{"id":"https://openalex.org/W3123461764","doi":"https://doi.org/10.1109/tac.2021.3054325","title":"On the Approximation of Moments for Nonlinear Systems","display_name":"On the Approximation of Moments for Nonlinear Systems","publication_year":2021,"publication_date":"2021-01-25","ids":{"openalex":"https://openalex.org/W3123461764","doi":"https://doi.org/10.1109/tac.2021.3054325","mag":"3123461764"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2021.3054325","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2021.3054325","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":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://zenodo.org/record/5948586","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076689396","display_name":"Nicol\u00e1s Faedo","orcid":"https://orcid.org/0000-0002-7455-9558"},"institutions":[{"id":"https://openalex.org/I157286207","display_name":"National University of Ireland, Maynooth","ror":"https://ror.org/048nfjm95","country_code":"IE","type":"education","lineage":["https://openalex.org/I157286207"]}],"countries":["IE"],"is_corresponding":false,"raw_author_name":"Nicolas Faedo","raw_affiliation_strings":["Centre for Ocean Energy Research, Maynooth University, W23 F2K8 Kildare, Ireland"],"raw_orcid":"https://orcid.org/0000-0002-7455-9558","affiliations":[{"raw_affiliation_string":"Centre for Ocean Energy Research, Maynooth University, W23 F2K8 Kildare, Ireland","institution_ids":["https://openalex.org/I157286207"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053775140","display_name":"Giordano Scarciotti","orcid":"https://orcid.org/0000-0001-5807-9004"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Giordano Scarciotti","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, Imperial College London, London, U.K"],"raw_orcid":"https://orcid.org/0000-0001-5807-9004","affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, Imperial College London, London, U.K","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018225150","display_name":"Alessandro Astolfi","orcid":"https://orcid.org/0000-0002-4331-454X"},"institutions":[{"id":"https://openalex.org/I116067653","display_name":"University of Rome Tor Vergata","ror":"https://ror.org/02p77k626","country_code":"IT","type":"education","lineage":["https://openalex.org/I116067653"]},{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB","IT"],"is_corresponding":false,"raw_author_name":"Alessandro Astolfi","raw_affiliation_strings":["Department of Civil Engineering and Computer Science Engineering, University of Rome \u201cTor Vergata,\u201d, Rome, Italy","Department of Electrical and Electronic Engineering, Imperial College London, London, SW7 2AZ, U.K","Department of Civil Engineering and Computer Science Engineering, University of Rome \"Tor Vergata,\", Rome, Italy"],"raw_orcid":"https://orcid.org/0000-0002-4331-454X","affiliations":[{"raw_affiliation_string":"Department of Civil Engineering and Computer Science Engineering, University of Rome \u201cTor Vergata,\u201d, Rome, Italy","institution_ids":["https://openalex.org/I116067653"]},{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, Imperial College London, London, SW7 2AZ, U.K","institution_ids":["https://openalex.org/I47508984"]},{"raw_affiliation_string":"Department of Civil Engineering and Computer Science Engineering, University of Rome \"Tor Vergata,\", Rome, Italy","institution_ids":["https://openalex.org/I116067653"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047675974","display_name":"John V. Ringwood","orcid":"https://orcid.org/0000-0003-0395-7943"},"institutions":[{"id":"https://openalex.org/I157286207","display_name":"National University of Ireland, Maynooth","ror":"https://ror.org/048nfjm95","country_code":"IE","type":"education","lineage":["https://openalex.org/I157286207"]}],"countries":["IE"],"is_corresponding":false,"raw_author_name":"John V. Ringwood","raw_affiliation_strings":["Centre for Ocean Energy Research, Maynooth University, W23 F2K8 Kildare, Ireland"],"raw_orcid":"https://orcid.org/0000-0003-0395-7943","affiliations":[{"raw_affiliation_string":"Centre for Ocean Energy Research, Maynooth University, W23 F2K8 Kildare, Ireland","institution_ids":["https://openalex.org/I157286207"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.0504,"has_fulltext":true,"cited_by_count":18,"citation_normalized_percentile":{"value":0.86932804,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"66","issue":"11","first_page":"5538","last_page":"5545"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9988999962806702,"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/T11372","display_name":"Hydraulic and Pneumatic Systems","score":0.9837999939918518,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/moment","display_name":"Moment (physics)","score":0.7497067451477051},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.7061886191368103},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6165081858634949},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5395085215568542},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5073069930076599},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.4998133182525635},{"id":"https://openalex.org/keywords/image-moment","display_name":"Image moment","score":0.48845115303993225},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.4802420437335968},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.46781134605407715},{"id":"https://openalex.org/keywords/approximation-theory","display_name":"Approximation theory","score":0.42208027839660645},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39918088912963867},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3918560743331909},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32627835869789124},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21537813544273376},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.17958930134773254},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.09460416436195374},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08491137623786926},{"id":"https://openalex.org/keywords/image-processing","display_name":"Image processing","score":0.08198738098144531},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08183154463768005}],"concepts":[{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.7497067451477051},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7061886191368103},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6165081858634949},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5395085215568542},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5073069930076599},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.4998133182525635},{"id":"https://openalex.org/C108311513","wikidata":"https://www.wikidata.org/wiki/Q841934","display_name":"Image