{"id":"https://openalex.org/W3155136512","doi":"https://doi.org/10.1109/tac.2021.3097704","title":"Hybrid Feedback for Global Tracking on Matrix Lie Groups $SO(3)$ and $SE(3)$","display_name":"Hybrid Feedback for Global Tracking on Matrix Lie Groups $SO(3)$ and $SE(3)$","publication_year":2021,"publication_date":"2021-08-24","ids":{"openalex":"https://openalex.org/W3155136512","doi":"https://doi.org/10.1109/tac.2021.3097704","mag":"3155136512"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2021.3097704","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2021.3097704","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2012.12470","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Miaomiao Wang","orcid":"https://orcid.org/0000-0001-7498-5162"},"institutions":[{"id":"https://openalex.org/I125749732","display_name":"Western University","ror":"https://ror.org/02grkyz14","country_code":"CA","type":"education","lineage":["https://openalex.org/I125749732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Miaomiao Wang","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Western University, London, ON, Canada"],"raw_orcid":"https://orcid.org/0000-0001-7498-5162","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Western University, London, ON, Canada","institution_ids":["https://openalex.org/I125749732"]}]},{"author_position":"last","author":{"id":null,"display_name":"Abdelhamid Tayebi","orcid":"https://orcid.org/0000-0002-9049-4651"},"institutions":[{"id":"https://openalex.org/I72541430","display_name":"Lakehead University","ror":"https://ror.org/023p7mg82","country_code":"CA","type":"education","lineage":["https://openalex.org/I72541430"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Abdelhamid Tayebi","raw_affiliation_strings":["Department of Electrical Engineering, Lakehead University, Thunder Bay, ON, Canada"],"raw_orcid":"https://orcid.org/0000-0002-9049-4651","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Lakehead University, Thunder Bay, ON, Canada","institution_ids":["https://openalex.org/I72541430"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2645,"currency":"USD","value_usd":2645},"apc_paid":null,"fwci":2.3052,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.87761576,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"67","issue":"6","first_page":"2930","last_page":"2945"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.38260000944137573,"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":0.38260000944137573,"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/T11615","display_name":"Control and Dynamics of Mobile Robots","score":0.3012000024318695,"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":0.10729999840259552,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6891999840736389},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.6586999893188477},{"id":"https://openalex.org/keywords/hybrid-system","display_name":"Hybrid system","score":0.5658000111579895},{"id":"https://openalex.org/keywords/classification-of-discontinuities","display_name":"Classification of discontinuities","score":0.5353000164031982},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.49880000948905945},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4562000036239624},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.45399999618530273},{"id":"https://openalex.org/keywords/tracking","display_name":"Tracking (education)","score":0.43549999594688416},{"id":"https://openalex.org/keywords/maxima-and-minima","display_name":"Maxima and minima","score":0.4081999957561493}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6891999840736389},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.6586999893188477},{"id":"https://openalex.org/C50897621","wikidata":"https://www.wikidata.org/wiki/Q2665508","display_name":"Hybrid system","level":2,"score":0.5658000111579895},{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.5353000164031982},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.49880000948905945},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4562000036239624},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.45399999618530273},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4537999927997589},{"id":"https://openalex.org/C2775936607","wikidata":"https://www.wikidata.org/wiki/Q466845","display_name":"Tracking (education)","level":2,"score":0.43549999594688416},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.4081999957561493},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.3797999918460846},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3772999942302704},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.3725999891757965},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3684000074863434},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.29660001397132874},{"id":"https://openalex.org/C2778925954","wikidata":"https://www.wikidata.org/wiki/Q16883749","display_name":"Stability criterion","level":3,"score":0.2962000072002411},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.2930000126361847},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.2924000024795532},{"id":"https://openalex.org/C5594486","wikidata":"https://www.wikidata.org/wiki/Q161635","display_name":"Angular velocity","level":2,"score":0.2856999933719635},{"id":"https://openalex.org/C110521144","wikidata":"https://www.wikidata.org/wiki/Q193460","display_name":"Scalar