{"id":"https://openalex.org/W4309026626","doi":"https://doi.org/10.3389/fnbot.2022.1065256","title":"A robust zeroing neural network and its applications to dynamic complex matrix equation solving and robotic manipulator trajectory tracking","display_name":"A robust zeroing neural network and its applications to dynamic complex matrix equation solving and robotic manipulator trajectory tracking","publication_year":2022,"publication_date":"2022-11-15","ids":{"openalex":"https://openalex.org/W4309026626","doi":"https://doi.org/10.3389/fnbot.2022.1065256","pmid":"https://pubmed.ncbi.nlm.nih.gov/36457416"},"language":"en","primary_location":{"id":"doi:10.3389/fnbot.2022.1065256","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fnbot.2022.1065256","pdf_url":"https://www.frontiersin.org/articles/10.3389/fnbot.2022.1065256/pdf","source":{"id":"https://openalex.org/S115606517","display_name":"Frontiers in Neurorobotics","issn_l":"1662-5218","issn":["1662-5218"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Neurorobotics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.frontiersin.org/articles/10.3389/fnbot.2022.1065256/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073881751","display_name":"Jie Jin","orcid":"https://orcid.org/0000-0002-7386-8412"},"institutions":[{"id":"https://openalex.org/I121296143","display_name":"Hunan University of Science and Technology","ror":"https://ror.org/02m9vrb24","country_code":"CN","type":"education","lineage":["https://openalex.org/I121296143"]},{"id":"https://openalex.org/I165911609","display_name":"Changsha Medical University","ror":"https://ror.org/05dt7z971","country_code":"CN","type":"education","lineage":["https://openalex.org/I165911609"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jie Jin","raw_affiliation_strings":["School of Information Engineering, Changsha Medical University, Changsha, China","School of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information Engineering, Changsha Medical University, Changsha, China","institution_ids":["https://openalex.org/I165911609"]},{"raw_affiliation_string":"School of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan, China","institution_ids":["https://openalex.org/I121296143"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103878761","display_name":"Lv Zhao","orcid":null},"institutions":[{"id":"https://openalex.org/I165911609","display_name":"Changsha Medical University","ror":"https://ror.org/05dt7z971","country_code":"CN","type":"education","lineage":["https://openalex.org/I165911609"]},{"id":"https://openalex.org/I121296143","display_name":"Hunan University of Science and Technology","ror":"https://ror.org/02m9vrb24","country_code":"CN","type":"education","lineage":["https://openalex.org/I121296143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lv Zhao","raw_affiliation_strings":["School of Information Engineering, Changsha Medical University, Changsha, China","School of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information Engineering, Changsha Medical University, Changsha, China","institution_ids":["https://openalex.org/I165911609"]},{"raw_affiliation_string":"School of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan, China","institution_ids":["https://openalex.org/I121296143"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100333510","display_name":"Lei Chen","orcid":"https://orcid.org/0000-0002-8000-7872"},"institutions":[{"id":"https://openalex.org/I121296143","display_name":"Hunan University of Science and Technology","ror":"https://ror.org/02m9vrb24","country_code":"CN","type":"education","lineage":["https://openalex.org/I121296143"]},{"id":"https://openalex.org/I165911609","display_name":"Changsha Medical University","ror":"https://ror.org/05dt7z971","country_code":"CN","type":"education","lineage":["https://openalex.org/I165911609"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lei Chen","raw_affiliation_strings":["School of Information Engineering, Changsha Medical University, Changsha, China","School of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information Engineering, Changsha Medical University, Changsha, China","institution_ids":["https://openalex.org/I165911609"]},{"raw_affiliation_string":"School of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan, China","institution_ids":["https://openalex.org/I121296143"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5107562254","display_name":"Weijie Chen","orcid":"https://orcid.org/0009-0003-3413-3186"},"institutions":[{"id":"https://openalex.org/I121296143","display_name":"Hunan University of Science and Technology","ror":"https://ror.org/02m9vrb24","country_code":"CN","type":"education","lineage":["https://openalex.org/I121296143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Weijie Chen","raw_affiliation_strings":["School