moment","level":4,"score":0.48845115303993225},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.4802420437335968},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.46781134605407715},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.42208027839660645},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39918088912963867},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3918560743331909},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32627835869789124},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21537813544273376},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.17958930134773254},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.09460416436195374},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08491137623786926},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.08198738098144531},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08183154463768005},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","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}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/tac.2021.3054325","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2021.3054325","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:mural.maynoothuniversity.ie:16106","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4377196372","display_name":"MURAL - Maynooth University Research Archive Library (National University of Ireland, Maynooth)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I157286207","host_organization_name":"National University of Ireland, Maynooth","host_organization_lineage":["https://openalex.org/I157286207"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:zenodo.org:5948586","is_oa":true,"landing_page_url":"https://zenodo.org/record/5948586","pdf_url":"https://zenodo.org/record/5948586","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":"IEEE Transactions on Automatic Control 66(11) 5538 -5545","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:art.torvergata.it:2108/303061","is_oa":false,"landing_page_url":"http://hdl.handle.net/2108/303061","pdf_url":null,"source":{"id":"https://openalex.org/S4306400993","display_name":"Cineca Institutional Research Information System (Tor Vergata University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I116067653","host_organization_name":"University of Rome Tor Vergata","host_organization_lineage":["https://openalex.org/I116067653"],"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":"info:eu-repo/semantics/article"},{"id":"pmh:oai:spiral.imperial.ac.uk:10044/1/86654","is_oa":false,"landing_page_url":"http://hdl.handle.net/10044/1/86654","pdf_url":null,"source":{"id":"https://openalex.org/S4306401396","display_name":"Spiral (Imperial College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I47508984","host_organization_name":"Imperial College London","host_organization_lineage":["https://openalex.org/I47508984"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":{"id":"pmh:oai:zenodo.org:5948586","is_oa":true,"landing_page_url":"https://zenodo.org/record/5948586","pdf_url":"https://zenodo.org/record/5948586","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":"IEEE Transactions on Automatic Control 66(11) 5538 -5545","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2428888754","display_name":"KIOS Research and Innovation Centre of Excellence","funder_award_id":"739551","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G3811734559","display_name":"Development of the next generation of controllers for wave energy devices","funder_award_id":"13/IA/1886","funder_id":"https://openalex.org/F4320320847","funder_display_name":"Science Foundation Ireland"},{"id":"https://openalex.org/G8144071556","display_name":null,"funder_award_id":"SFI/13/IA/1886","funder_id":"https://openalex.org/F4320320847","funder_display_name":"Science Foundation Ireland"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320320847","display_name":"Science Foundation Ireland","ror":"https://ror.org/0271asj38"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3123461764.pdf","grobid_xml":"https://content.openalex.org/works/W3123461764.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1481259946","https://openalex.org/W1484739396","https://openalex.org/W1551480811","https://openalex.org/W1556890730","https://openalex.org/W1559197676","https://openalex.org/W1805381866","https://openalex.org/W1887006513","https://openalex.org/W2000714860","https://openalex.org/W2045689494","https://openalex.org/W2071467620","https://openalex.org/W2103960654","https://openalex.org/W2147678154","https://openalex.org/W2344124355","https://openalex.org/W2408478130","https://openalex.org/W2464697260","https://openalex.org/W2592428685","https://openalex.org/W2606887410","https://openalex.org/W2744827903","https://openalex.org/W2807941499","https://openalex.org/W2890142862","https://openalex.org/W2914568423","https://openalex.org/W2972993380","https://openalex.org/W3160954918","https://openalex.org/W3207663632","https://openalex.org/W4229747687","https://openalex.org/W6633508401"],"related_works":["https://openalex.org/W2367098950","https://openalex.org/W1962481458","https://openalex.org/W2348634732","https://openalex.org/W2583923639","https://openalex.org/W2107344965","https://openalex.org/W2125978950","https://openalex.org/W2360294379","https://openalex.org/W2381942890","https://openalex.org/W2618778149","https://openalex.org/W2220224105"],"abstract_inverted_index":{"Model":[0],"reduction":[1],"by":[2,117],"moment-matching":[3],"relies":[4],"upon":[5],"the":[6,9,16,20,47,75,83,89,93,108],"availability":[7],"of":[8,22,49,77,85,119],"so-called":[10],"<italic":[11],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[12],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">moment</i>":[13],".":[14],"If":[15],"system":[17],"is":[18,95],"nonlinear,":[19],"computation":[21,76],"moments":[23,109],"depends":[24],"on":[25],"an":[26,71,103],"underlying":[27],"specific":[28],"invariance":[29],"equation,":[30],"which":[31,92],"can":[32],"be":[33],"difficult":[34],"or":[35],"impossible":[36],"to":[37,46,69,88,106],"solve.":[38],"This":[39],"article":[40],"presents":[41],"four":[42],"technical":[43],"contributions":[44],"related":[45],"theory":[48,59],"moment":[50,87],"matching:":[51],"first,":[52],"we":[53,65,81,101],"identify":[54],"a":[55],"connection":[56],"between":[57],"moment-based":[58],"and":[60],"weighted":[61],"residual":[62],"methods.":[63],"Second,":[64],"exploit":[66],"this":[67,111],"relation":[68],"provide":[70,102],"approximation":[72,104],"technique":[73,105],"for":[74],"nonlinear":[78,86],"moments.":[79],"Third,":[80],"extend":[82],"definition":[84],"case":[90],"in":[91,97,110],"generator":[94],"described":[96],"explicit":[98],"form.":[99],"Finally,":[100],"compute":[107],"scenario.":[112],"The":[113],"results":[114],"are":[115],"illustrated":[116],"means":[118],"two":[120],"examples.":[121]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":1}],"updated_date":"2026-07-11T18:08:03.149640","created_date":"2025-10-10T00:00:00"}