{"id":"https://openalex.org/W3179609542","doi":"https://doi.org/10.1109/tac.2023.3294101","title":"Recurrent Equilibrium Networks: Flexible Dynamic Models With Guaranteed Stability and Robustness","display_name":"Recurrent Equilibrium Networks: Flexible Dynamic Models With Guaranteed Stability and Robustness","publication_year":2023,"publication_date":"2023-07-11","ids":{"openalex":"https://openalex.org/W3179609542","doi":"https://doi.org/10.1109/tac.2023.3294101","mag":"3179609542"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2023.3294101","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2023.3294101","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005257254","display_name":"Max Revay","orcid":"https://orcid.org/0000-0002-8954-8907"},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"The University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]},{"id":"https://openalex.org/I4210127558","display_name":"Australian Centre for Robotic Vision","ror":"https://ror.org/02zv9xv82","country_code":"AU","type":"facility","lineage":["https://openalex.org/I4210127558"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Max Revay","raw_affiliation_strings":["Australian Centre for Robotics and School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, NSW, Australia"],"affiliations":[{"raw_affiliation_string":"Australian Centre for Robotics and School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, NSW, Australia","institution_ids":["https://openalex.org/I4210127558","https://openalex.org/I129604602"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101804818","display_name":"Ruigang Wang","orcid":"https://orcid.org/0000-0002-9954-4547"},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"The University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]},{"id":"https://openalex.org/I4210127558","display_name":"Australian Centre for Robotic Vision","ror":"https://ror.org/02zv9xv82","country_code":"AU","type":"facility","lineage":["https://openalex.org/I4210127558"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Ruigang Wang","raw_affiliation_strings":["Australian Centre for Robotics and School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, NSW, Australia"],"affiliations":[{"raw_affiliation_string":"Australian Centre for Robotics and School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, NSW, Australia","institution_ids":["https://openalex.org/I4210127558","https://openalex.org/I129604602"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026600708","display_name":"Ian R. Manchester","orcid":"https://orcid.org/0000-0002-7035-3173"},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"The University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]},{"id":"https://openalex.org/I4210127558","display_name":"Australian Centre for Robotic Vision","ror":"https://ror.org/02zv9xv82","country_code":"AU","type":"facility","lineage":["https://openalex.org/I4210127558"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Ian R. Manchester","raw_affiliation_strings":["Australian Centre for Robotics and School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, NSW, Australia"],"affiliations":[{"raw_affiliation_string":"Australian Centre for Robotics and School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, NSW, Australia","institution_ids":["https://openalex.org/I4210127558","https://openalex.org/I129604602"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5005257254"],"corresponding_institution_ids":["https://openalex.org/I129604602","https://openalex.org/I4210127558"],"apc_list":null,"apc_paid":null,"fwci":9.8747,"has_fulltext":false,"cited_by_count":57,"citation_normalized_percentile":{"value":0.98702961,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"69","issue":"5","first_page":"2855","last_page":"2870"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9984999895095825,"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"}},"topics":[{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9984999895095825,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9973000288009644,"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/T10621","display_name":"Gene Regulatory Network Analysis","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.756689727306366},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.547209620475769},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5407817959785461},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4454944431781769},{"id":"https://openalex.org/keywords/control-engineering","display_name":"Control engineering","score":0.3326374292373657},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.2046053111553192},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.12618058919906616},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11773961782455444},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.06313356757164001}],"concepts":[{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.756689727306366},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.547209620475769},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5407817959785461},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4454944431781769},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.3326374292373657},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.2046053111553192},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.12618058919906616},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11773961782455444},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.06313356757164001},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2023.3294101","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2023.3294101","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G650785078","display_name":null,"funder_award_id":"DP190102963","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"}],"funders":[{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":122,"referenced_works":["https://openalex.org/W124292005","https://openalex.org/W287703190","https://openalex.org/W618254468","https://openalex.org/W1134107867","https://openalex.org/W1533861849","https://openalex.org/W1546959115","https://openalex.org/W1598493736","https://openalex.org/W1601803999","https://openalex.org/W1611538460","https://openalex.org/W1964164732","https://openalex.org/W1969862729","https://openalex.org/W1989312953","https://openalex.org/W2014993114","https://openalex.org/W2026769037","