{"id":"https://openalex.org/W7123353754","doi":"https://doi.org/10.1109/tac.2026.3652909","title":"Guaranteed Reachability on Riemannian Manifolds for Unknown Nonlinear Systems","display_name":"Guaranteed Reachability on Riemannian Manifolds for Unknown Nonlinear Systems","publication_year":2026,"publication_date":"2026-01-12","ids":{"openalex":"https://openalex.org/W7123353754","doi":"https://doi.org/10.1109/tac.2026.3652909"},"language":null,"primary_location":{"id":"doi:10.1109/tac.2026.3652909","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2026.3652909","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/A5033958416","display_name":"Taha Shafa","orcid":"https://orcid.org/0000-0002-8121-585X"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Taha Shafa","raw_affiliation_strings":["Department of Aerospace Engineering and the Coordinated Science Laboratory, University of Illinois Urbana-Champaign, Urbana, IL, USA"],"raw_orcid":"https://orcid.org/0000-0002-8121-585X","affiliations":[{"raw_affiliation_string":"Department of Aerospace Engineering and the Coordinated Science Laboratory, University of Illinois Urbana-Champaign, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5107673093","display_name":"Melkior Ornik","orcid":null},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Melkior Ornik","raw_affiliation_strings":["Department of Aerospace Engineering and the Coordinated Science Laboratory, University of Illinois Urbana-Champaign, Urbana, IL, USA"],"raw_orcid":"https://orcid.org/0000-0002-8510-8787","affiliations":[{"raw_affiliation_string":"Department of Aerospace Engineering and the Coordinated Science Laboratory, University of Illinois Urbana-Champaign, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05076311,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"71","issue":"6","first_page":"4153","last_page":"4159"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11082","display_name":"Spacecraft Dynamics and Control","score":0.21310000121593475,"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":0.21310000121593475,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.09520000219345093,"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":0.08860000222921371,"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/reachability","display_name":"Reachability","score":0.8208000063896179},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.6406000256538391},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5370000004768372},{"id":"https://openalex.org/keywords/riemannian-manifold","display_name":"Riemannian manifold","score":0.5324000120162964},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.5303999781608582},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.5174000263214111},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.5},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.46630001068115234},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.45239999890327454},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.427700012922287}],"concepts":[{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.8208000063896179},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6406000256538391},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5385000109672546},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5370000004768372},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.5324000120162964},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.5303999781608582},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5174000263214111},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.5},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.46630001068115234},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.45239999890327454},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.427700012922287},{"id":"https://openalex.org/C77405623","wikidata":"https://www.wikidata.org/wiki/Q598451","display_name":"System dynamics","level":2,"score":0.4221000075340271},{"id":"https://openalex.org/C28903235","wikidata":"https://www.wikidata.org/wiki/Q746550","display_name":"Tangent bundle","level":3,"score":0.4174000024795532},{"id":"https://openalex.org/C181104567","wikidata":"https://www.wikidata.org/wiki/Q761383","display_name":"Riemannian geometry","level":2,"score":0.39250001311302185},{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.3887999951839447},{"id":"https://openalex.org/C157157409","wikidata":"https://www.wikidata.org/wiki/Q909601","display_name":"Tangent space","level":2,"score":0.3831000030040741},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3695000112056732},{"id":"https://openalex.org/C91581856","wikidata":"https://www.wikidata.org/wiki/Q2707001","display_name":"Nonlinear control","level":3,"score":0.3637999892234802},{"id":"https://openalex.org/C164953516","wikidata":"https://www.wikidata.org/wiki/Q320357","display_name":"Closed