{"id":"https://openalex.org/W4402139302","doi":"https://doi.org/10.1080/00207721.2024.2370313","title":"On embedding the Koopmanization into controlled nonlinear systems, its comparison with the Carleman linearisation and concerning results: beyond the feedback linearisation","display_name":"On embedding the Koopmanization into controlled nonlinear systems, its comparison with the Carleman linearisation and concerning results: beyond the feedback linearisation","publication_year":2024,"publication_date":"2024-09-02","ids":{"openalex":"https://openalex.org/W4402139302","doi":"https://doi.org/10.1080/00207721.2024.2370313"},"language":"en","primary_location":{"id":"doi:10.1080/00207721.2024.2370313","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1080/00207721.2024.2370313","pdf_url":null,"source":{"id":"https://openalex.org/S129640837","display_name":"International Journal of Systems Science","issn_l":"0020-7721","issn":["0020-7721","1464-5319"],"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 Systems Science","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/A5011799897","display_name":"Amruta Lambe","orcid":"https://orcid.org/0000-0002-4322-6654"},"institutions":[{"id":"https://openalex.org/I42014448","display_name":"Sardar Vallabhbhai National Institute of Technology Surat","ror":"https://ror.org/02y394t43","country_code":"IN","type":"education","lineage":["https://openalex.org/I42014448"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Amruta Lambe","raw_affiliation_strings":["Department of Electrical Engineering, Sardar Vallabhbhai National Institute of Technology, Surat, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Sardar Vallabhbhai National Institute of Technology, Surat, India","institution_ids":["https://openalex.org/I42014448"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022461617","display_name":"S. N. Sharma","orcid":null},"institutions":[{"id":"https://openalex.org/I42014448","display_name":"Sardar Vallabhbhai National Institute of Technology Surat","ror":"https://ror.org/02y394t43","country_code":"IN","type":"education","lineage":["https://openalex.org/I42014448"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"S. N. Sharma","raw_affiliation_strings":["Department of Electrical Engineering, Sardar Vallabhbhai National Institute of Technology, Surat, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Sardar Vallabhbhai National Institute of Technology, Surat, India","institution_ids":["https://openalex.org/I42014448"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5011799897"],"corresponding_institution_ids":["https://openalex.org/I42014448"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12720599,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"55","issue":"16","first_page":"3391","last_page":"3411"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9997000098228455,"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":0.9997000098228455,"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/T11236","display_name":"Control Systems and Identification","score":0.9975000023841858,"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/T11416","display_name":"Numerical methods for differential equations","score":0.993399977684021,"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/control-theory","display_name":"Control theory (sociology)","score":0.6916370987892151},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6754090785980225},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.6113511323928833},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.47010037302970886},{"id":"https://openalex.org/keywords/output-feedback","display_name":"Output feedback","score":0.417753666639328},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4083150029182434},{"id":"https://openalex.org/keywords/control-engineering","display_name":"Control engineering","score":0.3641166687011719},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3466428220272064},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.29699423909187317},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.19637611508369446},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.16145914793014526},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11332979798316956}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6916370987892151},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6754090785980225},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6113511323928833},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47010037302970886},{"id":"https://openalex.org/C3018623182","wikidata":"https://www.wikidata.org/wiki/Q154021","display_name":"Output