{"id":"https://openalex.org/W2015765360","doi":"https://doi.org/10.1109/tcst.2012.2192735","title":"Structured Model Order Reduction of Parallel Models in Feedback","display_name":"Structured Model Order Reduction of Parallel Models in Feedback","publication_year":2013,"publication_date":"2013-04-17","ids":{"openalex":"https://openalex.org/W2015765360","doi":"https://doi.org/10.1109/tcst.2012.2192735","mag":"2015765360"},"language":"en","primary_location":{"id":"doi:10.1109/tcst.2012.2192735","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcst.2012.2192735","pdf_url":null,"source":{"id":"https://openalex.org/S133363738","display_name":"IEEE Transactions on Control Systems Technology","issn_l":"1063-6536","issn":["1063-6536","1558-0865","2374-0159"],"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 Control Systems Technology","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://zenodo.org/record/3435146","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039552898","display_name":"Pavel Trnka","orcid":"https://orcid.org/0000-0002-7675-9094"},"institutions":[{"id":"https://openalex.org/I4210120083","display_name":"Honeywell (Czechia)","ror":"https://ror.org/0297sbd31","country_code":"CZ","type":"company","lineage":["https://openalex.org/I4210120083","https://openalex.org/I82514191"]}],"countries":["CZ"],"is_corresponding":true,"raw_author_name":"Pavel Trnka","raw_affiliation_strings":["Honeywell Prague Laboratory, Honeywell International, Inc., Prague, Czech Republic"],"affiliations":[{"raw_affiliation_string":"Honeywell Prague Laboratory, Honeywell International, Inc., Prague, Czech Republic","institution_ids":["https://openalex.org/I4210120083"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004522576","display_name":"Christopher Sturk","orcid":null},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Christopher Sturk","raw_affiliation_strings":["School of Electrical Engineering, Automatic Control Laboratory, ACCESS Linnaeus Center, Royal Institute of Technology (KTH), Stockholm, Sweden"],"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, Automatic Control Laboratory, ACCESS Linnaeus Center, Royal Institute of Technology (KTH), Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056120878","display_name":"Henrik Sandberg","orcid":"https://orcid.org/0000-0003-1835-2963"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Henrik Sandberg","raw_affiliation_strings":["School of Electrical Engineering, Automatic Control Laboratory, ACCESS Linnaeus Center, Royal Institute of Technology (KTH), Stockholm, Sweden"],"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, Automatic Control Laboratory, ACCESS Linnaeus Center, Royal Institute of Technology (KTH), Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068313516","display_name":"Vladim\u0131\u0301r Havlena","orcid":"https://orcid.org/0000-0002-1103-3030"},"institutions":[{"id":"https://openalex.org/I4210120083","display_name":"Honeywell (Czechia)","ror":"https://ror.org/0297sbd31","country_code":"CZ","type":"company","lineage":["https://openalex.org/I4210120083","https://openalex.org/I82514191"]},{"id":"https://openalex.org/I44504214","display_name":"Czech Technical University in Prague","ror":"https://ror.org/03kqpb082","country_code":"CZ","type":"education","lineage":["https://openalex.org/I44504214"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Vladimir Havlena","raw_affiliation_strings":["Department of Control Engineering, Czech Technical University, Prague, Czech Republic","Honeywell Prague Laboratory, Prague, Czech Republic"],"affiliations":[{"raw_affiliation_string":"Department of Control Engineering, Czech Technical University, Prague, Czech Republic","institution_ids":["https://openalex.org/I44504214"]},{"raw_affiliation_string":"Honeywell Prague Laboratory, Prague, Czech Republic","institution_ids":["https://openalex.org/I4210120083"]}]},{"author_position":"last","author":{"id":null,"display_name":"Jiri Rehor","orcid":null},"institutions":[{"id":"https://openalex.org/I4210120083","display_name":"Honeywell (Czechia)","ror":"https://ror.org/0297sbd31","country_code":"CZ","type":"company","lineage":["https://openalex.org/I4210120083","https://openalex.org/I82514191"]},{"id":"https://openalex.org/I44504214","display_name":"Czech Technical University in Prague","ror":"https://ror.org/03kqpb082","country_code":"CZ","type":"education","lineage":["https://openalex.org/I44504214"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Jiri Rehor","raw_affiliation_strings":["Department of Control Engineering, Czech Technical University, Prague, Czech Republic","Honeywell Prague Laboratory, Prague, Czech Republic"],"affiliations":[{"raw_affiliation_string":"Department of Control Engineering, Czech Technical University, Prague, Czech Republic","institution_ids":["https://openalex.org/I44504214"]},{"raw_affiliation_string":"Honeywell Prague Laboratory, Prague, Czech Republic","institution_ids":["https://openalex.org/I4210120083"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5039552898"],"corresponding_institution_ids":["https://openalex.org/I4210120083"],"apc_list":null,"apc_paid":null,"fwci":2.303,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.88189014,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"21","issue":"3","first_page":"739","last_page":"752"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12810","display_name":"Real-time simulation and control systems","score":0.9902999997138977,"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/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.6839689016342163},{"id":"https://openalex.org/keywords/heuristics","display_name":"Heuristics","score":0.5641883015632629},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5296390056610107},{"id":"https://openalex.org/keywords/cogeneration","display_name":"Cogeneration","score":0.524183452129364},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.521513044834137},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5204522609710693},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5199378728866577},{"id":"https://openalex.org/keywords/header","display_name":"Header","score":0.5111272931098938},{"id":"https://openalex.org/keywords/model-order-reduction","display_name":"Model