set","level":2,"score":0.36239999532699585},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3481999933719635},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.3456999957561493},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.33660000562667847},{"id":"https://openalex.org/C2779662365","wikidata":"https://www.wikidata.org/wiki/Q5416694","display_name":"Event (particle physics)","level":2,"score":0.33000001311302185},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3149000108242035},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3140000104904175},{"id":"https://openalex.org/C148047603","wikidata":"https://www.wikidata.org/wiki/Q1014612","display_name":"Parallelizable manifold","level":2,"score":0.3009999990463257},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.29019999504089355},{"id":"https://openalex.org/C2778134712","wikidata":"https://www.wikidata.org/wiki/Q1047307","display_name":"Bundle","level":2,"score":0.28999999165534973},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.27790001034736633},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.2757999897003174},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.27070000767707825},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2572000026702881},{"id":"https://openalex.org/C50897621","wikidata":"https://www.wikidata.org/wiki/Q2665508","display_name":"Hybrid system","level":2,"score":0.25690001249313354},{"id":"https://openalex.org/C81074085","wikidata":"https://www.wikidata.org/wiki/Q366872","display_name":"Motion planning","level":3,"score":0.2540999948978424},{"id":"https://openalex.org/C31531917","wikidata":"https://www.wikidata.org/wiki/Q915157","display_name":"Robust control","level":3,"score":0.25279998779296875}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2026.3652909","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2026.3652909","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":[{"score":0.47513434290885925,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G3995854737","display_name":null,"funder_award_id":"80NSSC22M0070","funder_id":"https://openalex.org/F4320306101","funder_display_name":"National Aeronautics and Space Administration"},{"id":"https://openalex.org/G7149411701","display_name":null,"funder_award_id":"FA9550-23-1-0131","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"}],"funders":[{"id":"https://openalex.org/F4320306101","display_name":"National Aeronautics and Space Administration","ror":"https://ror.org/027ka1x80"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Determining":[0],"the":[1,24,31,52,57,76,91,110,121,141,148,163,190,208],"reachable":[2,25,84,161],"set":[3,26,85,117,143,159,210],"for":[4,12,16],"a":[5,46,82,103,115,125,134,145,157,169,201],"given":[6,170],"nonlinear":[7],"system":[8,153,165,204],"is":[9,27],"critically":[10],"important":[11],"autonomous":[13],"trajectory":[14],"planning":[15],"reach-avoid":[17],"applications":[18],"and":[19,49],"safety":[20],"critical":[21],"scenarios.":[22],"Providing":[23],"generally":[28],"impossible":[29],"when":[30],"dynamics":[32,44,58],"are":[33,98,106,174],"unknown,":[34],"so":[35],"we":[36,78,196],"calculate":[37],"underapproximations":[38],"of":[39,54,56,86,90,118,124,150,160,193,211],"such":[40],"sets":[41],"using":[42],"local":[43],"at":[45],"single":[47],"point":[48],"bounds":[50],"on":[51,102,120,179,183,207],"rate":[53],"change":[55,74],"determined":[59],"from":[60],"known":[61,99],"physical":[62],"laws.":[63],"Motivated":[64],"by":[65,108],"scenarios":[66],"where":[67],"an":[68,72],"adverse":[69],"event":[70],"causes":[71],"abrupt":[73],"in":[75],"dynamics,":[77],"attempt":[79],"to":[80,100,113,177,200],"determine":[81],"provably":[83],"states":[87,162],"without":[88],"knowledge":[89,112],"dynamics.":[92],"This":[93],"paper":[94],"considers":[95],"systems":[96,180],"which":[97,205],"operate":[101,182],"manifold.":[104,187],"Underapproximations":[105],"calculated":[107],"utilizing":[109],"aforementioned":[111],"derive":[114],"guaranteed":[116,158],"velocities":[119],"tangent":[122],"bundle":[123],"complete":[126,185],"Riemannian":[127,186],"manifold":[128],"that":[129,181],"can":[130,166],"be":[131],"reached":[132],"within":[133,168],"finite":[135],"time":[136],"horizon.":[137],"We":[138],"then":[139],"interpret":[140],"underapproximated":[142],"as":[144],"control":[146,152],"system;":[147],"trajectories":[149],"this":[151],"provide":[154],"us":[155],"with":[156],"unknown":[164],"reach":[167],"time.":[171],"The":[172],"results":[173],"general":[175],"enough":[176],"apply":[178,197],"any":[184],"To":[188],"illustrate":[189],"practical":[191],"implementation":[192],"our":[194,198],"results,":[195],"algorithm":[199],"three-dimensional":[202],"rotational":[203],"lives":[206],"abstract":[209],"special":[212],"orthogonal":[213],"matrices.":[214]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-01-14T00:00:00"}