{"id":"https://openalex.org/W4289869146","doi":"https://doi.org/10.1515/auto-2022-0032","title":"Robustness analysis and training of recurrent neural networks using dissipativity theory","display_name":"Robustness analysis and training of recurrent neural networks using dissipativity theory","publication_year":2022,"publication_date":"2022-08-01","ids":{"openalex":"https://openalex.org/W4289869146","doi":"https://doi.org/10.1515/auto-2022-0032"},"language":"en","primary_location":{"id":"doi:10.1515/auto-2022-0032","is_oa":false,"landing_page_url":"https://doi.org/10.1515/auto-2022-0032","pdf_url":null,"source":{"id":"https://openalex.org/S4210170077","display_name":"at - Automatisierungstechnik","issn_l":"0178-2312","issn":["0178-2312","2196-677X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319967","host_organization_name":"R. Oldenbourg Verlag","host_organization_lineage":["https://openalex.org/P4310319967"],"host_organization_lineage_names":["R. Oldenbourg Verlag"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"at - Automatisierungstechnik","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/A5004815760","display_name":"Patricia Pauli","orcid":"https://orcid.org/0000-0001-5677-7095"},"institutions":[{"id":"https://openalex.org/I100066346","display_name":"University of Stuttgart","ror":"https://ror.org/04vnq7t77","country_code":"DE","type":"education","lineage":["https://openalex.org/I100066346"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Patricia Pauli","raw_affiliation_strings":["9149 Universit\u00e4t Stuttgart , Institut f\u00fcr Systemtheorie und Regelungstechnik , Stuttgart , Germany"],"affiliations":[{"raw_affiliation_string":"9149 Universit\u00e4t Stuttgart , Institut f\u00fcr Systemtheorie und Regelungstechnik , Stuttgart , Germany","institution_ids":["https://openalex.org/I100066346"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065926154","display_name":"Julian Berberich","orcid":"https://orcid.org/0000-0001-6366-6238"},"institutions":[{"id":"https://openalex.org/I100066346","display_name":"University of Stuttgart","ror":"https://ror.org/04vnq7t77","country_code":"DE","type":"education","lineage":["https://openalex.org/I100066346"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Julian Berberich","raw_affiliation_strings":["9149 Universit\u00e4t Stuttgart , Institut f\u00fcr Systemtheorie und Regelungstechnik , Stuttgart , Germany"],"affiliations":[{"raw_affiliation_string":"9149 Universit\u00e4t Stuttgart , Institut f\u00fcr Systemtheorie und Regelungstechnik , Stuttgart , Germany","institution_ids":["https://openalex.org/I100066346"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001090900","display_name":"Frank Allg\u00f6wer","orcid":"https://orcid.org/0000-0002-3702-3658"},"institutions":[{"id":"https://openalex.org/I100066346","display_name":"University of Stuttgart","ror":"https://ror.org/04vnq7t77","country_code":"DE","type":"education","lineage":["https://openalex.org/I100066346"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Frank Allg\u00f6wer","raw_affiliation_strings":["9149 Universit\u00e4t Stuttgart , Institut f\u00fcr Systemtheorie und Regelungstechnik , Stuttgart , Germany"],"affiliations":[{"raw_affiliation_string":"9149 Universit\u00e4t Stuttgart , Institut f\u00fcr Systemtheorie und Regelungstechnik , Stuttgart , Germany","institution_ids":["https://openalex.org/I100066346"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5004815760"],"corresponding_institution_ids":["https://openalex.org/I100066346"],"apc_list":null,"apc_paid":null,"fwci":0.0915,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.3963283,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"70","issue":"8","first_page":"730","last_page":"739"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10502","display_name":"Advanced Memory and Neural Computing","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10502","display_name":"Advanced Memory and Neural Computing","score":0.9998000264167786,"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"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.996399998664856,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9937999844551086,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.8621708750724792},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6069381237030029},{"id":"https://openalex.org/keywords/recurrent-neural-network","display_name":"Recurrent neural