order reduction","score":0.4931644797325134},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.45073121786117554},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3034229278564453},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.24356162548065186},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.22795233130455017},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.21197018027305603},{"id":"https://openalex.org/keywords/electricity-generation","display_name":"Electricity generation","score":0.1521318554878235},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09367761015892029}],"concepts":[{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.6839689016342163},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.5641883015632629},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5296390056610107},{"id":"https://openalex.org/C2776756539","wikidata":"https://www.wikidata.org/wiki/Q221620","display_name":"Cogeneration","level":4,"score":0.524183452129364},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.521513044834137},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5204522609710693},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5199378728866577},{"id":"https://openalex.org/C48105269","wikidata":"https://www.wikidata.org/wiki/Q1141160","display_name":"Header","level":2,"score":0.5111272931098938},{"id":"https://openalex.org/C2779277453","wikidata":"https://www.wikidata.org/wiki/Q12202921","display_name":"Model order reduction","level":3,"score":0.4931644797325134},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.45073121786117554},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3034229278564453},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.24356162548065186},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.22795233130455017},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21197018027305603},{"id":"https://openalex.org/C423512","wikidata":"https://www.wikidata.org/wiki/Q383973","display_name":"Electricity generation","level":3,"score":0.1521318554878235},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09367761015892029},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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":2,"locations":[{"id":"doi:10.1109/tcst.2012.2192735","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcst.2012.2192735","pdf_url":null,"source":{"id":"https://openalex.org/S133363738","display_name":"IEEE Transactions on Control Systems Technology","issn_l":"1063-6536","issn":["1063-6536","1558-0865","2374-0159"],"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 Control Systems Technology","raw_type":"journal-article"},{"id":"pmh:oai:zenodo.org:3435146","is_oa":true,"landing_page_url":"https://zenodo.org/record/3435146","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:zenodo.org:3435146","is_oa":true,"landing_page_url":"https://zenodo.org/record/3435146","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"display_name":"Affordable and clean energy","score":0.5600000023841858,"id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1967073510","https://openalex.org/W1968290793","https://openalex.org/W1984714339","https://openalex.org/W2039401467","https://openalex.org/W2047564874","https://openalex.org/W2067070250","https://openalex.org/W2105193327","https://openalex.org/W2128834174","https://openalex.org/W2159508300","https://openalex.org/W2182510773","https://openalex.org/W2492791808","https://openalex.org/W2536620281","https://openalex.org/W2562538259","https://openalex.org/W4231269850"],"related_works":["https://openalex.org/W2171597999","https://openalex.org/W2189136227","https://openalex.org/W1866537546","https://openalex.org/W630850086","https://openalex.org/W1998119461","https://openalex.org/W3200508093","https://openalex.org/W2522673987","https://openalex.org/W2359988301","https://openalex.org/W2495363594","https://openalex.org/W2601500142"],"abstract_inverted_index":{"Parallel":[0],"working":[1],"units":[2],"in":[3,9,168],"closed-loop":[4,74],"operation":[5],"are":[6,37,65,126,131],"frequently":[7],"encountered":[8],"industrial":[10],"applications":[11],"of":[12,31,111,113,119,137],"advanced":[13],"process":[14],"control":[15],"(boilers,":[16],"turbines,":[17],"chemical":[18],"reactors,":[19],"etc.).":[20],"Control":[21],"strategies":[22],"typically":[23],"require":[24],"different":[25,35],"low-order":[26],"models":[27,36,109],"for":[28,108],"each":[29],"configuration":[30],"parallel":[32,45],"units.":[33],"These":[34],"usually":[38],"obtained":[39],"by":[40],"heuristics":[41],"applied":[42,99,156],"to":[43,72,100,157,163],"the":[44,67,83,124,149,164],"models.":[46,102],"To":[47],"replace":[48],"these":[49],"heuristics,":[50],"this":[51,169],"paper":[52],"proposes":[53],"a":[54,79,134,138],"systematic":[55],"solution":[56],"based":[57],"on":[58,133],"structured":[59],"model":[60],"order":[61],"reduction.":[62],"Two":[63],"methods":[64,130],"considered,":[66],"first":[68],"has":[69],"general":[70,101,158],"applicability":[71],"stable":[73,114],"systems,":[75],"but":[76,96],"gives":[77],"no":[78],"priori":[80],"error":[81,94],"bounds;":[82],"second":[84,150],"linear":[85],"matrix":[86],"inequality":[87],"(LMI)-based":[88],"method":[89,152],"comes":[90],"with":[91,142,160],"an":[92],"explicit":[93],"bounds,":[95],"cannot":[97],"be":[98,155],"However,":[103],"it":[104],"is":[105,146],"shown":[106],"that":[107,148],"composed":[110],"cascades":[112],"subsystems":[115],"and":[116],"negative":[117],"feedbacks":[118],"strictly":[120],"positive":[121],"real":[122],"subsystems,":[123],"LMIs":[125],"always":[127,154],"feasible.":[128],"Both":[129],"demonstrated":[132],"practical":[135],"example":[136],"cogeneration":[139],"power":[140],"plant":[141],"multiple":[143],"boilers.":[144],"It":[145],"proved":[147],"LMI-based":[151],"can":[153],"problems":[159],"structures":[161],"similar":[162],"boiler-header":[165],"systems":[166],"considered":[167],"paper.":[170]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1}],"updated_date":"2026-03-25T23:56:10.502304","created_date":"2025-10-10T00:00:00"}