{"id":"https://openalex.org/W2051395555","doi":"https://doi.org/10.1080/00207179.2015.1007530","title":"Optimal bilinear observers for bilinear state-space models by interaction matrices","display_name":"Optimal bilinear observers for bilinear state-space models by interaction matrices","publication_year":2015,"publication_date":"2015-01-14","ids":{"openalex":"https://openalex.org/W2051395555","doi":"https://doi.org/10.1080/00207179.2015.1007530","mag":"2051395555"},"language":"en","primary_location":{"id":"doi:10.1080/00207179.2015.1007530","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207179.2015.1007530","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/A5001044398","display_name":"Minh Q. Phan","orcid":"https://orcid.org/0000-0001-8105-6943"},"institutions":[{"id":"https://openalex.org/I107672454","display_name":"Dartmouth College","ror":"https://ror.org/049s0rh22","country_code":"US","type":"education","lineage":["https://openalex.org/I107672454"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Minh Q. Phan","raw_affiliation_strings":["Thayer School of Engineering, Dartmouth College, Hanover, NH 03755, USA"],"affiliations":[{"raw_affiliation_string":"Thayer School of Engineering, Dartmouth College, Hanover, NH 03755, USA","institution_ids":["https://openalex.org/I107672454"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036553823","display_name":"Francesco Vicario","orcid":"https://orcid.org/0000-0003-2835-7135"},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Francesco Vicario","raw_affiliation_strings":["Department of Mechanical Engineering, Columbia University, New York, NY 10027, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Columbia University, New York, NY 10027, USA","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006447458","display_name":"Richard W. Longman","orcid":"https://orcid.org/0000-0002-1345-0487"},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Richard W. Longman","raw_affiliation_strings":["Department of Mechanical Engineering, Columbia University, New York, NY 10027, USA; Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, NY 10027, USA","Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, NY 10027, USA","Department of Mechanical Engineering, Columbia University, New York, NY 10027, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Columbia University, New York, NY 10027, USA; Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, NY 10027, USA","institution_ids":["https://openalex.org/I78577930"]},{"raw_affiliation_string":"Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, NY 10027, USA","institution_ids":["https://openalex.org/I78577930"]},{"raw_affiliation_string":"Department of Mechanical Engineering, Columbia University, New York, NY 10027, USA","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033492139","display_name":"Raimondo Betti","orcid":"https://orcid.org/0000-0002-6119-190X"},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Raimondo Betti","raw_affiliation_strings":["Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, NY 10027, USA"],"affiliations":[{"raw_affiliation_string":"Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, NY 10027, USA","institution_ids":["https://openalex.org/I78577930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5001044398"],"corresponding_institution_ids":["https://openalex.org/I107672454"],"apc_list":null,"apc_paid":null,"fwci":2.3562,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.89354509,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"88","issue":"8","first_page":"1504","last_page":"1522"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","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/T11236","display_name":"Control Systems and Identification","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/T10876","display_name":"Fault Detection and Control Systems","score":0.9994999766349792,"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/T10711","display_name":"Target Tracking and Data Fusion in Sensor Networks","score":0.9983999729156494,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.8774467706680298},{"id":"https://openalex.org/keywords/observer","display_name":"Observer (physics)","score":0.7149155735969543},{"id":"https://openalex.org/keywords/kalman-filter","display_name":"Kalman filter","score":0.6087042093276978},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5778310894966125},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5645514726638794},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5467509031295776},{"id":"https://openalex.org/keywords/symmetric-bilinear-form","display_name":"Symmetric bilinear form","score":0.542249321937561},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.5275266170501709},{"id":"https://openalex.org/keywords/extended-kalman-filter","display_name":"Extended Kalman filter","score":0.49534836411476135},{"id":"https://openalex.org/keywords/bilinear-map","display_name":"Bilinear map","score":0.4495566487312317},{"id":"https://openalex.org/keywords/identification","display_name":"Identification (biology)","score":0.4464525282382965},{"id":"https://openalex.org/keywords/bilinear-form","display_name":"Bilinear