{"id":"https://openalex.org/W2075092532","doi":"https://doi.org/10.1080/00207170903159285","title":"Efficient mode enumeration of compositional hybrid systems","display_name":"Efficient mode enumeration of compositional hybrid systems","publication_year":2009,"publication_date":"2009-11-02","ids":{"openalex":"https://openalex.org/W2075092532","doi":"https://doi.org/10.1080/00207170903159285","mag":"2075092532"},"language":"en","primary_location":{"id":"doi:10.1080/00207170903159285","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207170903159285","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of 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/A5062933986","display_name":"Tobias Geyer","orcid":null},"institutions":[{"id":"https://openalex.org/I154130895","display_name":"University of Auckland","ror":"https://ror.org/03b94tp07","country_code":"NZ","type":"education","lineage":["https://openalex.org/I154130895"]}],"countries":["NZ"],"is_corresponding":true,"raw_author_name":"Tobias Geyer","raw_affiliation_strings":["The University of Auckland","Department of Electrical and Computer Engineering , The University of Auckland , Auckland 1052, New Zealand"],"affiliations":[{"raw_affiliation_string":"The University of Auckland","institution_ids":["https://openalex.org/I154130895"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering , The University of Auckland , Auckland 1052, New Zealand","institution_ids":["https://openalex.org/I154130895"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048895200","display_name":"Fabio Danilo Torrisi","orcid":null},"institutions":[{"id":"https://openalex.org/I75380228","display_name":"McKinsey & Company (United States)","ror":"https://ror.org/01gmv5d77","country_code":"US","type":"company","lineage":["https://openalex.org/I75380228"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Fabio D. Torrisi","raw_affiliation_strings":["McKinsey & Company","McKinsey & Company , Zurich, Switzerland"],"affiliations":[{"raw_affiliation_string":"McKinsey & Company","institution_ids":["https://openalex.org/I75380228"]},{"raw_affiliation_string":"McKinsey & Company , Zurich, Switzerland","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025946191","display_name":"Manfred Morari","orcid":"https://orcid.org/0000-0002-7696-5058"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Manfred Morari","raw_affiliation_strings":["Automatic Control Laboratory, ETH Zurich","Automatic Control Laboratory, ETH Zurich , 8092 Zurich, Switzerland"],"affiliations":[{"raw_affiliation_string":"Automatic Control Laboratory, ETH Zurich","institution_ids":["https://openalex.org/I35440088"]},{"raw_affiliation_string":"Automatic Control Laboratory, ETH Zurich , 8092 Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5062933986"],"corresponding_institution_ids":["https://openalex.org/I154130895"],"apc_list":null,"apc_paid":null,"fwci":1.5061654,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.8578852,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"83","issue":"2","first_page":"313","last_page":"329"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9998999834060669,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9998999834060669,"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/T10142","display_name":"Formal Methods in Verification","score":0.9991999864578247,"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/T10933","display_name":"Real-Time Systems Scheduling","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/hyperplane","display_name":"Hyperplane","score":0.7897955179214478},{"id":"https://openalex.org/keywords/enumeration","display_name":"Enumeration","score":0.6891005039215088},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5488836765289307},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5295147895812988},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.49935388565063477},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4961036145687103},{"id":"https://openalex.org/keywords/position","display_name":"Position (finance)","score":0.45297685265541077},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4397999942302704},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.42901164293289185},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36292070150375366},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2563183009624481},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.16721734404563904},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.08504700660705566}],"concepts":[{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.7897955179214478},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.6891005039215088},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5488836765289307},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5295147895812988},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.49935388565063477},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4961036145687103},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.45297685265541077},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4397999942302704},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.42901164293289185},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36292070150375366},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2563183009624481},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.16721734404563904},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.08504700660705566},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207170903159285","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207170903159285","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321652","display_name":"Eidgen\u00f6ssische Technische Hochschule Z\u00fcrich","ror":"https://ror.org/05a28rw58"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W1498631091","https://openalex.org/W1505326867","https://openalex.org/W1511213320","https://openalex.org/W1519532587","https://openalex.org/W1521695632","https://openalex.org/W1536934246","https://openalex.org/W1544715633","https://openalex.org/W1549845529","https://openalex.org/W1553814243","https://openalex.org/W1569787476","https://openalex.org/W1592788962","https://openalex.org/W1608135958","https://openalex.org/W1845049437","https://openalex.org/W1977985274","https://openalex.org/W1984325782","https://openalex.org/W2020574634","https://openalex.org/W2022266599","https://openalex.org/W2023599497","https://openalex.org/W2030996579","https://openalex.org/W2057084070","https://openalex.org/W2058702778","https://openalex.org/W2072508748","https://openalex.org/W2105708535","https://openalex.org/W2109175736","https://openalex.org/W2138947309","https://openalex.org/W2138988438","https://openalex.org/W2152156200","https://openalex.org/W2164277868","https://openalex.org/W2331952463","https://openalex.org/W2524114918","https://openalex.org/W2744286487","https://openalex.org/W2911432472","https://openalex.org/W3150565301","https://openalex.org/W4242409733","https://openalex.org/W4300640952"],"related_works":["https://openalex.org/W108845024","https://openalex.org/W4300125793","https://openalex.org/W2578985712","https://openalex.org/W2406961474","https://openalex.org/W2143566611","https://openalex.org/W2013740965","https://openalex.org/W2369655046","https://openalex.org/W588267724","https://openalex.org/W4297743441","https://openalex.org/W2375279953"],"abstract_inverted_index":{"A":[0],"hyperplane":[1],"arrangement":[2,17],"is":[3,67],"a":[4,25,41],"polyhedral":[5],"cell":[6,14],"complex":[7],"where":[8],"the":[9,16,19,38,48,65,76,81,89,92,96,100,113],"relative":[10],"position":[11],"of":[12,15,40,50,80,91,99],"each":[13],"and":[18,43,61,95,105,115],"composing":[20],"hyperplanes":[21],"are":[22,110],"summarised":[23],"by":[24],"sign":[26],"vector":[27],"computable":[28],"in":[29],"polynomial":[30],"time.":[31],"This":[32],"tool":[33,71],"from":[34],"computational":[35,118],"geometry":[36],"enables":[37],"development":[39],"fast":[42],"efficient":[44],"algorithm":[45,114],"to":[46,62,87],"translate":[47],"composition":[49,66],"discrete-time":[51],"linear":[52],"hybrid":[53],"systems":[54],"into":[55],"an":[56],"equivalent":[57],"piecewise":[58],"affine":[59],"model":[60,106],"determine":[63],"if":[64],"well":[68],"posed.":[69],"The":[70],"also":[72],"provides":[73],"information":[74],"on":[75],"real":[77],"combinatorial":[78],"degree":[79],"system":[82],"which":[83],"can":[84],"be":[85],"used":[86],"reduce":[88],"size":[90],"search":[93],"tree":[94],"computation":[97],"time":[98],"optimisation":[101],"algorithms":[102],"underlying":[103],"optimal":[104],"predictive":[107],"control.":[108],"Examples":[109],"presented":[111],"illustrating":[112],"showing":[116],"its":[117],"effectiveness.":[119]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-01-22T23:29:09.771500","created_date":"2025-10-10T00:00:00"}
