{"id":"https://openalex.org/W2530996620","doi":"https://doi.org/10.1137/16m1098280","title":"$\\mathcal H_2$-Quasi-Optimal Model Order Reduction for Quadratic-Bilinear Control Systems","display_name":"$\\mathcal H_2$-Quasi-Optimal Model Order Reduction for Quadratic-Bilinear Control Systems","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2530996620","doi":"https://doi.org/10.1137/16m1098280","mag":"2530996620"},"language":"en","primary_location":{"id":"doi:10.1137/16m1098280","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1098280","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/11858/00-001M-0000-002C-4677-C","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060985095","display_name":"Peter Benner","orcid":"https://orcid.org/0000-0003-3362-4103"},"institutions":[{"id":"https://openalex.org/I4210127568","display_name":"Max Planck Institute for Dynamics of Complex Technical Systems","ror":"https://ror.org/030h7k016","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210127568"]},{"id":"https://openalex.org/I95793202","display_name":"Otto-von-Guericke-Universit\u00e4t Magdeburg","ror":"https://ror.org/00ggpsq73","country_code":"DE","type":"education","lineage":["https://openalex.org/I95793202"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Peter Benner","raw_affiliation_strings":["Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstra\u00dfe 1, 39106 Magdeburg, Germany, and Fakult\u00e4t f\u00fcr Mathematik, Otto-von-Guericke-Universit\u00e4t Magdeburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstra\u00dfe 1, 39106 Magdeburg, Germany, and Fakult\u00e4t f\u00fcr Mathematik, Otto-von-Guericke-Universit\u00e4t Magdeburg, Germany","institution_ids":["https://openalex.org/I4210127568","https://openalex.org/I95793202"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080481874","display_name":"Pawan Goyal","orcid":"https://orcid.org/0000-0003-3072-7780"},"institutions":[{"id":"https://openalex.org/I4210127568","display_name":"Max Planck Institute for Dynamics of Complex Technical Systems","ror":"https://ror.org/030h7k016","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210127568"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Pawan Goyal","raw_affiliation_strings":["Max Planck Institute for Dynamics of Complex Technical Systems, Sand-torstra\u00dfe 1, 39106 Magdeburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Max Planck Institute for Dynamics of Complex Technical Systems, Sand-torstra\u00dfe 1, 39106 Magdeburg, Germany","institution_ids":["https://openalex.org/I4210127568"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028332862","display_name":"Serkan Gugercin","orcid":"https://orcid.org/0000-0003-4564-5999"},"institutions":[{"id":"https://openalex.org/I859038795","display_name":"Virginia Tech","ror":"https://ror.org/02smfhw86","country_code":"US","type":"education","lineage":["https://openalex.org/I859038795"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Serkan Gugercin","raw_affiliation_strings":["Department of Mathematics, Virginia Tech, Blacksburg, VA 24061-0123"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Virginia Tech, Blacksburg, VA 24061-0123","institution_ids":["https://openalex.org/I859038795"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.46,"has_fulltext":true,"cited_by_count":88,"citation_normalized_percentile":{"value":0.97341555,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"39","issue":"2","first_page":"983","last_page":"1032"},"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":0.9908999800682068,"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/T10305","display_name":"Power System Optimization and Stability","score":0.9794999957084656,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/hessian-matrix","display_name":"Hessian matrix","score":0.8227697610855103},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8105109930038452},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5811821222305298},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5772149562835693},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.5315667986869812},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5302987098693848},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5044387578964233},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.5014455318450928},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.47545310854911804},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4295978546142578},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.26912277936935425},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1433473527431488}],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.8227697610855103},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8105109930038452},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5811821222305298},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5772149562835693},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.5315667986869812},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5302987098693848},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5044387578964233},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.5014455318450928},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.47545310854911804},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4295978546142578},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.26912277936935425},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1433473527431488},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/16m1098280","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1098280","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:escidoc.org:escidoc:2351757","is_oa":true,"landing_page_url":"http://hdl.handle.net/11858/00-001M-0000-002C-4677-C","pdf_url":"http://hdl.handle.net/11858/00-001M-0000-002C-4677-C","source":{"id":"https://openalex.org/S7407052962","display_name":"Max