{"id":"https://openalex.org/W2397436697","doi":"https://doi.org/10.1080/00207179.2016.1186845","title":"<i>H</i><sub>2</sub>optimal model order reduction by two-sided technique on Grassmann manifold via the cross-gramian of bilinear systems","display_name":"<i>H</i><sub>2</sub>optimal model order reduction by two-sided technique on Grassmann manifold via the cross-gramian of bilinear systems","publication_year":2016,"publication_date":"2016-05-16","ids":{"openalex":"https://openalex.org/W2397436697","doi":"https://doi.org/10.1080/00207179.2016.1186845","mag":"2397436697"},"language":"en","primary_location":{"id":"doi:10.1080/00207179.2016.1186845","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207179.2016.1186845","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/A5100440745","display_name":"Kang Xu","orcid":"https://orcid.org/0000-0002-6946-8635"},"institutions":[{"id":"https://openalex.org/I96908189","display_name":"Xinjiang University","ror":"https://ror.org/059gw8r13","country_code":"CN","type":"education","lineage":["https://openalex.org/I96908189"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kang-Li Xu","raw_affiliation_strings":["College of Mathematics and Systems Science, Xinjiang University, Urumuqi, P.R. China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Systems Science, Xinjiang University, Urumuqi, P.R. China","institution_ids":["https://openalex.org/I96908189"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034372090","display_name":"Yao\u2010Lin Jiang","orcid":"https://orcid.org/0000-0002-5541-1136"},"institutions":[{"id":"https://openalex.org/I96908189","display_name":"Xinjiang University","ror":"https://ror.org/059gw8r13","country_code":"CN","type":"education","lineage":["https://openalex.org/I96908189"]},{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yao-Lin Jiang","raw_affiliation_strings":["College of Mathematics and Systems Science, Xinjiang University, Urumuqi, P.R. China; College of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xi\u2019an, P.R. China","College of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, P.R. China","College of Mathematics and Systems Science, Xinjiang University, Urumuqi, P.R. China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Systems Science, Xinjiang University, Urumuqi, P.R. China; College of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xi\u2019an, P.R. China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"College of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, P.R. China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"College of Mathematics and Systems Science, Xinjiang University, Urumuqi, P.R. China","institution_ids":["https://openalex.org/I96908189"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051273783","display_name":"Zhixia Yang","orcid":"https://orcid.org/0000-0003-0446-4278"},"institutions":[{"id":"https://openalex.org/I96908189","display_name":"Xinjiang University","ror":"https://ror.org/059gw8r13","country_code":"CN","type":"education","lineage":["https://openalex.org/I96908189"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhi-Xia Yang","raw_affiliation_strings":["College of Mathematics and Systems Science, Xinjiang University, Urumuqi, P.R. China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Systems Science, Xinjiang University, Urumuqi, P.R. China","institution_ids":["https://openalex.org/I96908189"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5034372090"],"corresponding_institution_ids":["https://openalex.org/I87445476","https://openalex.org/I96908189"],"apc_list":null,"apc_paid":null,"fwci":1.7679,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.85271596,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"90","issue":"3","first_page":"616","last_page":"626"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9934999942779541,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9865000247955322,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.819353461265564},{"id":"https://openalex.org/keywords/tangent-space","display_name":"Tangent space","score":0.5773943662643433},{"id":"https://openalex.org/keywords/pseudo-riemannian-manifold","display_name":"Pseudo-Riemannian manifold","score":0.5369631052017212},{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.5196384191513062},{"id":"https://openalex.org/keywords/grassmannian","display_name":"Grassmannian","score":0.516014575958252},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.4989333152770996},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.49303337931632996},{"id":"https://openalex.org/keywords/invariant-manifold","display_name":"Invariant manifold","score":0.46882909536361694},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4533970355987549},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.43985801935195923},{"id":"https://openalex.org/keywords/riemannian-manifold","display_name":"Riemannian