https://openalex.org/W2055337535","https://openalex.org/W2064675550","https://openalex.org/W2065313971","https://openalex.org/W2066666591","https://openalex.org/W2084233036","https://openalex.org/W2097944741","https://openalex.org/W2101773087","https://openalex.org/W2105239319","https://openalex.org/W2112822418","https://openalex.org/W2116196416","https://openalex.org/W2117349054","https://openalex.org/W2119158876","https://openalex.org/W2121863487","https://openalex.org/W2128904261","https://openalex.org/W2129202194","https://openalex.org/W2129644659","https://openalex.org/W2134889984","https://openalex.org/W2135604683","https://openalex.org/W2143075842","https://openalex.org/W2144355672","https://openalex.org/W2155007355","https://openalex.org/W2160068178","https://openalex.org/W2168011765","https://openalex.org/W2181030348","https://openalex.org/W2296039882","https://openalex.org/W2490900388","https://openalex.org/W2496713483","https://openalex.org/W2581472888","https://openalex.org/W2624761220","https://openalex.org/W2755589696","https://openalex.org/W2782580911","https://openalex.org/W2791909561","https://openalex.org/W2807040120","https://openalex.org/W2809760328","https://openalex.org/W2884629900","https://openalex.org/W2884801476","https://openalex.org/W2894844669","https://openalex.org/W2897405124","https://openalex.org/W2911631246","https://openalex.org/W2915638893","https://openalex.org/W2919115771","https://openalex.org/W2962711206","https://openalex.org/W2962847566","https://openalex.org/W2963575866","https://openalex.org/W2963626025","https://openalex.org/W2963664410","https://openalex.org/W2964050716","https://openalex.org/W2964121744","https://openalex.org/W2964153729","https://openalex.org/W2964161785","https://openalex.org/W2964725706","https://openalex.org/W2968953580","https://openalex.org/W2970362693","https://openalex.org/W2970620827","https://openalex.org/W2970900903","https://openalex.org/W2997330246","https://openalex.org/W2998277219","https://openalex.org/W3022782115","https://openalex.org/W3025456519","https://openalex.org/W3046519016","https://openalex.org/W3090968963","https://openalex.org/W3097602886","https://openalex.org/W3098955748","https://openalex.org/W3100383449","https://openalex.org/W3104105596","https://openalex.org/W3105768446","https://openalex.org/W3106729350","https://openalex.org/W3112185765","https://openalex.org/W3112912317","https://openalex.org/W3113374047","https://openalex.org/W3117881175","https://openalex.org/W3129345461","https://openalex.org/W3133218159","https://openalex.org/W3155520207","https://openalex.org/W3159659315","https://openalex.org/W3185441898","https://openalex.org/W3185519452","https://openalex.org/W3195133498","https://openalex.org/W3195968524","https://openalex.org/W3201167453","https://openalex.org/W3202366558","https://openalex.org/W4200635938","https://openalex.org/W4214717370","https://openalex.org/W4226183374","https://openalex.org/W4226326022","https://openalex.org/W4234350010","https://openalex.org/W4251684636","https://openalex.org/W4381826983","https://openalex.org/W6631190155","https://openalex.org/W6631943919","https://openalex.org/W6637162671","https://openalex.org/W6682849425","https://openalex.org/W6739659843","https://openalex.org/W6748277150","https://openalex.org/W6748311976","https://openalex.org/W6751834733","https://openalex.org/W6757170499","https://openalex.org/W6763711611","https://openalex.org/W6765807149","https://openalex.org/W6767563556","https://openalex.org/W6771747237","https://openalex.org/W6772225279","https://openalex.org/W6772931863","https://openalex.org/W6779581272","https://openalex.org/W6783862537","https://openalex.org/W6791113056","https://openalex.org/W6848864830","https://openalex.org/W6854136331"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W4396696052"],"abstract_inverted_index":{"This":[0],"paper":[1,175],"introduces":[2],"<italic":[3],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[4,122],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">recurrent":[5],"equilibrium":[6],"networks</i>":[7],"(RENs),":[8],"a":[9,47,118],"new":[10,26,162],"class":[11,28,43],"of":[12,34,50,85,160],"nonlinear":[13,51,111,169,181],"dynamical":[14],"models":[15,39,55],"for":[16,142],"applications":[17,178],"in":[18,40,120,179],"machine":[19],"learning,":[20],"system":[21,170],"identification":[22,171],"and":[23,36,54,67,90,99,104,109,129,150,158,173,184],"control.":[24],"The":[25,156],"model":[27,163],"admits":[29],"\u201cbuilt":[30],"in\u201d":[31],"behavioural":[32],"guarantees":[33],"stability":[35,52,128,187],"robustness.":[37],"All":[38],"the":[41,161,174],"proposed":[42],"are":[44,71,114,131],"contracting":[45,86,110],"\u2013":[46,53],"strong":[48],"form":[49],"can":[56,76,105,153],"satisfy":[57],"prescribed":[58],"incremental":[59,68],"integral":[60],"quadratic":[61],"constraints":[62],"(IQC),":[63],"including":[64],"Lipschitz":[65],"bounds":[66],"passivity.":[69],"RENs":[70,113],"otherwise":[72],"very":[73],"flexible:":[74],"they":[75],"represent":[77],"all":[78,82,94,100,107],"stable":[79,101],"linear":[80],"systems,":[81],"previously-known":[83],"sets":[84],"recurrent":[87],"neural":[88,97],"networks":[89],"echo":[91],"state":[92],"networks,":[93,98],"deep":[95],"feedforward":[96],"Wiener/Hammerstein":[102],"models,":[103],"approximate":[106],"fading-memory":[108],"systems.":[112],"parameterized":[115],"directly":[116],"by":[117],"vector":[119],"<inline-formula":[121],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex-math":[123],"notation=\"LaTeX\">$\\mathbb":[124],"{R}^{N}$</tex-math></inline-formula>":[125],",":[126],"i.e.":[127],"robustness":[130,159],"ensured":[132],"without":[133],"parameter":[134],"constraints,":[135],"which":[136],"simplifies":[137],"learning":[138],"since":[139],"generic":[140],"methods":[141],"unconstrained":[143],"optimization":[144],"such":[145],"as":[146],"stochastic":[147],"gradient":[148],"descent":[149],"its":[151],"variants":[152],"be":[154],"used.":[155],"performance":[157],"set":[164],"is":[165],"evaluated":[166],"on":[167],"benchmark":[168],"problems,":[172],"also":[176],"presents":[177],"data-driven":[180],"observer":[182],"design":[183],"control":[185],"with":[186],"guarantees.":[188]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":19},{"year":2024,"cited_by_count":25},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-03-29T08:15:47.926485","created_date":"2025-10-10T00:00:00"}