{"id":"https://openalex.org/W2592297590","doi":"https://doi.org/10.1109/tac.2017.2679479","title":"Reduction of Second-Order Network Systems With Structure Preservation","display_name":"Reduction of Second-Order Network Systems With Structure Preservation","publication_year":2017,"publication_date":"2017-03-10","ids":{"openalex":"https://openalex.org/W2592297590","doi":"https://doi.org/10.1109/tac.2017.2679479","mag":"2592297590"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2017.2679479","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2017.2679479","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://research.rug.nl/en/publications/06e02d8e-682c-4075-b5c5-23085f5f0fac","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Xiaodong Cheng","orcid":null},"institutions":[{"id":"https://openalex.org/I169381384","display_name":"University of Groningen","ror":"https://ror.org/012p63287","country_code":"NL","type":"education","lineage":["https://openalex.org/I169381384"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Xiaodong Cheng","raw_affiliation_strings":["Faculty of Science and Engineering, University of Groningen, Groningen, AG, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Science and Engineering, University of Groningen, Groningen, AG, The Netherlands","institution_ids":["https://openalex.org/I169381384"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Yu Kawano","orcid":null},"institutions":[{"id":"https://openalex.org/I169381384","display_name":"University of Groningen","ror":"https://ror.org/012p63287","country_code":"NL","type":"education","lineage":["https://openalex.org/I169381384"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Yu Kawano","raw_affiliation_strings":["Faculty of Science and Engineering, University of Groningen, Groningen, AG, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Science and Engineering, University of Groningen, Groningen, AG, The Netherlands","institution_ids":["https://openalex.org/I169381384"]}]},{"author_position":"last","author":{"id":null,"display_name":"Jacquelien M. A. Scherpen","orcid":null},"institutions":[{"id":"https://openalex.org/I169381384","display_name":"University of Groningen","ror":"https://ror.org/012p63287","country_code":"NL","type":"education","lineage":["https://openalex.org/I169381384"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Jacquelien M. A. Scherpen","raw_affiliation_strings":["Faculty of Science and Engineering, University of Groningen, Groningen, AG, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Science and Engineering, University of Groningen, Groningen, AG, The Netherlands","institution_ids":["https://openalex.org/I169381384"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I169381384"],"apc_list":null,"apc_paid":null,"fwci":4.2069,"has_fulltext":true,"cited_by_count":49,"citation_normalized_percentile":{"value":0.94725682,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"62","issue":"10","first_page":"5026","last_page":"5038"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9866999983787537,"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":0.9866999983787537,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.0017999999690800905,"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/T12303","display_name":"Tensor decomposition and applications","score":0.00139999995008111,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/controllability","display_name":"Controllability","score":0.717199981212616},{"id":"https://openalex.org/keywords/transfer-function","display_name":"Transfer function","score":0.616599977016449},{"id":"https://openalex.org/keywords/controllability-gramian","display_name":"Controllability Gramian","score":0.550599992275238},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.536300003528595},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.531499981880188},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.4708999991416931},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.45820000767707825},{"id":"https://openalex.org/keywords/adjacency-matrix","display_name":"Adjacency matrix","score":0.447299987077713},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.44429999589920044},{"id":"https://openalex.org/keywords/laplacian-matrix","display_name":"Laplacian matrix","score":0.429500013589859}],"concepts":[{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.717199981212616},{"id":"https://openalex.org/C81299745","wikidata":"https://www.wikidata.org/wiki/Q334269","display_name":"Transfer function","level":2,"score":0.616599977016449},{"id":"https://openalex.org/C143461762","wikidata":"https://www.wikidata.org/wiki/Q83587","display_name":"Controllability Gramian","level":3,"score":0.550599992275238},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.536300003528595},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.531499981880188},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4968999922275543},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.4708999991416931},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.45820000767707825},{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.447299987077713},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.44429999589920044},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4392000138759613},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.429500013589859},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.40369999408721924},{"id":"https://openalex.org/C123745756","wikidata":"https://www.wikidata.org/wiki/Q1665949","display_name":"Interconnection","level":2,"score":0.37700000405311584},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.376800000667572},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35440000891685486},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.34299999475479126},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3409999907016754},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3361999988555908},{"id":"https://openalex.org/C104122410","wikidata":"https://www.wikidata.org/wiki/Q1416406","display_name":"Network model","level":2,"score":0.33320000767707825},{"id":"https://openalex.org/C34947359","wikidata":"https://www.wikidata.org/wiki/Q665189","display_name":"Complex network","level":2,"score":0.31779998540878296},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3174999952316284},{"id":"https://openalex.org/C77405623","wikidata":"https://www.wikidata.org/wiki/Q598451","display_name":"System