{"id":"https://openalex.org/W2146979191","doi":"https://doi.org/10.1109/cdc.2011.6160872","title":"Zonotope bundles for the efficient computation of reachable sets","display_name":"Zonotope bundles for the efficient computation of reachable sets","publication_year":2011,"publication_date":"2011-12-01","ids":{"openalex":"https://openalex.org/W2146979191","doi":"https://doi.org/10.1109/cdc.2011.6160872","mag":"2146979191"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2011.6160872","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6160872","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Conference on Decision and Control and European Control Conference","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://mediatum.ub.tum.de/1287219","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005383495","display_name":"Matthias Althoff","orcid":"https://orcid.org/0000-0003-3733-842X"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Matthias Althoff","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, USA","Dept. of Electrical and Computer Engineering, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, PA 15213, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Dept. of Electrical and Computer Engineering, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, PA 15213, USA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026562535","display_name":"Bruce H. Krogh","orcid":"https://orcid.org/0000-0003-1300-3553"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bruce H. Krogh","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, USA","Dept. of Electrical and Computer Engineering, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, PA 15213, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Dept. of Electrical and Computer Engineering, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, PA 15213, USA","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5005383495"],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":null,"apc_paid":null,"fwci":2.2495,"has_fulltext":false,"cited_by_count":120,"citation_normalized_percentile":{"value":0.8816501,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"6814","last_page":"6821"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9976999759674072,"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":0.9976999759674072,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.992900013923645,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.972599983215332,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.7966840267181396},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6888201236724854},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.6278248429298401},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.591559886932373},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5559885501861572},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5109783411026001},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.47097209095954895},{"id":"https://openalex.org/keywords/set-operations","display_name":"Set operations","score":0.4450909197330475},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.33239907026290894},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1632249355316162},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.05869913101196289},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05819499492645264}],"concepts":[{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.7966840267181396},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6888201236724854},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.6278248429298401},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.591559886932373},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5559885501861572},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5109783411026001},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47097209095954895},{"id":"https://openalex.org/C2777168461","wikidata":"https://www.wikidata.org/wiki/Q42196253","display_name":"Set operations","level":3,"score":0.4450909197330475},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33239907026290894},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1632249355316162},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.05869913101196289},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05819499492645264},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/cdc.2011.6160872","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6160872","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Conference on Decision and Control and European Control Conference","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.665.3088","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.665.3088","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www6.in.tum.de/Main/Publications/Althoff2011f.pdf","raw_type":"text"},{"id":"pmh:oai:mediatum.ub.tum.de:node/1287219","is_oa":true,"landing_page_url":"https://mediatum.ub.tum.de/1287219","pdf_url":null,"source":{"id":"https://openalex.org/S4377196330","display_name":"mediaTUM  (Technical University of Munich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I62916508","host_organization_name":"Technical University of Munich","host_organization_lineage":["https://openalex.org/I62916508"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"ConferencePaper"}],"best_oa_location":{"id":"pmh:oai:mediatum.ub.tum.de:node/1287219","is_oa":true,"landing_page_url":"https://mediatum.ub.tum.de/1287219","pdf_url":null,"source":{"id":"https://openalex.org/S4377196330","display_name":"mediaTUM  (Technical University of Munich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I62916508","host_organization_name":"Technical University of Munich","host_organization_lineage":["https://openalex.org/I62916508"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"ConferencePaper"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W611235695","https://openalex.org/W1504868247","https://openalex.org/W1511213320","https://openalex.org/W1522694098","https://openalex.org/W1532859487","https://openalex.org/W1536651105","https://openalex.org/W1550314527","https://openalex.org/W1569692898","https://openalex.org/W1600235415","https://openalex.org/W1698848442","https://openalex.org/W1726255445","https://openalex.org/W1972596071","https://openalex.org/W1975630497","https://openalex.org/W1994475353","https://openalex.org/W1994826906","https://openalex.org/W1997398211","https://openalex.org/W2026019548","https://openalex.org/W2046691604","https://openalex.org/W2051110650","https://openalex.org/W2062873592","https://openalex.org/W2071775092","https://openalex.org/W2102022978","https://openalex.org/W2113922565","https://openalex.org/W2116364955","https://openalex.org/W2116679494","https://openalex.org/W2127067432","https://openalex.org/W2131441094","https://openalex.org/W2145201569","https://openalex.org/W2147936671","https://openalex.org/W2158451642","https://openalex.org/W2162305089","https://openalex.org/W2165276844","https://openalex.org/W2750147881","https://openalex.org/W2904982962","https://openalex.org/W4236306094","https://openalex.org/W4300995080","https://openalex.org/W6637971106","https://openalex.org/W6643373946","https://openalex.org/W6657187930","https://openalex.org/W6681835926","https://openalex.org/W6682072896"],"related_works":["https://openalex.org/W2990978680","https://openalex.org/W4242736492","https://openalex.org/W2385407215","https://openalex.org/W2990792327","https://openalex.org/W578461542","https://openalex.org/W2950627472","https://openalex.org/W3169083941","https://openalex.org/W4385627906","https://openalex.org/W2901706453","https://openalex.org/W3173668982"],"abstract_inverted_index":{"We":[0,59],"introduce":[1,60],"zonotope":[2,61,99],"bundles":[3,62,74,100],"for":[4,38,89],"computing":[5,70],"the":[6,18,26,64,71],"set":[7,22],"of":[8,28,66,84,98],"states":[9],"reachable":[10,19],"by":[11,35],"a":[12],"dynamical":[13],"system,":[14],"also":[15],"known":[16],"as":[17,63],"set.":[20],"Reachable":[21],"computations":[23],"suffer":[24],"from":[25],"curse":[27],"dimensionality,":[29],"which":[30],"has":[31],"been":[32],"successfully":[33],"addressed":[34],"using":[36],"zonotopes":[37,42,67],"linear":[39],"systems.":[40,94],"However,":[41],"are":[43,75],"not":[44],"closed":[45,76],"under":[46,77],"intersection":[47,65],"leading":[48],"to":[49,54],"challenges":[50],"when":[51],"applying":[52],"them":[53],"nonlinear":[55],"and":[56,92],"hybrid":[57,93],"problems.":[58],"(without":[68],"explicitly":[69],"intersection).":[72],"Zonotope":[73],"intersection,":[78],"while":[79],"inheriting":[80],"many":[81],"positive":[82],"properties":[83],"zonotopes.":[85],"This":[86],"is":[87,101],"demonstrated":[88],"linear,":[90],"nonlinear,":[91],"A":[95],"further":[96],"property":[97],"that":[102],"their":[103],"computation":[104],"can":[105],"be":[106],"easily":[107],"parallelized.":[108]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":12},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":13},{"year":2021,"cited_by_count":14},{"year":2020,"cited_by_count":18},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
