{"id":"https://openalex.org/W2170240498","doi":"https://doi.org/10.1109/tac.2010.2045696","title":"Probabilistic Estimates for Mixed Model Validation Problems With ${\\cal H}_{\\infty}$ Type Uncertainties","display_name":"Probabilistic Estimates for Mixed Model Validation Problems With ${\\cal H}_{\\infty}$ Type Uncertainties","publication_year":2010,"publication_date":"2010-03-16","ids":{"openalex":"https://openalex.org/W2170240498","doi":"https://doi.org/10.1109/tac.2010.2045696","mag":"2170240498"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2010.2045696","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2010.2045696","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic 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/A5076740621","display_name":"Wenguo Liu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wenguo Liu","raw_affiliation_strings":["General Electric, China Technology Center, Shanghai, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"General Electric, China Technology Center, Shanghai, China","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100428821","display_name":"Jie Chen","orcid":"https://orcid.org/0000-0003-3171-1887"},"institutions":[{"id":"https://openalex.org/I103635307","display_name":"University of California, Riverside","ror":"https://ror.org/03nawhv43","country_code":"US","type":"education","lineage":["https://openalex.org/I103635307"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jie Chen","raw_affiliation_strings":["Department of Electrical Engineering, University of California, Riverside, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of California, Riverside, CA, USA","institution_ids":["https://openalex.org/I103635307"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5721,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.76513865,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"55","issue":"6","first_page":"1488","last_page":"1494"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9966999888420105,"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":0.9961000084877014,"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/covariance","display_name":"Covariance","score":0.6735717058181763},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.6514208912849426},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.6139166951179504},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5217298269271851},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.4873214662075043},{"id":"https://openalex.org/keywords/statistical-model","display_name":"Statistical model","score":0.4677842855453491},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.4618726074695587},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4466623067855835},{"id":"https://openalex.org/keywords/gaussian-noise","display_name":"Gaussian noise","score":0.43664854764938354},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.43578851222991943},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.399884432554245},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3779188394546509},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3710371255874634},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3455507159233093},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.28294479846954346},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.21727928519248962}],"concepts":[{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.6735717058181763},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.6514208912849426},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.6139166951179504},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5217298269271851},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.4873214662075043},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.4677842855453491},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4618726074695587},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4466623067855835},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.43664854764938354},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.43578851222991943},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.399884432554245},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3779188394546509},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3710371255874634},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3455507159233093},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.28294479846954346},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.21727928519248962},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2010.2045696","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2010.2045696","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W7639229","https://openalex.org/W1504633463","https://openalex.org/W1557797024","https://openalex.org/W1586493213","https://openalex.org/W1868559974","https://openalex.org/W1966538802","https://openalex.org/W1972284617","https://openalex.org/W2042945636","https://openalex.org/W2044497211","https://openalex.org/W2055561145","https://openalex.org/W2061293389","https://openalex.org/W2095257032","https://openalex.org/W2095457418","https://openalex.org/W2117921285","https://openalex.org/W2122512060","https://openalex.org/W2142269750","https://openalex.org/W2155076415","https://openalex.org/W2171411472","https://openalex.org/W3210839039","https://openalex.org/W3212877690","https://openalex.org/W4294968333","https://openalex.org/W6633430259"],"related_works":["https://openalex.org/W2788344745","https://openalex.org/W2062336688","https://openalex.org/W2910677864","https://openalex.org/W2148213881","https://openalex.org/W2046078371","https://openalex.org/W2383820648","https://openalex.org/W4245445763","https://openalex.org/W3162209258","https://openalex.org/W2599529561","https://openalex.org/W4288910996"],"abstract_inverted_index":{"A":[0],"mixed":[1],"deterministic/probabilistic":[2],"model":[3,18,20,51],"validation":[4,29],"problem":[5,90],"is":[6,42,81],"investigated":[7],"in":[8,14],"this":[9,65],"technical":[10],"note,":[11],"which":[12],"consists":[13],"an":[15,49,88],"additive":[16],"uncertain":[17,50],"with":[19],"uncertainty":[21],"characterized":[22],"by":[23,35,55],"theH\u221enorm.":[24],"The":[25],"data":[26,33],"available":[27],"for":[28,47],"are":[30,62,68,104],"time-domain":[31],"experimental":[32],"corrupted":[34],"a":[36,82],"random":[37,76],"noise":[38,80,103],"sequence.":[39],"Our":[40],"aim":[41],"to":[43,52],"compute":[44],"the":[45,56,72,79,97,102],"probability":[46,66],"such":[48,95],"be":[53],"validated":[54],"data,":[57],"and":[58,85,99],"our":[59],"main":[60],"results":[61],"bounds":[63],"on":[64,71],"that":[67],"computable":[69],"based":[70],"distribution":[73],"of":[74,101],"Chi-square":[75],"variables":[77],"when":[78,91],"Gaussian":[83],"variable,":[84],"solvable":[86],"as":[87,96],"LMI":[89],"only":[92],"statistical":[93],"information":[94],"expectation":[98],"covariance":[100],"known.":[105]},"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}