{"id":"https://openalex.org/W3195647294","doi":"https://doi.org/10.1109/tac.2021.3105491","title":"High-Order Control Barrier Functions","display_name":"High-Order Control Barrier Functions","publication_year":2021,"publication_date":"2021-08-18","ids":{"openalex":"https://openalex.org/W3195647294","doi":"https://doi.org/10.1109/tac.2021.3105491","mag":"3195647294"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2021.3105491","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2021.3105491","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/A5058590941","display_name":"Wei Xiao","orcid":"https://orcid.org/0000-0001-9622-6415"},"institutions":[{"id":"https://openalex.org/I111088046","display_name":"Boston University","ror":"https://ror.org/05qwgg493","country_code":"US","type":"education","lineage":["https://openalex.org/I111088046"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Wei Xiao","raw_affiliation_strings":["Division of Systems Engineering, Boston University, Brookline, MA, USA"],"affiliations":[{"raw_affiliation_string":"Division of Systems Engineering, Boston University, Brookline, MA, USA","institution_ids":["https://openalex.org/I111088046"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086742095","display_name":"C\u0103lin Belta","orcid":"https://orcid.org/0000-0002-7141-2657"},"institutions":[{"id":"https://openalex.org/I111088046","display_name":"Boston University","ror":"https://ror.org/05qwgg493","country_code":"US","type":"education","lineage":["https://openalex.org/I111088046"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Calin Belta","raw_affiliation_strings":["Division of Systems Engineering, Boston University, Brookline, MA, USA"],"affiliations":[{"raw_affiliation_string":"Division of Systems Engineering, Boston University, Brookline, MA, USA","institution_ids":["https://openalex.org/I111088046"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5058590941"],"corresponding_institution_ids":["https://openalex.org/I111088046"],"apc_list":null,"apc_paid":null,"fwci":21.771,"has_fulltext":false,"cited_by_count":320,"citation_normalized_percentile":{"value":0.99811131,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":100},"biblio":{"volume":"67","issue":"7","first_page":"3655","last_page":"3662"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9994999766349792,"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/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9994999766349792,"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":0.9958999752998352,"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/T10586","display_name":"Robotic Path Planning Algorithms","score":0.9958999752998352,"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/cruise-control","display_name":"Cruise control","score":0.6629269123077393},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.6101912260055542},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5903212428092957},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.5032753348350525},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.48544198274612427},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.46778616309165955},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.46281325817108154},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.453899085521698},{"id":"https://openalex.org/keywords/adaptive-control","display_name":"Adaptive control","score":0.45298466086387634},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.43558403849601746},{"id":"https://openalex.org/keywords/control-lyapunov-function","display_name":"Control-Lyapunov function","score":0.4322279095649719},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4185481369495392},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.4158990979194641},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.3536433279514313},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.338874489068985},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.30062127113342285},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.2506352663040161},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.13161256909370422},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09064134955406189}],"concepts":[{"id":"https://openalex.org/C113168747","wikidata":"https://www.wikidata.org/wiki/Q507295","display_name":"Cruise control","level":3,"score":0.6629269123077393},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.6101912260055542},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5903212428092957},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.5032753348350525},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.48544198274612427},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.46778616309165955},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.46281325817108154},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.453899085521698},{"id":"https://openalex.org/C107464732","wikidata":"https://www.wikidata.org/wiki/Q235781","display_name":"Adaptive control","level":3,"score":0.45298466086387634},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.43558403849601746},{"id":"https://openalex.org/C201030206","wikidata":"https://www.wikidata.org/wiki/Q5165805","display_name":"Control-Lyapunov