network","score":0.6015622615814209},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.47344017028808594},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.46074429154396057},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4374198019504547},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35615599155426025},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.27746784687042236},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.12661853432655334},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1187334954738617}],"concepts":[{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.8621708750724792},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6069381237030029},{"id":"https://openalex.org/C147168706","wikidata":"https://www.wikidata.org/wiki/Q1457734","display_name":"Recurrent neural network","level":3,"score":0.6015622615814209},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.47344017028808594},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.46074429154396057},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4374198019504547},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35615599155426025},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.27746784687042236},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.12661853432655334},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1187334954738617},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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":1,"locations":[{"id":"doi:10.1515/auto-2022-0032","is_oa":false,"landing_page_url":"https://doi.org/10.1515/auto-2022-0032","pdf_url":null,"source":{"id":"https://openalex.org/S4210170077","display_name":"at - Automatisierungstechnik","issn_l":"0178-2312","issn":["0178-2312","2196-677X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319967","host_organization_name":"R. Oldenbourg Verlag","host_organization_lineage":["https://openalex.org/P4310319967"],"host_organization_lineage_names":["R. Oldenbourg Verlag"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"at - Automatisierungstechnik","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4121301992","display_name":null,"funder_award_id":"468094890","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8784604414","display_name":null,"funder_award_id":"390740016","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W2062839027","https://openalex.org/W2076467525","https://openalex.org/W2095830039","https://openalex.org/W2115129628","https://openalex.org/W2120793916","https://openalex.org/W2124214538","https://openalex.org/W2146327506","https://openalex.org/W2260372933","https://openalex.org/W2408541880","https://openalex.org/W3112185765","https://openalex.org/W3118784488","https://openalex.org/W3142744390","https://openalex.org/W3178467133","https://openalex.org/W3196740281","https://openalex.org/W3204184136","https://openalex.org/W3217437324","https://openalex.org/W4226157892","https://openalex.org/W4314947432"],"related_works":["https://openalex.org/W2150830839","https://openalex.org/W2123102751","https://openalex.org/W2376419853","https://openalex.org/W2946566599","https://openalex.org/W2100428849","https://openalex.org/W2579663521","https://openalex.org/W2012038446","https://openalex.org/W1509121458","https://openalex.org/W2142604943","https://openalex.org/W2161833043"],"abstract_inverted_index":{"Abstract":[0],"Neural":[1],"networks":[2,15,35],"are":[3],"widely":[4],"applied":[5],"in":[6,111,121],"control":[7,39],"applications,":[8],"yet":[9],"providing":[10],"safety":[11],"guarantees":[12],"for":[13],"neural":[14,34],"is":[16],"challenging":[17],"due":[18],"to":[19,29,76,85,108,115],"their":[20],"highly":[21],"nonlinear":[22],"nature.":[23],"We":[24],"provide":[25],"a":[26,122],"comprehensive":[27],"introduction":[28],"the":[30,61,78,91,96,126,130],"analysis":[31],"of":[32,80,93,113,132],"recurrent":[33],"(RNNs)":[36],"using":[37,95],"robust":[38],"and":[40,60,100],"dissipativity":[41],"theory.":[42],"Specifically,":[43],"we":[44,89,102,119],"consider":[45],"<m:math":[46,62],"xmlns:m=\"http://www.w3.org/1998/Math/MathML\">":[47,63],"<m:msub>":[48,64],"<m:mrow>":[49,53,65,68],"<m:mi":[50],"mathvariant=\"script\">H</m:mi>":[51],"</m:mrow>":[52,55,67,70],"<m:mn>2</m:mn>":[54,69],"</m:msub>":[56,71],"</m:math>":[57,72],"{\\mathcal{H}_{2}}":[58],"-performance":[59],"<m:mi>\u2113</m:mi>":[66],"{\\ell":[73],"_{2}}":[74],"-gain":[75],"quantify":[77],"robustness":[79,92,98,131],"dynamic":[81],"RNNs":[82,94,114],"with":[83],"respect":[84],"input":[86],"perturbations.":[87],"First,":[88],"analyze":[90],"proposed":[97,127],"certificates":[99],"then,":[101],"present":[103],"linear":[104],"matrix":[105],"inequality":[106],"constraints":[107],"be":[109],"used":[110],"training":[112],"enforce":[116],"robustness.":[117],"Finally,":[118],"illustrate":[120],"numerical":[123],"example":[124],"that":[125],"approach":[128],"enhances":[129],"RNNs.":[133]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