form","score":0.4194122552871704},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4130285382270813},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30434972047805786},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.27722907066345215},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08734655380249023},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08587568998336792},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.06017449498176575}],"concepts":[{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.8774467706680298},{"id":"https://openalex.org/C2780704645","wikidata":"https://www.wikidata.org/wiki/Q9251458","display_name":"Observer (physics)","level":2,"score":0.7149155735969543},{"id":"https://openalex.org/C157286648","wikidata":"https://www.wikidata.org/wiki/Q846780","display_name":"Kalman filter","level":2,"score":0.6087042093276978},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5778310894966125},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5645514726638794},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5467509031295776},{"id":"https://openalex.org/C79940087","wikidata":"https://www.wikidata.org/wiki/Q2100018","display_name":"Symmetric bilinear form","level":3,"score":0.542249321937561},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.5275266170501709},{"id":"https://openalex.org/C206833254","wikidata":"https://www.wikidata.org/wiki/Q5421817","display_name":"Extended Kalman filter","level":3,"score":0.49534836411476135},{"id":"https://openalex.org/C142685569","wikidata":"https://www.wikidata.org/wiki/Q1086961","display_name":"Bilinear map","level":3,"score":0.4495566487312317},{"id":"https://openalex.org/C116834253","wikidata":"https://www.wikidata.org/wiki/Q2039217","display_name":"Identification (biology)","level":2,"score":0.4464525282382965},{"id":"https://openalex.org/C8828549","wikidata":"https://www.wikidata.org/wiki/Q837924","display_name":"Bilinear form","level":2,"score":0.4194122552871704},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4130285382270813},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30434972047805786},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27722907066345215},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08734655380249023},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08587568998336792},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06017449498176575},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","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},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207179.2015.1007530","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207179.2015.1007530","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":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W135863185","https://openalex.org/W153559495","https://openalex.org/W1512798540","https://openalex.org/W1520892678","https://openalex.org/W1597839575","https://openalex.org/W1977036703","https://openalex.org/W1984246174","https://openalex.org/W1988949676","https://openalex.org/W2008854997","https://openalex.org/W2020657791","https://openalex.org/W2029986546","https://openalex.org/W2032745063","https://openalex.org/W2047088178","https://openalex.org/W2057922474","https://openalex.org/W2064823755","https://openalex.org/W2066134327","https://openalex.org/W2069488440","https://openalex.org/W2082802505","https://openalex.org/W2094600658","https://openalex.org/W2096971893","https://openalex.org/W2102296335","https://openalex.org/W2102745335","https://openalex.org/W2116118179","https://openalex.org/W2158208985","https://openalex.org/W2159391054","https://openalex.org/W2314298801","https://openalex.org/W2317638036","https://openalex.org/W2798813531","https://openalex.org/W3093755648","https://openalex.org/W3167551172","https://openalex.org/W4232480361","https://openalex.org/W4241352934"],"related_works":["https://openalex.org/W113171773","https://openalex.org/W1963546854","https://openalex.org/W2050512396","https://openalex.org/W2031905258","https://openalex.org/W2946208069","https://openalex.org/W3183197589","https://openalex.org/W1976961250","https://openalex.org/W1176376190","https://openalex.org/W2051395555","https://openalex.org/W1504088230"],"abstract_inverted_index":{"This":[0],"paper":[1,48],"formulates":[2],"optimal":[3],"bilinear":[4,7,12,35,41,54,68],"observers":[5],"for":[6,30],"state-space":[8,36,69],"models.":[9],"Observers":[10],"in":[11,116],"form,":[13],"as":[14,120],"opposed":[15],"to":[16,22,64,71,83],"other":[17],"nonlinear":[18],"forms,":[19],"are":[20,62,88],"required":[21],"develop":[23],"an":[24,39],"extension":[25],"of":[26,33,78,93,100,108,135],"observer/Kalman":[27],"filter":[28],"identification":[29,32,77],"simultaneous":[31],"a":[34,72,80,121],"model":[37,70],"and":[38,57,132],"associated":[40],"observer":[42,55],"from":[43],"noisy":[44],"input\u2013output":[45],"measurements.":[46],"The":[47],"establishes":[49],"the":[50,53,58,66,76,85,91,98,101,106,112,117,130,136],"relationship":[51],"between":[52],"gains":[56,99],"interaction":[59,86],"matrices":[60,87,96],"which":[61],"used":[63],"convert":[65],"original":[67],"form":[73],"that":[74],"simplifies":[75],"such":[79],"model.":[81],"Techniques":[82],"find":[84],"developed.":[89],"In":[90,105],"absence":[92],"noises,":[94,109],"these":[95],"produce":[97],"fastest":[102],"converging":[103],"observer.":[104],"presence":[107],"they":[110],"minimise":[111],"state":[113],"estimation":[114],"error":[115],"same":[118],"manner":[119],"standard":[122],"steady-state":[123],"Kalman":[124],"filter.":[125],"Numerical":[126],"examples":[127],"illustrate":[128],"both":[129],"theoretical":[131],"computational":[133],"aspects":[134],"proposed":[137],"algorithms.":[138]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}