{"id":"https://openalex.org/W1604854193","doi":"https://doi.org/10.1109/cdc.2002.1184522","title":"Nonsmooth controllability theory and an example","display_name":"Nonsmooth controllability theory and an example","publication_year":2003,"publication_date":"2003-08-27","ids":{"openalex":"https://openalex.org/W1604854193","doi":"https://doi.org/10.1109/cdc.2002.1184522","mag":"1604854193"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2002.1184522","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2002.1184522","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 41st IEEE Conference on Decision and Control, 2002.","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/A5067725461","display_name":"Todd D. Murphey","orcid":"https://orcid.org/0000-0003-2262-8176"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"T.D. Murphey","raw_affiliation_strings":["Engineering and Applied Science, California Institute of Technology, Pasadena, CA, USA","Dept. of Eng. & Appl. Sci., California Inst. of Technol., Pasadena, CA, USA"],"affiliations":[{"raw_affiliation_string":"Engineering and Applied Science, California Institute of Technology, Pasadena, CA, USA","institution_ids":["https://openalex.org/I122411786"]},{"raw_affiliation_string":"Dept. of Eng. & Appl. Sci., California Inst. of Technol., Pasadena, CA, USA","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002930599","display_name":"Joel W. Burdick","orcid":"https://orcid.org/0000-0002-3091-540X"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J.W. Burdick","raw_affiliation_strings":["Engineering and Applied Science, California Institute of Technology, Pasadena, CA, USA","Dept. of Eng. & Appl. Sci., California Inst. of Technol., Pasadena, CA, USA"],"affiliations":[{"raw_affiliation_string":"Engineering and Applied Science, California Institute of Technology, Pasadena, CA, USA","institution_ids":["https://openalex.org/I122411786"]},{"raw_affiliation_string":"Dept. of Eng. & Appl. Sci., California Inst. of Technol., Pasadena, CA, USA","institution_ids":["https://openalex.org/I122411786"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5067725461"],"corresponding_institution_ids":["https://openalex.org/I122411786"],"apc_list":null,"apc_paid":null,"fwci":4.0899,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.92559175,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"1","issue":null,"first_page":"370","last_page":"376"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9979000091552734,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9979000091552734,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9968000054359436,"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/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9965000152587891,"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/controllability","display_name":"Controllability","score":0.9873783588409424},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.6119136214256287},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5412887930870056},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.5355176329612732},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5338645577430725},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5324232578277588},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.5017905235290527},{"id":"https://openalex.org/keywords/bracket","display_name":"Bracket","score":0.4632839560508728},{"id":"https://openalex.org/keywords/network-controllability","display_name":"Network controllability","score":0.43121904134750366},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4235379099845886},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.4171903431415558},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40020304918289185},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3871663808822632},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.3808167576789856},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3313555121421814},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32842111587524414},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.09464743733406067},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08498620986938477}],"concepts":[{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.9873783588409424},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.6119136214256287},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5412887930870056},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.5355176329612732},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5338645577430725},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5324232578277588},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.5017905235290527},{"id":"https://openalex.org/C133769200","wikidata":"https://www.wikidata.org/wiki/Q174565","display_name":"Bracket","level":2,"score":0.4632839560508728},{"id":"https://openalex.org/C41982775","wikidata":"https://www.wikidata.org/wiki/Q7000977","display_name":"Network controllability","level":4,"score":0.43121904134750366},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4235379099845886},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.4171903431415558},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40020304918289185},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3871663808822632},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.3808167576789856},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3313555121421814},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32842111587524414},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.09464743733406067},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08498620986938477},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","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/C53811970","wikidata":"https://www.wikidata.org/wiki/Q5062194","display_name":"Centrality","level":2,"score":0.0},{"id":"https://openalex.org/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C117045392","wikidata":"https://www.wikidata.org/wiki/Q4899215","display_name":"Betweenness centrality","level":3,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/cdc.2002.1184522","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2002.1184522","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 41st IEEE Conference on Decision and Control, 2002.","raw_type":"proceedings-article"},{"id":"pmh:oai:authors.library.caltech.edu:96689","is_oa":false,"landing_page_url":"https://resolver.caltech.edu/CaltechAUTHORS:20190625-095046034","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Book Section"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.5.5742","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.5.5742","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://robotics.caltech.edu/~murphey/murpheycdc02.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W19586736","https://openalex.org/W122658514","https://openalex.org/W1519743817","https://openalex.org/W1592648094","https://openalex.org/W1856256779","https://openalex.org/W1960239420","https://openalex.org/W1995063858","https://openalex.org/W2027475520","https://openalex.org/W2035518322","https://openalex.org/W2118741873","https://openalex.org/W2120181385","https://openalex.org/W2120944681","https://openalex.org/W2124052803","https://openalex.org/W2129965357","https://openalex.org/W2140289735","https://openalex.org/W2149455028","https://openalex.org/W2153009152","https://openalex.org/W2154026842","https://openalex.org/W2154510168","https://openalex.org/W2158564182","https://openalex.org/W2168413510","https://openalex.org/W2188904792","https://openalex.org/W2565969279","https://openalex.org/W4293078920","https://openalex.org/W6600788792","https://openalex.org/W6604969532","https://openalex.org/W6639047951","https://openalex.org/W7021158690"],"related_works":["https://openalex.org/W2895969319","https://openalex.org/W2594902070","https://openalex.org/W2288444165","https://openalex.org/W2229005201","https://openalex.org/W2910288441","https://openalex.org/W2886366616","https://openalex.org/W2508095019","https://openalex.org/W2765453580","https://openalex.org/W1982821381","https://openalex.org/W2904341178"],"abstract_inverted_index":{"Extends":[0],"results":[1,16,55],"in":[2,37,49],"local":[3],"controllability":[4,15,36],"analysis":[5],"for":[6],"multiple":[7,73],"model":[8,74],"driftless":[9],"affine":[10],"(MMDA)":[11],"control":[12,61],"systems.":[13,66],"Such":[14],"can":[17,56],"be":[18],"interpreted":[19],"as":[20],"non-smooth":[21],"extensions":[22],"of":[23,39,62,77],"Chow's":[24],"theorem,":[25],"and":[26],"use":[27],"a":[28,72],"set-valued":[29],"Lie":[30],"bracket.":[31],"In":[32],"particular,":[33],"we":[34,44],"formulate":[35],"terms":[38],"generalized":[40],"differential":[41],"quotients.":[42],"Additionally,":[43],"present":[45],"an":[46],"extensive":[47],"example":[48],"order":[50],"to":[51],"illustrate":[52],"how":[53],"these":[54],"provide":[57],"insight":[58],"into":[59],"the":[60,68],"some":[63],"specific":[64],"physical":[65],"Moreover,":[67],"paper":[69],"indicates":[70],"that":[71],"system":[75],"consisting":[76],"individually":[78],"controllable":[79],"models":[80],"is":[81],"not":[82],"necessarily":[83],"controllable.":[84]},"counts_by_year":[{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}