function","level":5,"score":0.4322279095649719},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4185481369495392},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4158990979194641},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3536433279514313},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.338874489068985},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.30062127113342285},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.2506352663040161},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.13161256909370422},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09064134955406189},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2021.3105491","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2021.3105491","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":[{"id":"https://openalex.org/G2925537517","display_name":null,"funder_award_id":"IIS-1723995","funder_id":"https://openalex.org/F4320335353","funder_display_name":"National Science Foundation of Sri Lanka"},{"id":"https://openalex.org/G7505967209","display_name":null,"funder_award_id":"IIS-2024606","funder_id":"https://openalex.org/F4320335353","funder_display_name":"National Science Foundation of Sri Lanka"}],"funders":[{"id":"https://openalex.org/F4320335353","display_name":"National Science Foundation of Sri Lanka","ror":"https://ror.org/010xaa060"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1563025442","https://openalex.org/W1749724378","https://openalex.org/W1891170951","https://openalex.org/W1972149633","https://openalex.org/W1980569135","https://openalex.org/W1986164962","https://openalex.org/W2023126268","https://openalex.org/W2023250353","https://openalex.org/W2026616272","https://openalex.org/W2033118636","https://openalex.org/W2057950931","https://openalex.org/W2062373349","https://openalex.org/W2140531311","https://openalex.org/W2489231587","https://openalex.org/W2560504659","https://openalex.org/W2620840602","https://openalex.org/W2765203865","https://openalex.org/W2841721725","https://openalex.org/W2973005513","https://openalex.org/W2991303041","https://openalex.org/W3011888914","https://openalex.org/W3119862069","https://openalex.org/W3120233333","https://openalex.org/W3145799606","https://openalex.org/W4241586728"],"related_works":["https://openalex.org/W4285388621","https://openalex.org/W2771706547","https://openalex.org/W1983059685","https://openalex.org/W1607043069","https://openalex.org/W2190128593","https://openalex.org/W2375061895","https://openalex.org/W1980569135","https://openalex.org/W2356016423","https://openalex.org/W2098467803","https://openalex.org/W1541307762"],"abstract_inverted_index":{"We":[0,119,165,209],"approach":[1],"the":[2,52,80,83,87,101,148,159,162,184,188,211],"problem":[3,55],"of":[4,59,86,128,144,150,153,161],"stabilizing":[5],"a":[6,11,57,92,95,142,151],"dynamical":[7],"system":[8,88],"while":[9],"optimizing":[10],"cost":[12],"and":[13,17,25,39,115,175,177,183,218],"satisfying":[14],"safety":[15,38,96,113,134],"constraints":[16,114,171],"control":[18,23,33,40,54,117,168,217,220],"limitations.":[19,71,118],"For":[20,132],"(nonlinear)":[21],"affine":[22],"systems":[24,127],"quadratic":[26,60],"costs,":[27],"it":[28],"has":[29],"been":[30],"shown":[31],"that":[32,82,146],"barrier":[34],"functions":[35,42],"(CBFs)":[36],"guaranteeing":[37],"Lyapunov":[41],"(CLFs)":[43],"enforcing":[44,94],"convergence":[45],"can":[46,103,125,197],"be":[47,198],"used":[48],"to":[49,56,91],"(conservatively)":[50],"reduce":[51],"optimal":[53,167],"sequence":[58],"programs":[61],"(QPs).":[62],"Existing":[63],"works":[64],"in":[65,107,203],"this":[66],"category":[67],"have":[68],"two":[69,179],"main":[70],"First,":[72],"with":[73,89,111,170,206],"one":[74],"exception,":[75],"they":[76],"are":[77],"based":[78],"on":[79,214],"assumption":[81],"relative":[84,130],"degree":[85],"respect":[90],"function":[93],"constraint":[97],"is":[98],"one.":[99],"Second,":[100],"QPs":[102],"easily":[104],"become":[105],"infeasible,":[106],"particular":[108],"for":[109,200],"problems":[110,169],"many":[112],"tight":[116],"propose":[120,178],"high-order":[121],"CBFs":[122],"(HOCBFs),":[123],"which":[124,157],"accommodate":[126],"arbitrary":[129],"degrees.":[131],"each":[133],"constraint,":[135],"by":[136,173],"using":[137],"Lyapunov-like":[138],"conditions,":[139],"we":[140,192],"construct":[141],"set":[143,152],"controls":[145],"renders":[147],"intersection":[149],"sets":[154],"forward":[155],"invariant,":[156],"implies":[158],"satisfaction":[160],"original":[163],"constraint.":[164],"formulate":[166],"given":[172],"HOCBF":[174],"CLF,":[176],"methods\u2014the":[180],"penalty":[181],"method":[182],"parameterization":[185],"method\u2014to":[186],"address":[187],"feasibility":[189],"problem.":[190],"Finally,":[191],"show":[193],"how":[194],"our":[195],"methodology":[196],"extended":[199],"safe":[201],"navigation":[202],"unknown":[204],"environments":[205],"long-term":[207],"feasibility.":[208],"illustrate":[210],"proposed":[212],"framework":[213],"adaptive":[215],"cruise":[216],"robot":[219],"problems.":[221]},"counts_by_year":[{"year":2026,"cited_by_count":19},{"year":2025,"cited_by_count":144},{"year":2024,"cited_by_count":92},{"year":2023,"cited_by_count":48},{"year":2022,"cited_by_count":14},{"year":2021,"cited_by_count":3}],"updated_date":"2026-04-12T07:58:50.170612","created_date":"2025-10-10T00:00:00"}
