equation":[131],"form":[134],"double-obstacle":[137],"variational":[138],"inequality,":[139],"prove":[141],"that":[142],"zero":[144],"sublevel":[145],"its":[148,203],"viscosity":[149],"solution":[150],"characterizes":[151],"capture":[153,170],"basin":[154,171],"under":[158],"constraints.":[161],"Through":[162],"formulation,":[164],"our":[165,216],"method":[166,195,217],"can":[167],"compute":[168],"games":[177],"at":[178],"virtually":[179],"additional":[181],"computational":[182],"cost":[183],"relative":[184],"time-invariant":[187],"case.":[188],"provide":[190],"implementation":[192],"based":[196],"on":[197],"well-known":[198],"numerical":[199],"schemes":[200],"show":[202],"convergence":[204],"through":[205],"simple":[207],"example;":[208],"second":[212],"example":[213],"substantially":[218],"outperforms":[219],"augmentation":[222],"approach.":[223]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":17},{"year":2024,"cited_by_count":31},{"year":2023,"cited_by_count":23},{"year":2022,"cited_by_count":22},{"year":2021,"cited_by_count":28},{"year":2020,"cited_by_count":24},{"year":2019,"cited_by_count":19},{"year":2018,"cited_by_count":19},{"year":2017,"cited_by_count":13},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":8}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}