manifold","score":0.41255882382392883},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33049800992012024},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.29806482791900635},{"id":"https://openalex.org/keywords/scalar-curvature","display_name":"Scalar curvature","score":0.12518349289894104},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1021663248538971}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.819353461265564},{"id":"https://openalex.org/C157157409","wikidata":"https://www.wikidata.org/wiki/Q909601","display_name":"Tangent space","level":2,"score":0.5773943662643433},{"id":"https://openalex.org/C121705324","wikidata":"https://www.wikidata.org/wiki/Q1510587","display_name":"Pseudo-Riemannian manifold","level":4,"score":0.5369631052017212},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.5196384191513062},{"id":"https://openalex.org/C162929932","wikidata":"https://www.wikidata.org/wiki/Q129638","display_name":"Grassmannian","level":2,"score":0.516014575958252},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.4989333152770996},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.49303337931632996},{"id":"https://openalex.org/C20483540","wikidata":"https://www.wikidata.org/wiki/Q4200516","display_name":"Invariant manifold","level":2,"score":0.46882909536361694},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4533970355987549},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.43985801935195923},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.41255882382392883},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33049800992012024},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29806482791900635},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.12518349289894104},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1021663248538971},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207179.2016.1186845","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207179.2016.1186845","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/W37887877","https://openalex.org/W834768259","https://openalex.org/W1551480811","https://openalex.org/W1561445488","https://openalex.org/W1964491345","https://openalex.org/W1966992674","https://openalex.org/W1990059832","https://openalex.org/W2001773339","https://openalex.org/W2002858896","https://openalex.org/W2006678442","https://openalex.org/W2009180289","https://openalex.org/W2015671498","https://openalex.org/W2018850201","https://openalex.org/W2030861715","https://openalex.org/W2034590496","https://openalex.org/W2045512849","https://openalex.org/W2069049088","https://openalex.org/W2071045420","https://openalex.org/W2081604815","https://openalex.org/W2092272609","https://openalex.org/W2101706500","https://openalex.org/W2106165817","https://openalex.org/W2121917995","https://openalex.org/W2135680841","https://openalex.org/W2137874355","https://openalex.org/W2140153041","https://openalex.org/W2147631863","https://openalex.org/W2155711822","https://openalex.org/W2159122878","https://openalex.org/W2621919695","https://openalex.org/W4205293427","https://openalex.org/W4252959020"],"related_works":["https://openalex.org/W2543460896","https://openalex.org/W1551994473","https://openalex.org/W4297731962","https://openalex.org/W4297690660","https://openalex.org/W4362679437","https://openalex.org/W2555115694","https://openalex.org/W2546668543","https://openalex.org/W2059474323","https://openalex.org/W1532125927","https://openalex.org/W2152578424"],"abstract_inverted_index":{"In":[0,60],"this":[1],"paper,":[2],"we":[3,69,99],"discuss":[4],"the":[5,27,41,66,71,75,79,84,89,107,129,135,142],"optimal":[6,18,108],"H2":[7,17],"model":[8],"order":[9],"reduction":[10],"(MOR)":[11],"problem":[12,20,29],"for":[13],"bilinear":[14,22,122,137],"systems.":[15],"The":[16],"MOR":[19,113],"of":[21,40,74,83,91,134,144],"systems":[23],"is":[24,34,50,56,116,125],"considered":[25],"as":[26,36],"minimisation":[28],"on":[30,93],"Grassmann":[31,45,94],"manifold,":[32],"which":[33,124],"stored":[35],"a":[37,53,57,111],"quotient":[38],"space":[39,49,63],"noncompact":[42],"Stifiel":[43],"manifold.":[44,59],"manifold":[46,95],"whose":[47],"tangent":[48,62],"endowed":[51],"with":[52,65],"Riemannian":[54,58,67],"metric":[55],"its":[61],"equipped":[64],"metric,":[68],"derive":[70],"negative":[72],"gradients":[73],"cost":[76,85],"function,":[77],"i.e.":[78],"steepest":[80],"descent":[81],"direction":[82],"function.":[86],"After":[87],"that,":[88],"formulas":[90],"geodesic":[92],"are":[96],"given.":[97],"Then":[98],"perform":[100],"linear":[101],"searches":[102],"along":[103],"geodesics":[104],"to":[105,118,127],"obtain":[106],"solutions.":[109],"Thereby,":[110],"two-sided":[112],"iterative":[114],"algorithm":[115],"proposed":[117],"construct":[119],"an":[120],"order-reduced":[121],"system,":[123],"used":[126],"simulate":[128],"output":[130],"and":[131],"input":[132],"responses":[133],"original":[136],"system.":[138],"Numerical":[139],"examples":[140],"demonstrate":[141],"effectiveness":[143],"our":[145],"algorithm.":[146]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
