{"id":"https://openalex.org/W2065905935","doi":"https://doi.org/10.1109/tnnls.2014.2357451","title":"Globally Stable Adaptive Backstepping Neural Network Control for Uncertain Strict-Feedback Systems With Tracking Accuracy Known &lt;italic&gt;a Priori&lt;/italic&gt;","display_name":"Globally Stable Adaptive Backstepping Neural Network Control for Uncertain Strict-Feedback Systems With Tracking Accuracy Known &lt;italic&gt;a Priori&lt;/italic&gt;","publication_year":2014,"publication_date":"2014-09-25","ids":{"openalex":"https://openalex.org/W2065905935","doi":"https://doi.org/10.1109/tnnls.2014.2357451","mag":"2065905935","pmid":"https://pubmed.ncbi.nlm.nih.gov/25265634"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2014.2357451","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2014.2357451","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 Neural Networks and Learning Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5101435243","display_name":"Weisheng Chen","orcid":"https://orcid.org/0000-0002-0430-1201"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Weisheng Chen","raw_affiliation_strings":["School of Mathematics and Statistics, Xidian University, Xi\u2019an, China","School of Mathematics and Statistics, Xidian University, Xi'an, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Xidian University, Xi\u2019an, China","institution_ids":["https://openalex.org/I149594827"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Xidian University, Xi'an, China","institution_ids":["https://openalex.org/I149594827"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008501506","display_name":"Shuzhi Sam Ge","orcid":"https://orcid.org/0000-0001-5549-312X"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]},{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN","SG"],"is_corresponding":false,"raw_author_name":"Shuzhi Sam Ge","raw_affiliation_strings":["Department of Electrical and Computer Engineering, and the Social Robotics Laboratory, Interactive Digital Media Institute, National University of Singapore, Singapore","School of Computer Science and Engineering, Center for Robotics, University of Electronic Science and Technology of China, Chengdu, China"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, and the Social Robotics Laboratory, Interactive Digital Media Institute, National University of Singapore, Singapore","institution_ids":["https://openalex.org/I165932596"]},{"raw_affiliation_string":"School of Computer Science and Engineering, Center for Robotics, University of Electronic Science and Technology of China, Chengdu, China","institution_ids":["https://openalex.org/I150229711"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101932506","display_name":"Jian Wu","orcid":"https://orcid.org/0000-0003-1508-7105"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jian Wu","raw_affiliation_strings":["School of Mathematics and Statistics, Xidian University, Xi\u2019an, China","School of Mathematics and Statistics, Xidian University, Xi'an, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Xidian University, Xi\u2019an, China","institution_ids":["https://openalex.org/I149594827"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Xidian University, Xi'an, China","institution_ids":["https://openalex.org/I149594827"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091227928","display_name":"Maoguo Gong","orcid":"https://orcid.org/0000-0002-0415-8556"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Maoguo Gong","raw_affiliation_strings":["Key Laboratory of Intelligent Perception and Image Understanding, Ministry of Education, Xidian University, Xi\u2019an, China","Key Laboratory of Intelligent Perception and Image Understanding, Ministry of Education, Xidian University, Xi'an, China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Intelligent Perception and Image Understanding, Ministry of Education, Xidian University, Xi\u2019an, China","institution_ids":["https://openalex.org/I149594827"]},{"raw_affiliation_string":"Key Laboratory of Intelligent Perception and Image Understanding, Ministry of Education, Xidian University, Xi'an, China","institution_ids":["https://openalex.org/I149594827"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5101435243"],"corresponding_institution_ids":["https://openalex.org/I149594827"],"apc_list":null,"apc_paid":null,"fwci":20.9532,"has_fulltext":false,"cited_by_count":226,"citation_normalized_percentile":{"value":0.9950799,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"26","issue":"9","first_page":"1842","last_page":"1854"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9997000098228455,"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/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9997000098228455,"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/T10320","display_name":"Neural Networks and Applications","score":0.9939000010490417,"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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9937999844551086,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/backstepping","display_name":"Backstepping","score":0.9188780784606934},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.7138732075691223},{"id":"https://openalex.org/keywords/tracking-error","display_name":"Tracking error","score":0.6405370235443115},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.6353512406349182},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5690618753433228},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5001707077026367},{"id":"https://openalex.org/keywords/adaptive-control","display_name":"Adaptive control","score":0.49614033102989197},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.48256388306617737},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.47824278473854065},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4675183594226837},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44765177369117737},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.436772882938385},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3300706148147583},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.2552453875541687},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.19125154614448547},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1537354290485382}],"concepts":[{"id":"https://openalex.org/C72218879","wikidata":"https://www.wikidata.org/wiki/Q4839759","display_name":"Backstepping","level":4,"score":0.9188780784606934},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.7138732075691223},{"id":"https://openalex.org/C183356978","wikidata":"https://www.wikidata.org/wiki/Q1779213","display_name":"Tracking error","level":3,"score":0.6405370235443115},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.6353512406349182},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5690618753433228},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5001707077026367},{"id":"https://openalex.org/C107464732","wikidata":"https://www.wikidata.org/wiki/Q235781","display_name":"Adaptive