Planck Digital Library","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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:escidoc.org:escidoc:2351757","is_oa":true,"landing_page_url":"http://hdl.handle.net/11858/00-001M-0000-002C-4677-C","pdf_url":"http://hdl.handle.net/11858/00-001M-0000-002C-4677-C","source":{"id":"https://openalex.org/S7407052962","display_name":"Max Planck Digital Library","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":[],"awards":[{"id":"https://openalex.org/G2149260794","display_name":"Interpolatory Model Reduction for the Control of Fluids","funder_award_id":"1522616","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5768123558","display_name":null,"funder_award_id":"RTG 2297/1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6775672643","display_name":null,"funder_award_id":"RTG 2297","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8780415384","display_name":null,"funder_award_id":"DMS-1522616","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320308269","display_name":"Alexander von Humboldt-Stiftung","ror":"https://ror.org/012kf4317"},{"id":"https://openalex.org/F4320317967","display_name":"International Max Planck Research School for Environmental, Cellular and Molecular Microbiology","ror":null},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320327553","display_name":"International Max Planck Research School for Advanced Methods in Process and Systems Engineering","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2530996620.pdf","grobid_xml":"https://content.openalex.org/works/W2530996620.grobid-xml"},"referenced_works_count":44,"referenced_works":["https://openalex.org/W37887877","https://openalex.org/W201848369","https://openalex.org/W297328598","https://openalex.org/W1511438772","https://openalex.org/W1522399516","https://openalex.org/W1545626707","https://openalex.org/W1551480811","https://openalex.org/W1570007728","https://openalex.org/W1966992674","https://openalex.org/W1967795974","https://openalex.org/W1993134778","https://openalex.org/W2002858896","https://openalex.org/W2007657466","https://openalex.org/W2014269742","https://openalex.org/W2024165284","https://openalex.org/W2028671192","https://openalex.org/W2033712589","https://openalex.org/W2049753327","https://openalex.org/W2056064986","https://openalex.org/W2059316647","https://openalex.org/W2064733273","https://openalex.org/W2069049088","https://openalex.org/W2088748973","https://openalex.org/W2090292347","https://openalex.org/W2091325846","https://openalex.org/W2098077093","https://openalex.org/W2098980185","https://openalex.org/W2119695238","https://openalex.org/W2123947147","https://openalex.org/W2124500362","https://openalex.org/W2126903321","https://openalex.org/W2127135659","https://openalex.org/W2137874355","https://openalex.org/W2140820418","https://openalex.org/W2146247463","https://openalex.org/W2152609732","https://openalex.org/W2159651350","https://openalex.org/W2168568158","https://openalex.org/W2169328438","https://openalex.org/W2480611454","https://openalex.org/W2521239849","https://openalex.org/W2563746148","https://openalex.org/W3101859848","https://openalex.org/W3105351150"],"related_works":["https://openalex.org/W2611031068","https://openalex.org/W1704347466","https://openalex.org/W4283017538","https://openalex.org/W1996936972","https://openalex.org/W1545275724","https://openalex.org/W2802707792","https://openalex.org/W2075777916","https://openalex.org/W3021699548","https://openalex.org/W3169007055","https://openalex.org/W1854082044"],"abstract_inverted_index":{"We":[0,31,83,106,127],"investigate":[1],"the":[2,20,24,34,43,46,75,80,101,113,117,122,125,129,132,170,175],"optimal":[3,66],"model":[4,88,154],"reduction":[5,89,155],"problem":[6],"for":[7,28,37,64,163],"large-scale":[8],"quadratic-bilinear":[9],"(QB)":[10],"control":[11],"systems.":[12,30],"Our":[13],"contributions":[14],"are":[15],"threefold.":[16],"First,":[17],"we":[18,59],"discuss":[19,108],"variational":[21],"analysis":[22],"and":[23,50,148,160,173],"Volterra":[25,48],"series":[26,49],"formulation":[27],"QB":[29,39,164],"then":[32,84],"define":[33],"$\\mathcal":[35,54,77,177],"H_2$-norm":[36,55,78],"a":[38,52,95],"system":[40,97],"based":[41],"on":[42],"kernels":[44],"of":[45,74,79,112,121,124,131,137],"underlying":[47],"propose":[51,85],"truncated":[53,76,176],"as":[56,158],"well.":[57],"Next,":[58],"derive":[60],"first-order":[61],"necessary":[62],"conditions":[63],"an":[65,86,109],"approximation,":[67],"where":[68],"optimality":[69,104],"is":[70],"measured":[71],"in":[72,169,174],"terms":[73],"error":[81],"system.":[82,126],"iterative":[87],"algorithm,":[90],"which":[91],"upon":[92],"convergence":[93],"yields":[94],"reduced-order":[96],"that":[98],"approximately":[99],"satisfies":[100],"newly":[102],"derived":[103],"conditions.":[105],"also":[107],"efficient":[110],"computation":[111],"reduced":[114],"Hessian,":[115],"using":[116],"special":[118],"Kronecker":[119],"structure":[120],"Hessian":[123],"illustrate":[128],"efficiency":[130],"proposed":[133],"method":[134],"by":[135,166],"means":[136],"several":[138],"numerical":[139],"examples":[140],"resulting":[141],"from":[142],"semidiscretized":[143],"nonlinear":[144],"partial":[145],"differential":[146],"equations":[147],"show":[149],"its":[150],"competitiveness":[151],"with":[152],"existing":[153],"schemes":[156],"such":[157],"moment-matching":[159],"balanced":[161],"truncation":[162],"systems":[165],"comparing":[167],"accuracy":[168],"time-domain":[171],"simulations":[172],"H_2$-norm.":[178]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":15},{"year":2021,"cited_by_count":19},{"year":2020,"cited_by_count":12},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":3}],"updated_date":"2026-06-19T17:40:00.097472","created_date":"2025-10-10T00:00:00"}
