{"id":"https://openalex.org/W1555280118","doi":"https://doi.org/10.1137/s0363012901384302","title":"Learning Complexity Dimensions for a Continuous-Time Control System","display_name":"Learning Complexity Dimensions for a Continuous-Time Control System","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W1555280118","doi":"https://doi.org/10.1137/s0363012901384302","mag":"1555280118"},"language":"en","primary_location":{"id":"doi:10.1137/s0363012901384302","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012901384302","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","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/A5068920129","display_name":"Pirkko Kuusela","orcid":"https://orcid.org/0000-0003-2470-1664"},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]},{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"education","lineage":["https://openalex.org/I9927081"]}],"countries":["FI","US"],"is_corresponding":false,"raw_author_name":"Pirkko Kuusela","raw_affiliation_strings":["Aalto University","Rutgers - The State University of New Jersey, New Brunswick"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Aalto University","institution_ids":["https://openalex.org/I9927081"]},{"raw_affiliation_string":"Rutgers - The State University of New Jersey, New Brunswick","institution_ids":["https://openalex.org/I102322142"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030513162","display_name":"Daniel Ocone","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Daniel Ocone","raw_affiliation_strings":["School of Arts and Sciences, Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Arts and Sciences, Mathematics","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068753451","display_name":"Eduardo D. Sontag","orcid":"https://orcid.org/0000-0001-8020-5783"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Eduardo D. Sontag","raw_affiliation_strings":["School of Arts and Sciences, Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Arts and Sciences, Mathematics","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0857,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.84329514,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"43","issue":"3","first_page":"872","last_page":"898"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11236","display_name":"Control Systems and Identification","score":0.9970999956130981,"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/T10876","display_name":"Fault Detection and Control Systems","score":0.9936000108718872,"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/mathematics","display_name":"Mathematics","score":0.8239588737487793},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.673258364200592},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5226927995681763},{"id":"https://openalex.org/keywords/identification","display_name":"Identification (biology)","score":0.5031577944755554},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5019185543060303},{"id":"https://openalex.org/keywords/instant","display_name":"Instant","score":0.4415956437587738},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.43559882044792175},{"id":"https://openalex.org/keywords/system-identification","display_name":"System identification","score":0.41720470786094666},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.40249601006507874},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3478392958641052},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3374154567718506},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32054418325424194},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3116496205329895},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1738460659980774},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.16452836990356445},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14809364080429077},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13449081778526306},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13337859511375427},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.08068853616714478}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8239588737487793},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.673258364200592},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5226927995681763},{"id":"https://openalex.org/C116834253","wikidata":"https://www.wikidata.org/wiki/Q2039217","display_name":"Identification (biology)","level":2,"score":0.5031577944755554},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5019185543060303},{"id":"https://openalex.org/C2779432360","wikidata":"https://www.wikidata.org/wiki/Q16963779","display_name":"Instant","level":2,"score":0.4415956437587738},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.43559882044792175},{"id":"https://openalex.org/C119247159","wikidata":"https://www.wikidata.org/wiki/Q1366192","display_name":"System identification","level":3,"score":0.41720470786094666},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.40249601006507874},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3478392958641052},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3374154567718506},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32054418325424194},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3116496205329895},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1738460659980774},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.16452836990356445},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14809364080429077},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13449081778526306},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13337859511375427},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.08068853616714478},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/s0363012901384302","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012901384302","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.234.7117","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.234.7117","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0012163v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.76.6199","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.76.6199","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.rutgers.edu/~sontag/FTP_DIR/kuusela-ocone-sontag-as-published-SIAM04.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.83.5675","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.83.5675","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.rutgers.edu/pub/sontag/vcdim-ctlinsys.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321726","display_name":"Suomen Kulttuurirahasto","ror":"https://ror.org/027xav248"},{"id":"https://openalex.org/F4320332467","display_name":"U.S. Air Force","ror":"https://ror.org/006gmme17"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1519789693","https://openalex.org/W1563736811","https://openalex.org/W1585638233","https://openalex.org/W1974198300","https://openalex.org/W1977517560","https://openalex.org/W1978418345","https://openalex.org/W2001148522","https://openalex.org/W2010029425","https://openalex.org/W2017753243","https://openalex.org/W2019671617","https://openalex.org/W2020771639","https://openalex.org/W2025263811","https://openalex.org/W2029538739","https://openalex.org/W2046907549","https://openalex.org/W2053955420","https://openalex.org/W2059811159","https://openalex.org/W2066946967","https://openalex.org/W2071570468","https://openalex.org/W2075469705","https://openalex.org/W2082210980","https://openalex.org/W2106491486","https://openalex.org/W2155020618","https://openalex.org/W2156582723","https://openalex.org/W2156909104","https://openalex.org/W4238284510","https://openalex.org/W4249716558","https://openalex.org/W4292025355"],"related_works":["https://openalex.org/W176335707","https://openalex.org/W2049809670","https://openalex.org/W2008235938","https://openalex.org/W1574879732","https://openalex.org/W3152884818","https://openalex.org/W2612630795","https://openalex.org/W2089621528","https://openalex.org/W2976354175","https://openalex.org/W1557881547","https://openalex.org/W2895985422"],"abstract_inverted_index":{"This":[0],"paper":[1],"takes":[2],"a":[3,9,24],"computational":[4],"learning":[5],"theory":[6],"approach":[7],"to":[8],"problem":[10],"of":[11,28,31,36,45,54,69],"linear":[12,29],"systems":[13],"identification.":[14],"It":[15],"is":[16,39],"assumed":[17],"that":[18,51],"inputs":[19],"are":[20],"generated":[21],"randomly":[22],"from":[23,66],"known":[25],"class":[26],"consisting":[27],"combinations":[30],"k":[32],"sinusoidals.":[33],"The":[34,47],"output":[35],"the":[37,52,67,75],"system":[38,76],"classified":[40],"at":[41],"some":[42],"single":[43],"instant":[44],"time.":[46],"main":[48],"result":[49],"establishes":[50],"number":[53],"samples":[55],"needed":[56],"for":[57],"identification":[58],"with":[59,73,80],"small":[60],"error":[61],"and":[62,78],"high":[63],"probability,":[64],"independently":[65],"distribution":[68],"inputs,":[70],"scales":[71],"polynomially":[72],"n,":[74],"dimension,":[77],"logarithmically":[79],"k.":[81]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-07-26T07:53:14.480251","created_date":"2025-10-10T00:00:00"}