feedback","level":3,"score":0.417753666639328},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4083150029182434},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.3641166687011719},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3466428220272064},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.29699423909187317},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.19637611508369446},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16145914793014526},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11332979798316956},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00207721.2024.2370313","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1080/00207721.2024.2370313","pdf_url":null,"source":{"id":"https://openalex.org/S129640837","display_name":"International Journal of Systems Science","issn_l":"0020-7721","issn":["0020-7721","1464-5319"],"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 Systems Science","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:taf:tsysxx:v:55:y:2024:i:16:p:3391-3411","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1080/00207721.2024.2370313","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W87809706","https://openalex.org/W119295074","https://openalex.org/W1496554474","https://openalex.org/W1520892678","https://openalex.org/W1992447120","https://openalex.org/W1997054581","https://openalex.org/W2000778604","https://openalex.org/W2051716090","https://openalex.org/W2086267335","https://openalex.org/W2093352963","https://openalex.org/W2157300063","https://openalex.org/W2159391054","https://openalex.org/W2494897867","https://openalex.org/W2782591075","https://openalex.org/W2911452639","https://openalex.org/W2986587829","https://openalex.org/W3013462221","https://openalex.org/W3038118776","https://openalex.org/W3126331428","https://openalex.org/W3217481449","https://openalex.org/W4239216443","https://openalex.org/W4239539940","https://openalex.org/W4252130364","https://openalex.org/W4320707263"],"related_works":["https://openalex.org/W2081900870","https://openalex.org/W2345479200","https://openalex.org/W2183306018","https://openalex.org/W2849310602","https://openalex.org/W3006008237","https://openalex.org/W2419146053","https://openalex.org/W4388890789","https://openalex.org/W2088247287","https://openalex.org/W2963903416","https://openalex.org/W4313153715"],"abstract_inverted_index":{"The":[0,41,94,133],"feedback":[1],"linearisation":[2,25],"has":[3],"found":[4],"its":[5],"striking":[6],"applications":[7],"in":[8,103,123],"many":[9],"practical":[10,170],"situations":[11],"for":[12,27,168],"control":[13,104,171],"problems":[14],"that":[15,97],"exploit":[16],"the":[17,20,54,57,60,70,73,78,81,86,91,98,101,107,119,124,128,137,147,150,158,161,193,197],"ideas":[18],"from":[19,33],"linear":[21],"system":[22,76,177,185],"theory.":[23],"Towards":[24],"techniques":[26],"controlled":[28,74,130,175,184],"nonlinear":[29,75,131],"systems,":[30],"operator-theoretic":[31],"frameworks":[32],"functional":[34],"analysis":[35],"have":[36],"received":[37],"attentions":[38],"as":[39,143],"well.":[40,144],"Koopman":[42,125,151,166,194],"operator":[43],"is":[44,141],"a":[45,64,174,179,183,187],"linear,":[46],"but":[47],"an":[48,116],"infinite":[49],"dimensional":[50],"operator.":[51],"Most":[52],"notably,":[53],"novelties":[55],"of":[56,69,72,80,115,127,136,149,157,160],"paper":[58],"are":[59],"following.":[61],"(i)":[62],"Sketching":[63],"rigorous":[65],"and":[66,84,182],"comprehensive":[67],"proof":[68,95],"Koopmanization":[71,99],"using":[77],"notion":[79],"operator-invariant":[82],"subspace":[83],"unifying":[85],"minimiser":[87],"inequality":[88],"formula":[89],"with":[90,106,178,186,196],"Koopmanized":[92],"system.":[93,132],"unfolds":[96],"meets":[100],"bilinearisation":[102],"context":[105],"augmented":[108],"state":[109],"space.":[110],"(ii)":[111],"A":[112],"formal":[113],"construction":[114],"observer":[117],"encompassing":[118],"generalised":[120,138],"Riccati":[121,139],"equation":[122,140],"setting":[126],"original":[129],"Carleman":[134,198],"version":[135],"rephrased":[142],"(iii)":[145],"Unfolding":[146],"usefulness":[148],"observer.":[152],"To":[153],"achieve":[154],"extensive":[155],"illustrations":[156],"theory":[159],"paper,":[162],"we":[163,191],"construct":[164],"two":[165,169],"observers":[167,195],"problems,":[172],"i.e.":[173],"Duffing":[176],"cubic":[180],"nonlinearity":[181],"square":[188],"nonlinearity.":[189],"Then,":[190],"compare":[192],"observers.":[199]},"counts_by_year":[],"updated_date":"2026-06-14T06:11:07.267592","created_date":"2025-10-10T00:00:00"}