{"id":"https://openalex.org/W2146269846","doi":"https://doi.org/10.1109/cdc.2007.4434805","title":"Reachability and control of affine hypersurface systems on polytopes","display_name":"Reachability and control of affine hypersurface systems on polytopes","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2146269846","doi":"https://doi.org/10.1109/cdc.2007.4434805","mag":"2146269846"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2007.4434805","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2007.4434805","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 46th IEEE Conference on Decision and Control","raw_type":"proceedings-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/A5042932080","display_name":"Zhiyun Lin","orcid":"https://orcid.org/0000-0002-5523-4467"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Zhiyun Lin","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Toronto, Toronto, ONT, Canada","University of Toronto, (Toronto)"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Toronto, Toronto, ONT, Canada","institution_ids":["https://openalex.org/I185261750"]},{"raw_affiliation_string":"University of Toronto, (Toronto)","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016807277","display_name":"Mireille E. Broucke","orcid":"https://orcid.org/0000-0001-8275-3716"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Mireille E. Broucke","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Toronto, Toronto, ONT, Canada","University of Toronto, (Toronto)"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Toronto, Toronto, ONT, Canada","institution_ids":["https://openalex.org/I185261750"]},{"raw_affiliation_string":"University of Toronto, (Toronto)","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5042932080"],"corresponding_institution_ids":["https://openalex.org/I185261750"],"apc_list":null,"apc_paid":null,"fwci":2.1858,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.88026515,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"40","issue":null,"first_page":"733","last_page":"738"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9939000010490417,"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":0.9939000010490417,"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/T10586","display_name":"Robotic Path Planning Algorithms","score":0.9937999844551086,"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"}},{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9707000255584717,"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":0.9662567973136902},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.8794037103652954},{"id":"https://openalex.org/keywords/hypersurface","display_name":"Hypersurface","score":0.795029878616333},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.7790627479553223},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5280581116676331},{"id":"https://openalex.org/keywords/polytope-model","display_name":"Polytope model","score":0.4959324300289154},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.47828325629234314},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4767116904258728},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.455314040184021},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4481755495071411},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4431203007698059},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.39640629291534424},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2718629240989685},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.27078330516815186},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.22428101301193237},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07787367701530457}],"concepts":[{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.9662567973136902},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.8794037103652954},{"id":"https://openalex.org/C114410712","wikidata":"https://www.wikidata.org/wiki/Q973321","display_name":"Hypersurface","level":2,"score":0.795029878616333},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.7790627479553223},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5280581116676331},{"id":"https://openalex.org/C113391598","wikidata":"https://www.wikidata.org/wiki/Q1681391","display_name":"Polytope model","level":3,"score":0.4959324300289154},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.47828325629234314},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4767116904258728},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.455314040184021},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4481755495071411},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4431203007698059},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39640629291534424},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2718629240989685},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27078330516815186},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22428101301193237},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07787367701530457},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","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/cdc.2007.4434805","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2007.4434805","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 46th IEEE Conference on Decision and Control","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W199642525","https://openalex.org/W1551489551","https://openalex.org/W2099840010","https://openalex.org/W2111791229","https://openalex.org/W2115927900","https://openalex.org/W2139230981","https://openalex.org/W2147970103","https://openalex.org/W2166691751","https://openalex.org/W2172806547","https://openalex.org/W2614571955"],"related_works":["https://openalex.org/W2290025547","https://openalex.org/W2072480381","https://openalex.org/W2027575605","https://openalex.org/W1501102059","https://openalex.org/W1956734396","https://openalex.org/W2123065190","https://openalex.org/W3012067785","https://openalex.org/W4280529077","https://openalex.org/W934099117","https://openalex.org/W3128178508"],"abstract_inverted_index":{"This":[0],"paper":[1],"studies":[2],"the":[3,26,38,52,60,75],"reachability":[4,28],"problem":[5,39],"with":[6],"state":[7],"constraints;":[8],"that":[9,73],"is,":[10],"to":[11],"reach":[12],"a":[13,17,22,48],"target":[14],"without":[15],"leaving":[16],"polytope.":[18],"First,":[19],"we":[20,31,46],"provide":[21,47],"conceptual":[23],"framework":[24],"for":[25,37,40],"constrained":[27],"problem.":[29],"Then":[30],"obtain":[32],"necessary":[33],"and":[34],"sufficient":[35],"conditions":[36],"affine":[41,70],"hypersurface":[42],"systems.":[43],"In":[44],"addition,":[45],"geometric":[49],"characterization":[50],"of":[51,55],"maximal":[53],"set":[54],"initial":[56],"states":[57],"from":[58],"which":[59],"objective":[61,76],"can":[62],"be":[63],"met.":[64],"Finally,":[65],"algorithms":[66],"on":[67],"constructing":[68],"piecewise":[69],"feedback":[71],"controls":[72],"accomplish":[74],"are":[77],"presented.":[78]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