field","level":2,"score":0.28450000286102295},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.28189998865127563},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.27730000019073486},{"id":"https://openalex.org/C143170015","wikidata":"https://www.wikidata.org/wiki/Q17007850","display_name":"Stability conditions","level":3,"score":0.26489999890327454},{"id":"https://openalex.org/C183356978","wikidata":"https://www.wikidata.org/wiki/Q1779213","display_name":"Tracking error","level":3,"score":0.26330000162124634},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.25920000672340393},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.257999986410141},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.2554999887943268},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.2540999948978424},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.25200000405311584}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tac.2021.3097704","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2021.3097704","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"},{"id":"pmh:oai:arXiv.org:2012.12470","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2012.12470","pdf_url":"https://arxiv.org/pdf/2012.12470","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2012.12470","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2012.12470","pdf_url":"https://arxiv.org/pdf/2012.12470","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4762275927","display_name":"Advanced Autonomous Navigation Systems for UAVs","funder_award_id":"rgpin-2020-06270","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W1486721501","https://openalex.org/W1515493836","https://openalex.org/W1913840001","https://openalex.org/W1980330256","https://openalex.org/W1989230227","https://openalex.org/W1990181132","https://openalex.org/W2010359902","https://openalex.org/W2018431869","https://openalex.org/W2046079947","https://openalex.org/W2046287268","https://openalex.org/W2053442363","https://openalex.org/W2097020018","https://openalex.org/W2099308299","https://openalex.org/W2099388669","https://openalex.org/W2107615213","https://openalex.org/W2124228020","https://openalex.org/W2125691646","https://openalex.org/W2127918239","https://openalex.org/W2128972576","https://openalex.org/W2134961099","https://openalex.org/W2137427741","https://openalex.org/W2138151497","https://openalex.org/W2139799964","https://openalex.org/W2164259133","https://openalex.org/W2171133852","https://openalex.org/W2284537696","https://openalex.org/W2341206624","https://openalex.org/W2607474514","https://openalex.org/W2614898534","https://openalex.org/W2790828129","https://openalex.org/W2943966153","https://openalex.org/W2947014877","https://openalex.org/W2950202372","https://openalex.org/W2962022437","https://openalex.org/W2962965379","https://openalex.org/W2973341089","https://openalex.org/W3012254807","https://openalex.org/W3103458591","https://openalex.org/W4255043376","https://openalex.org/W6748532899"],"related_works":[],"abstract_inverted_index":{"We":[0],"introduce":[1],"a":[2,43,75,92,122],"new":[3,89],"hybrid":[4,16,90,93,135,159,182,197],"control":[5,95,116,136,160],"strategy,":[6],"which":[7,59],"is":[8,113,118],"conceptually":[9],"different":[10],"from":[11,64],"the":[12,22,25,61,65,71,78,82,98,127,130,143,146,152,157,169,179,192,195],"commonly":[13],"used":[14],"synergistic":[15,181],"approaches,":[17],"to":[18,168,178,190],"efficiently":[19],"deal":[20],"with":[21,54,104,176],"problem":[23,101,171],"of":[24,77,145,156,194],"undesired":[26,66],"equilibria":[27],"that":[28,125],"precludes":[29],"smooth":[30],"vectors":[31],"fields":[32],"on$SO(3)$from":[33],"achieving":[34],"global":[35,105],"stability.":[36],"The":[37,133],"key":[38],"idea":[39],"consists":[40],"in":[41,129,139],"constructing":[42],"suitable":[44],"potential":[45,79],"function":[46,80],"on$SO(3)\\times":[47],"\\mathbb":[48],"{R}$involving":[49],"an":[50],"auxiliary":[51],"scalar":[52],"variable,":[53],"flow":[55],"and":[56,84,108],"jump":[57],"dynamics,":[58],"keeps":[60],"state":[62],"away":[63],"critical":[67],"points":[68],"while,":[69],"at":[70],"same":[72],"time,":[73],"guarantees":[74,155],"decrease":[76],"over":[81],"flows":[83],"jumps.":[85],"Based":[86],"on":[87],"this":[88,140],"mechanism,":[91],"feedback":[94],"scheme":[96,117],"for":[97],"attitude":[99],"tracking":[100,170],"on$SO(3)$,":[102],"endowed":[103],"asymptotic":[106],"stability":[107,111,154],"semiglobal":[109],"exponential":[110],"guarantees,":[112],"proposed.":[114],"This":[115,162],"further":[119],"improved":[120],"through":[121],"smoothing":[123],"mechanism":[124],"removes":[126,142],"discontinuities":[128],"input":[131],"torque.":[132],"third":[134],"scheme,":[137],"proposed":[138,196],"article,":[141],"requirement":[144],"angular":[147],"velocity":[148],"measurements,":[149],"while":[150],"preserving":[151],"strong":[153],"first":[158],"scheme.":[161],"approach":[163],"has":[164],"also":[165],"been":[166],"applied":[167],"on$SE(3)$to":[172],"illustrate":[173,191],"its":[174],"advantages":[175],"respect":[177],"existing":[180],"approaches.":[183],"Finally,":[184],"some":[185],"simulation":[186],"results":[187],"are":[188],"presented":[189],"performance":[193],"controllers.":[198]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":4}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2021-04-26T00:00:00"}