乐胖代购免代理版

{"id":"https://openalex.org/W2156564598","doi":"https://doi.org/10.1109/tcsi.2008.925816","title":"Convergence Analysis of a Class of Nonsmooth Gradient Systems","display_name":"Convergence Analysis of a Class of Nonsmooth Gradient Systems","publication_year":2008,"publication_date":"2008-12-01","ids":{"openalex":"https://openalex.org/W2156564598","doi":"https://doi.org/10.1109/tcsi.2008.925816","mag":"2156564598"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2008.925816","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"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":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-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/A5030103251","display_name":"Wenlian Lu","orcid":"https://orcid.org/0000-0003-1880-6240"},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"funder","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"None Wenlian Lu","raw_affiliation_strings":["School of Mathematical Sciences, Fudan University, Shanghai, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Fudan University, Shanghai, China","institution_ids":["https://openalex.org/I24943067"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100384686","display_name":"Jun Wang","orcid":"https://orcid.org/0000-0002-1305-5735"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"funder","lineage":["https://openalex.org/I177725633"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"None Jun Wang","raw_affiliation_strings":["Department of Mechanical and Automatic Engineering, Chinese University of Hong Kong, Sha Tin, Hong Kong, China"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Automatic Engineering, Chinese University of Hong Kong, Sha Tin, Hong Kong, China","institution_ids":["https://openalex.org/I177725633"]}]}],"institution_assertions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.296,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":32,"citation_normalized_percentile":{"value":0.917361,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":92},"biblio":{"volume":"55","issue":"11","first_page":"3514","last_page":"3527"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9999,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9999,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9987,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9847,"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/smoothness","display_name":"Smoothness","score":0.57320535},{"id":"https://openalex.org/keywords/activation-function","display_name":"Activation function","score":0.5566479},{"id":"https://openalex.org/keywords/differential-inclusion","display_name":"Differential inclusion","score":0.5144503},{"id":"https://openalex.org/keywords/normal-convergence","display_name":"Normal convergence","score":0.47980478}],"concepts":[{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6246158},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6228602},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.57320535},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5668502},{"id":"https://openalex.org/C38365724","wikidata":"https://www.wikidata.org/wiki/Q4677469","display_name":"Activation function","level":3,"score":0.5566479},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.556151},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5410823},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5251826},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.51865834},{"id":"https://openalex.org/C70834904","wikidata":"https://www.wikidata.org/wiki/Q1054638","display_name":"Differential inclusion","level":2,"score":0.5144503},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.50735587},{"id":"https://openalex.org/C14928880","wikidata":"https://www.wikidata.org/wiki/Q1512559","display_name":"Normal convergence","level":4,"score":0.47980478},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.47667006},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.47214678},{"id":"https://openalex.org/C5871375","wikidata":"https://www.wikidata.org/wiki/Q1780715","display_name":"Compact convergence","level":4,"score":0.44129443},{"id":"https://openalex.org/C538505008","wikidata":"https://www.wikidata.org/wiki/Q3979448","display_name":"Convergence tests","level":4,"score":0.43469095},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.42451078},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3491363},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34868544},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24223137},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07212326},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","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},{"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2008.925816","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"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":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.79,"display_name":"Reduced inequalities"}],"grants":[],"datasets":[],"versions":[],"referenced_works_count":36,"referenced_works":["https://openalex.org/W1551360398","https://openalex.org/W1557899381","https://openalex.org/W1966864455","https://openalex.org/W1967509211","https://openalex.org/W1974469776","https://openalex.org/W1974672421","https://openalex.org/W1996195522","https://openalex.org/W2010141219","https://openalex.org/W2021361347","https://openalex.org/W2031529027","https://openalex.org/W2044083366","https://openalex.org/W2056717940","https://openalex.org/W2057553352","https://openalex.org/W2062210787","https://openalex.org/W2065134213","https://openalex.org/W2080803951","https://openalex.org/W2084820442","https://openalex.org/W2086635487","https://openalex.org/W2112056482","https://openalex.org/W2112246162","https://openalex.org/W2117488025","https://openalex.org/W2121752938","https://openalex.org/W2126681784","https://openalex.org/W2128084896","https://openalex.org/W2133838859","https://openalex.org/W2148418614","https://openalex.org/W2150534338","https://openalex.org/W2155660320","https://openalex.org/W2160121923","https://openalex.org/W2169273485","https://openalex.org/W2170790343","https://openalex.org/W2310420328","https://openalex.org/W2331639718","https://openalex.org/W2612952478","https://openalex.org/W4210718478","https://openalex.org/W4249513058"],"related_works":["https://openalex.org/W4253827225","https://openalex.org/W3105212187","https://openalex.org/W2951265198","https://openalex.org/W2482464444","https://openalex.org/W2102183453","https://openalex.org/W2099365622","https://openalex.org/W2060809327","https://openalex.org/W2042111348","https://openalex.org/W2034145661","https://openalex.org/W2028595206"],"abstract_inverted_index":{"In":[0,83],"this":[1,54],"paper,":[2],"we":[3,74,95,101],"present":[4,127],"new":[5],"results":[6,125],"on":[7],"convergence":[8,51,78,108],"of":[9,12,20,26,39,53,64,70,79,113,131],"a":[10,37],"class":[11,25],"nonlinear":[13],"dynamical":[14],"systems":[15,27],"modeled":[16],"by":[17],"the":[18,44,50,62,65,71,76,80,86,97,104,107,111,123,128,132],"gradients":[19],"nonsmooth":[21],"cost":[22,66],"functions.":[23],"This":[24],"arises":[28],"from":[29],"neural-network":[30,41],"research":[31],"and":[32,110,126],"can":[33],"be":[34],"regarded":[35],"as":[36],"generalization":[38],"existing":[40],"models.":[42],"Using":[43],"recently":[45],"developed":[46],"Lstrokojasiewicz":[47],"gradient":[48],"inequality,":[49],"analysis":[52],"gradient-like":[55],"differential":[56,81],"inclusion":[57],"is":[58],"given.":[59],"Without":[60],"assuming":[61],"smoothness":[63],"function":[67,90],"or":[68],"analyticity":[69],"activation":[72,89],"function,":[73],"prove":[75,96],"output":[77],"system.":[82],"addition,":[84],"for":[85],"piecewise":[87],"analytic":[88],"with":[91],"positive":[92],"first-order":[93],"derivative,":[94],"state":[98],"convergence.":[99],"Furthermore,":[100],"also":[102],"discuss":[103],"relationship":[105],"between":[106],"rate":[109],"location":[112],"terminal":[114],"limit":[115],"point.":[116],"Numerical":[117],"examples":[118],"are":[119],"provided":[120],"to":[121],"illustrate":[122],"theoretical":[124],"goal-seeking":[129],"capability":[130],"systems.":[133]},"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2156564598","counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":4}],"updated_date":"2025-04-15T20:02:26.502621","created_date":"2016-06-24"}