of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan, China","institution_ids":["https://openalex.org/I121296143"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5073881751"],"corresponding_institution_ids":["https://openalex.org/I121296143","https://openalex.org/I165911609"],"apc_list":{"value":2950,"currency":"USD","value_usd":2950},"apc_paid":{"value":2950,"currency":"USD","value_usd":2950},"fwci":3.6403,"has_fulltext":true,"cited_by_count":42,"citation_normalized_percentile":{"value":0.93341771,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"16","issue":null,"first_page":"1065256","last_page":"1065256"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10571","display_name":"Robotic Mechanisms and Dynamics","score":0.9973999857902527,"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/T10571","display_name":"Robotic Mechanisms and Dynamics","score":0.9973999857902527,"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/T11325","display_name":"Inertial Sensor and Navigation","score":0.9898999929428101,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9884999990463257,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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":0.7822670340538025},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7518145442008972},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6635763645172119},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.6317405104637146},{"id":"https://openalex.org/keywords/robot-manipulator","display_name":"Robot manipulator","score":0.5871286392211914},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5157340168952942},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5132567882537842},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.4784429371356964},{"id":"https://openalex.org/keywords/tracking","display_name":"Tracking (education)","score":0.4599074721336365},{"id":"https://openalex.org/keywords/recurrent-neural-network","display_name":"Recurrent neural network","score":0.45843392610549927},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.36158931255340576},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.28143882751464844},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.2328183948993683}],"concepts":[{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.7822670340538025},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7518145442008972},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6635763645172119},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.6317405104637146},{"id":"https://openalex.org/C2985527887","wikidata":"https://www.wikidata.org/wiki/Q1587588","display_name":"Robot manipulator","level":3,"score":0.5871286392211914},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5157340168952942},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5132567882537842},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4784429371356964},{"id":"https://openalex.org/C2775936607","wikidata":"https://www.wikidata.org/wiki/Q466845","display_name":"Tracking (education)","level":2,"score":0.4599074721336365},{"id":"https://openalex.org/C147168706","wikidata":"https://www.wikidata.org/wiki/Q1457734","display_name":"Recurrent neural network","level":3,"score":0.45843392610549927},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.36158931255340576},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.28143882751464844},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.2328183948993683},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","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/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/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C19417346","wikidata":"https://www.wikidata.org/wiki/Q7922","display_name":"Pedagogy","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3389/fnbot.2022.1065256","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fnbot.2022.1065256","pdf_url":"https://www.frontiersin.org/articles/10.3389/fnbot.2022.1065256/pdf","source":{"id":"https://openalex.org/S115606517","display_name":"Frontiers in Neurorobotics","issn_l":"1662-5218","issn":["1662-5218"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Neurorobotics","raw_type":"journal-article"},{"id":"pmid:36457416","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/36457416","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in neurorobotics","raw_type":null},{"id":"pmh:oai:doaj.org/article:a894078ed9304a9e96981dfb2959b7f9","is_oa":true,"landing_page_url":"https://doaj.org/article/a894078ed9304a9e96981dfb2959b7f9","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Frontiers in Neurorobotics, Vol 16 (2022)","raw_type":"article"},{"id":"pmh:oai:pubmedcentral.nih.gov:9705728","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/9705728","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Front