dynamics","level":2,"score":0.3131999969482422},{"id":"https://openalex.org/C41982775","wikidata":"https://www.wikidata.org/wiki/Q7000977","display_name":"Network controllability","level":4,"score":0.3111000061035156},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.31040000915527344},{"id":"https://openalex.org/C77246614","wikidata":"https://www.wikidata.org/wiki/Q1409400","display_name":"Gramian matrix","level":3,"score":0.27950000762939453},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.26660001277923584},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.26589998602867126},{"id":"https://openalex.org/C122890649","wikidata":"https://www.wikidata.org/wiki/Q7834016","display_name":"Transfer matrix","level":2,"score":0.2549000084400177},{"id":"https://openalex.org/C2776175482","wikidata":"https://www.wikidata.org/wiki/Q1195816","display_name":"Transfer (computing)","level":2,"score":0.25290000438690186},{"id":"https://openalex.org/C51823790","wikidata":"https://www.wikidata.org/wiki/Q504353","display_name":"Greedy algorithm","level":2,"score":0.2515999972820282},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.2506999969482422}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tac.2017.2679479","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2017.2679479","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"},{"id":"pmh:oai:pure.rug.nl:openaire/06e02d8e-682c-4075-b5c5-23085f5f0fac","is_oa":true,"landing_page_url":"https://research.rug.nl/en/publications/06e02d8e-682c-4075-b5c5-23085f5f0fac","pdf_url":null,"source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cheng, X, Kawano, Y & Scherpen, J M A 2017, 'Reduction of Second-Order Network Systems with Structure Preservation', IEEE Transactions on Automatic Control, vol. 62, no. 10, pp. 5026-5038. https://doi.org/10.1109/TAC.2017.2679479","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:arXiv.org:1706.01751","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1706.01751","pdf_url":"https://arxiv.org/pdf/1706.01751","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:pure.rug.nl:publications/06e02d8e-682c-4075-b5c5-23085f5f0fac","is_oa":true,"landing_page_url":"https://hdl.handle.net/11370/06e02d8e-682c-4075-b5c5-23085f5f0fac","pdf_url":null,"source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"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":"Cheng, X, Kawano, Y & Scherpen, J M A 2017, 'Reduction of Second-Order Network Systems with Structure Preservation', IEEE Transactions on Automatic Control, vol. 62, no. 10, pp. 5026-5038. https://doi.org/10.1109/TAC.2017.2679479","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:pure.rug.nl:openaire/06e02d8e-682c-4075-b5c5-23085f5f0fac","is_oa":true,"landing_page_url":"https://research.rug.nl/en/publications/06e02d8e-682c-4075-b5c5-23085f5f0fac","pdf_url":null,"source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cheng, X, Kawano, Y & Scherpen, J M A 2017, 'Reduction of Second-Order Network Systems with Structure Preservation', IEEE Transactions on Automatic Control, vol. 62, no. 10, pp. 5026-5038. https://doi.org/10.1109/TAC.2017.2679479","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W613360614","https://openalex.org/W1551480811","https://openalex.org/W1590821414","https://openalex.org/W1891861977","https://openalex.org/W1992419399","https://openalex.org/W1993650658","https://openalex.org/W2007101284","https://openalex.org/W2009484965","https://openalex.org/W2009762405","https://openalex.org/W2024691050","https://openalex.org/W2047994306","https://openalex.org/W2052005273","https://openalex.org/W2056503846","https://openalex.org/W2070722739","https://openalex.org/W2074132271","https://openalex.org/W2087608839","https://openalex.org/W2088748973","https://openalex.org/W2112090702","https://openalex.org/W2140440476","https://openalex.org/W2147539438","https://openalex.org/W2343609308","https://openalex.org/W2401920424","https://openalex.org/W2568277395","https://openalex.org/W2569924641","https://openalex.org/W2576142414","https://openalex.org/W2727835700","https://openalex.org/W2963870191","https://openalex.org/W4301410675","https://openalex.org/W6605881956","https://openalex.org/W6684557030","https://openalex.org/W6733489610"],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1,119],"proposes":[2],"a":[3,11,109,114,162],"general":[4],"framework":[5],"for":[6],"structure-preserving":[7],"model":[8,70],"reduction":[9],"of":[10,38,45,86,123,161],"second-order":[12,110,128],"network":[13,89,124,129],"system":[14,97,111],"based":[15],"on":[16,132],"graph":[17],"clustering.":[18,90],"In":[19],"this":[20,118],"approach,":[21],"vertex":[22],"dynamics":[23,63],"are":[24,40],"captured":[25],"by":[26,42,73,82,158],"the":[27,36,43,46,68,74,78,83,87,95,121,144,148,154,159],"transfer":[28,47],"functions":[29],"from":[30],"inputs":[31],"to":[32,57,127,139],"individual":[33],"states,":[34],"and":[35,142,150],"dissimilarities":[37],"vertices":[39,60],"quantified":[41],"H2-norms":[44,141],"function":[48],"discrepancies.":[49],"A":[50],"greedy":[51],"hierarchical":[52],"clustering":[53],"algorithm":[54],"is":[55,71,80,92,156],"proposed":[56],"place":[58],"those":[59],"with":[61],"similar":[62],"into":[64],"same":[65],"clusters.":[66],"Then,":[67],"reduced-order":[69,151],"generated":[72],"Petrov-Galerkin":[75],"method,":[76],"where":[77],"projection":[79],"formed":[81],"characteristic":[84],"matrix":[85],"resulting":[88],"It":[91],"shown":[93],"that":[94],"simplified":[96],"preserves":[98],"an":[99,136],"interconnection":[100],"structure,":[101],"i.e.,":[102],"it":[103],"can":[104],"be":[105],"again":[106],"interpreted":[107],"as":[108],"evolving":[112],"over":[113],"reduced":[115],"graph.":[116],"Furthermore,":[117],"generalizes":[120],"definition":[122],"controllability":[125],"Gramian":[126],"systems.":[130],"Based":[131],"it,":[133],"we":[134],"develop":[135],"efficient":[137],"method":[138],"compute":[140],"derive":[143],"approximation":[145],"error":[146],"between":[147],"full-order":[149],"models.":[152],"Finally,":[153],"approach":[155],"illustrated":[157],"example":[160],"small-world":[163],"network.":[164]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":14},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":3}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2017-03-16T00:00:00"}