control","level":3,"score":0.49614033102989197},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.48256388306617737},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.47824278473854065},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4675183594226837},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44765177369117737},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.436772882938385},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3300706148147583},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.2552453875541687},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.19125154614448547},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1537354290485382},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D005246","descriptor_name":"Feedback","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D005246","descriptor_name":"Feedback","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D005246","descriptor_name":"Feedback","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D035501","descriptor_name":"Uncertainty","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D035501","descriptor_name":"Uncertainty","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D035501","descriptor_name":"Uncertainty","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2014.2357451","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2014.2357451","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 Neural Networks and Learning Systems","raw_type":"journal-article"},{"id":"pmid:25265634","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/25265634","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":"IEEE transactions on neural networks and learning systems","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.7699999809265137,"display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G318458462","display_name":null,"funder_award_id":"61203074","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4112548190","display_name":null,"funder_award_id":"NCET-10-0665","funder_id":"https://openalex.org/F4320334924","funder_display_name":"Program for New Century Excellent Talents in University"},{"id":"https://openalex.org/G5809087347","display_name":null,"funder_award_id":"61174213","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334924","display_name":"Program for New Century Excellent Talents in University","ror":"https://ror.org/01mv9t934"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":55,"referenced_works":["https://openalex.org/W1480635300","https://openalex.org/W1487112583","https://openalex.org/W1487127700","https://openalex.org/W1496777766","https://openalex.org/W1572326640","https://openalex.org/W1906755568","https://openalex.org/W1969540296","https://openalex.org/W1977485777","https://openalex.org/W1982214011","https://openalex.org/W1989421683","https://openalex.org/W1994507996","https://openalex.org/W1998433168","https://openalex.org/W2013728047","https://openalex.org/W2015768593","https://openalex.org/W2050246747","https://openalex.org/W2051671655","https://openalex.org/W2062373349","https://openalex.org/W2065184457","https://openalex.org/W2072156826","https://openalex.org/W2076597241","https://openalex.org/W2090167557","https://openalex.org/W2092689064","https://openalex.org/W2098732944","https://openalex.org/W2102057409","https://openalex.org/W2102844581","https://openalex.org/W2103658214","https://openalex.org/W2110638818","https://openalex.org/W2113442785","https://openalex.org/W2116444233","https://openalex.org/W2117070017","https://openalex.org/W2124359248","https://openalex.org/W2124766031","https://openalex.org/W2130462650","https://openalex.org/W2130762434","https://openalex.org/W2131086551","https://openalex.org/W2132179668","https://openalex.org/W2133594302","https://openalex.org/W2142129363","https://openalex.org/W2142148039","https://openalex.org/W2142572589","https://openalex.org/W2147577555","https://openalex.org/W2150535417","https://openalex.org/W2154088208","https://openalex.org/W2160917764","https://openalex.org/W2165341314","https://openalex.org/W2166778519","https://openalex.org/W2167656575","https://openalex.org/W2170346869","https://openalex.org/W2171574462","https://openalex.org/W2179457994","https://openalex.org/W2501928905","https://openalex.org/W2564949869","https://openalex.org/W3023665282","https://openalex.org/W4205940976","https://openalex.org/W6678232880"],"related_works":["https://openalex.org/W1847613412","https://openalex.org/W2376449068","https://openalex.org/W4382203996","https://openalex.org/W4365392829","https://openalex.org/W2100998971","https://openalex.org/W2002811656","https://openalex.org/W2990087644","https://openalex.org/W2517897957","https://openalex.org/W2104457306","https://openalex.org/W1934622834"],"abstract_inverted_index":{"This":[0],"paper":[1,50],"addresses":[2],"the":[3,25,28,31,42,52,55,67,72,75,88,118,121,126,137,142],"problem":[4],"of":[5,20,30,54,74,141],"globally":[6,95],"stable":[7],"direct":[8],"adaptive":[9,44,127],"backstepping":[10,45],"neural":[11],"network":[12],"(NN)":[13],"tracking":[14,33,56,77],"control":[15,47,119,123,144],"design":[16,117],"for":[17],"a":[18,37,85],"class":[19],"uncertain":[21],"strict-feedback":[22],"systems":[23],"under":[24],"assumption":[26],"that":[27],"accuracy":[29,73],"ultimate":[32,76],"error":[34,57,78],"is":[35,91,103],"given":[36,134],"priori.":[38],"In":[39],"contrast":[40],"to":[41,93,104,116,135],"classical":[43],"NN":[46],"schemes,":[48],"this":[49],"analyzes":[51],"convergence":[53],"using":[58],"Barbalat's":[59],"Lemma":[60],"via":[61],"some":[62],"nonnegative":[63],"functions":[64],"rather":[65],"than":[66],"positive-definite":[68],"Lyapunov":[69],"functions.":[70],"Thus,":[71],"can":[79],"be":[80,94],"determined":[81],"and":[82,87,125,139],"adjusted":[83],"accurately":[84],"priori,":[86],"closed-loop":[89],"system":[90],"guaranteed":[92],"uniformly":[96],"ultimately":[97],"bounded.":[98],"The":[99],"main":[100],"technical":[101],"novelty":[102],"construct":[105],"three":[106],"new":[107],"n":[108],"th-order":[109],"continuously":[110],"differentiable":[111],"functions,":[112],"which":[113],"are":[114,133],"used":[115],"law,":[120],"virtual":[122],"variables,":[124],"laws.":[128],"Finally,":[129],"two":[130],"simulation":[131],"examples":[132],"illustrate":[136],"effectiveness":[138],"advantages":[140],"proposed":[143],"method.":[145]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":17},{"year":2024,"cited_by_count":18},{"year":2023,"cited_by_count":18},{"year":2022,"cited_by_count":14},{"year":2021,"cited_by_count":29},{"year":2020,"cited_by_count":27},{"year":2019,"cited_by_count":31},{"year":2018,"cited_by_count":17},{"year":2017,"cited_by_count":25},{"year":2016,"cited_by_count":18},{"year":2015,"cited_by_count":8},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-02T15:55:50.835912","created_date":"2016-06-24T00:00:00"}