Neurorobot","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3389/fnbot.2022.1065256","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fnbot.2022.1065256","pdf_url":"https://www.frontiersin.org/articles/10.3389/fnbot.2022.1065256/pdf","source":{"id":"https://openalex.org/S115606517","display_name":"Frontiers in Neurorobotics","issn_l":"1662-5218","issn":["1662-5218"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Neurorobotics","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/9","display_name":"Industry, innovation and infrastructure","score":0.6399999856948853}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322843","display_name":"Natural Science Foundation of\u00a0Hunan Province","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4309026626.pdf","grobid_xml":"https://content.openalex.org/works/W4309026626.grobid-xml"},"referenced_works_count":52,"referenced_works":["https://openalex.org/W1726428156","https://openalex.org/W1973446088","https://openalex.org/W1998578040","https://openalex.org/W2042948601","https://openalex.org/W2124523346","https://openalex.org/W2130317597","https://openalex.org/W2158831443","https://openalex.org/W2164342016","https://openalex.org/W2343558730","https://openalex.org/W2344929049","https://openalex.org/W2390401404","https://openalex.org/W2941887520","https://openalex.org/W2968043153","https://openalex.org/W2978371710","https://openalex.org/W2989156307","https://openalex.org/W2991486793","https://openalex.org/W3003250870","https://openalex.org/W3045439836","https://openalex.org/W3092811059","https://openalex.org/W3093300421","https://openalex.org/W3093347455","https://openalex.org/W3119566912","https://openalex.org/W3120862948","https://openalex.org/W3196353935","https://openalex.org/W3199885834","https://openalex.org/W3212851478","https://openalex.org/W4200200460","https://openalex.org/W4206211217","https://openalex.org/W4207001613","https://openalex.org/W4213015918","https://openalex.org/W4214708851","https://openalex.org/W4214829631","https://openalex.org/W4220798077","https://openalex.org/W4221118739","https://openalex.org/W4226194519","https://openalex.org/W4282918380","https://openalex.org/W4285983667","https://openalex.org/W4289654464","https://openalex.org/W4293211510","https://openalex.org/W4296969162","https://openalex.org/W4303520539","https://openalex.org/W4313011332","https://openalex.org/W6637680738","https://openalex.org/W6683502422","https://openalex.org/W6798544130","https://openalex.org/W6806487735","https://openalex.org/W6809787241","https://openalex.org/W6810598392","https://openalex.org/W6842064560","https://openalex.org/W6843281440","https://openalex.org/W6846177236","https://openalex.org/W6847760493"],"related_works":["https://openalex.org/W4225394202","https://openalex.org/W4298287631","https://openalex.org/W2953061907","https://openalex.org/W1847088711","https://openalex.org/W2373557848","https://openalex.org/W2002488624","https://openalex.org/W2088970451","https://openalex.org/W4309225183","https://openalex.org/W2157008402","https://openalex.org/W2592302855"],"abstract_inverted_index":{"Dynamic":[0],"complex":[1],"matrix":[2],"equation":[3],"(DCME)":[4],"is":[5,85,119],"frequently":[6],"encountered":[7],"in":[8,32,40,82,89],"the":[9,28,51,97,115,129],"fields":[10],"of":[11,30,53,96],"mathematics":[12],"and":[13,15,42,87,94,107,126],"industry,":[14],"numerous":[16],"recurrent":[17],"neural":[18,55,75],"network":[19,56,76],"(RNN)":[20],"models":[21,57],"have":[22],"been":[23],"reported":[24],"to":[25,61,121],"effectively":[26],"find":[27],"solution":[29],"DCME":[31,81],"no":[33],"noise":[34],"environment.":[35],"However,":[36],"noises":[37],"are":[38,101],"unavoidable":[39],"reality,":[41],"dynamic":[43],"systems":[44],"must":[45],"be":[46],"affected":[47],"by":[48,103,109],"noises.":[49],"Thus,":[50],"invention":[52],"anti-noise":[54],"becomes":[58],"increasingly":[59],"important":[60],"address":[62],"this":[63,90],"issue.":[64],"By":[65],"introducing":[66],"a":[67,72],"new":[68],"activation":[69],"function":[70],"(NAF),":[71],"robust":[73],"zeroing":[74],"(RZNN)":[77],"model":[78,100,118],"for":[79],"solving":[80],"noisy-polluted":[83],"environment":[84],"proposed":[86,98,116],"investigated":[88],"paper.":[91],"The":[92],"robustness":[93],"convergence":[95],"RZNN":[99,117],"proved":[102],"strict":[104],"mathematical":[105],"proof":[106],"verified":[108],"comparative":[110],"numerical":[111],"simulation":[112],"results.":[113],"Furthermore,":[114],"applied":[120,139],"manipulator":[122],"trajectory":[123,130],"tracking":[124,131],"control,":[125],"it":[127],"completes":[128],"task":[132],"successfully,":[133],"which":[134],"further":[135],"validates":[136],"its":[137],"practical":[138],"prospects.":[140]},"counts_by_year":[{"year":2026,"cited_by_count":12},{"year":2025,"cited_by_count":14},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":8}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
