{"id":"https://openalex.org/W4398151265","doi":"https://doi.org/10.1109/lcsys.2024.3403468","title":"Reachable Sets of Homogeneous Polynomial Dynamical Systems Using Exact Solutions","display_name":"Reachable Sets of Homogeneous Polynomial Dynamical Systems Using Exact Solutions","publication_year":2024,"publication_date":"2024-01-01","ids":{"openalex":"https://openalex.org/W4398151265","doi":"https://doi.org/10.1109/lcsys.2024.3403468"},"language":"en","primary_location":{"id":"doi:10.1109/lcsys.2024.3403468","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/lcsys.2024.3403468","pdf_url":null,"source":{"id":"https://openalex.org/S4306422535","display_name":"IEEE Control Systems Letters","issn_l":"2475-1456","issn":["2475-1456"],"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 Control Systems Letters","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/A5098716584","display_name":"Soham Sachin Purohit","orcid":"https://orcid.org/0009-0006-6604-2870"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Soham Sachin Purohit","raw_affiliation_strings":["Robotics Department, University of Michigan, Ann Arbor, MI, USA"],"raw_orcid":"https://orcid.org/0009-0006-6604-2870","affiliations":[{"raw_affiliation_string":"Robotics Department, University of Michigan, Ann Arbor, MI, USA","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100761812","display_name":"Can Chen","orcid":"https://orcid.org/0000-0003-2310-0074"},"institutions":[{"id":"https://openalex.org/I114027177","display_name":"University of North Carolina at Chapel Hill","ror":"https://ror.org/0130frc33","country_code":"US","type":"education","lineage":["https://openalex.org/I114027177"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Can Chen","raw_affiliation_strings":["Department of Mathematics, School of Data Science and Society, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA","School of Data Science and Society and the Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA"],"raw_orcid":"https://orcid.org/0000-0003-2310-0074","affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Data Science and Society, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA","institution_ids":["https://openalex.org/I114027177"]},{"raw_affiliation_string":"School of Data Science and Society and the Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA","institution_ids":["https://openalex.org/I114027177"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053632225","display_name":"Ram Vasudevan","orcid":"https://orcid.org/0000-0003-1978-0572"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ram Vasudevan","raw_affiliation_strings":["Robotics Department, University of Michigan, Ann Arbor, MI, USA"],"raw_orcid":"https://orcid.org/0000-0003-1978-0572","affiliations":[{"raw_affiliation_string":"Robotics Department, University of Michigan, Ann Arbor, MI, USA","institution_ids":["https://openalex.org/I27837315"]}]}],"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":0.08568955,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"8","issue":null,"first_page":"742","last_page":"747"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9606999754905701,"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"}},"topics":[{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9606999754905701,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9549999833106995,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10586","display_name":"Robotic Path Planning Algorithms","score":0.9348999857902527,"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/reachability","display_name":"Reachability","score":0.9490053653717041},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.7892411947250366},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.6306264996528625},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.5571131706237793},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5531432628631592},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.545700192451477},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.5366361141204834},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.4893609881401062},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.46585187315940857},{"id":"https://openalex.org/keywords/reachability-problem","display_name":"Reachability problem","score":0.452513724565506},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.4463389217853546},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.41401612758636475},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4093261957168579},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3940422236919403},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.35478687286376953},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3388161361217499},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.19341295957565308},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1268315315246582},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07023480534553528},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.06896176934242249}],"concepts":[{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.9490053653717041},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.7892411947250366},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6306264996528625},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.5571131706237793},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5531432628631592},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.545700192451477},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.5366361141204834},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.4893609881401062},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.46585187315940857},{"id":"https://openalex.org/C2777669093","wikidata":"https://www.wikidata.org/wiki/Q17141570","display_name":"Reachability problem","level":3,"score":0.452513724565506},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.4463389217853546},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.41401612758636475},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4093261957168579},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3940422236919403},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.35478687286376953},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3388161361217499},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19341295957565308},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1268315315246582},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07023480534553528},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.06896176934242249},{"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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:10.1109/lcsys.2024.3403468","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/lcsys.2024.3403468","pdf_url":null,"source":{"id":"https://openalex.org/S4306422535","display_name":"IEEE Control Systems Letters","issn_l":"2475-1456","issn":["2475-1456"],"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 Control Systems Letters","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5808432839","display_name":"CAREER: Automating the Construction and Analysis of Models of Motion for Prehabilitative Care","funder_award_id":"1751093","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"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1546990169","https://openalex.org/W1987592584","https://openalex.org/W1996286784","https://openalex.org/W2093350522","https://openalex.org/W2156841851","https://openalex.org/W2158451642","https://openalex.org/W2576277975","https://openalex.org/W2911202212","https://openalex.org/W2962780963","https://openalex.org/W3081975785","https://openalex.org/W3093840532","https://openalex.org/W3138965496","https://openalex.org/W4307539204","https://openalex.org/W4391473767"],"related_works":["https://openalex.org/W4253760428","https://openalex.org/W2047831585","https://openalex.org/W3208672221","https://openalex.org/W3017277461","https://openalex.org/W2099490078","https://openalex.org/W4287199681","https://openalex.org/W3172202899","https://openalex.org/W4224983736","https://openalex.org/W4389158950","https://openalex.org/W5179970"],"abstract_inverted_index":{"Reachability":[0],"analysis":[1,83],"is":[2],"a":[3,24,39,78,121],"powerful":[4],"tool":[5],"to":[6,18,53,68,104,132],"analyze":[7],"the":[8,21,54,58,109,125],"behavior":[9],"of":[10,23,35,42,57,84,108,127],"dynamical":[11,59],"systems.":[12,70],"Typically,":[13],"these":[14,48],"tools":[15,49],"are":[16],"used":[17],"evaluate":[19],"whether":[20],"dynamics":[22],"system":[25],"beginning":[26],"from":[27],"some":[28,32],"initial":[29],"set":[30,111,129],"reaches":[31],"unsafe":[33],"region":[34],"state":[36],"space":[37],"in":[38,124],"finite":[40],"amount":[41],"time.":[43],"To":[44,71],"answer":[45],"this":[46,73,75,100],"question,":[47],"often":[50],"construct":[51],"over-approximations":[52,107],"reachable":[55,110,128],"sets":[56],"systems,":[60],"which":[61],"can":[62],"be":[63],"overly":[64],"conservative":[65],"when":[66],"applied":[67],"arbitrary":[69],"address":[72],"challenge,":[74],"letter":[76,101],"develops":[77],"novel":[79],"technique":[80],"for":[81,112,135],"reachability":[82],"Homogeneous":[85],"Polynomial":[86],"Dynamical":[87],"Systems":[88],"(HPDSs)":[89],"by":[90],"computing":[91],"their":[92],"exact":[93],"solutions":[94],"using":[95],"tensor":[96],"theory.":[97],"In":[98],"addition,":[99],"illustrates":[102],"how":[103],"build":[105],"tight":[106],"HPDSs":[113],"with":[114],"constant":[115],"control":[116],"inputs.":[117],"Simulation":[118],"results":[119],"highlight":[120],"significant":[122],"improvement":[123],"accuracy":[126],"estimates":[130],"compared":[131],"established":[133],"methods":[134],"HPDSs.":[136]},"counts_by_year":[],"updated_date":"2025-12-26T23:08:49.675405","created_date":"2025-10-10T00:00:00"}
