{"id":"https://openalex.org/W7108217369","doi":"https://doi.org/10.1109/tfuzz.2025.3639438","title":"Reinforcement Learning-Based IT-2 Fuzzy Fractional-Order Sliding Mode Control for Leader\u2013Follower Formation Tracking of Flexible-Joint Robots","display_name":"Reinforcement Learning-Based IT-2 Fuzzy Fractional-Order Sliding Mode Control for Leader\u2013Follower Formation Tracking of Flexible-Joint Robots","publication_year":2025,"publication_date":"2025-12-02","ids":{"openalex":"https://openalex.org/W7108217369","doi":"https://doi.org/10.1109/tfuzz.2025.3639438"},"language":null,"primary_location":{"id":"doi:10.1109/tfuzz.2025.3639438","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2025.3639438","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"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 Fuzzy Systems","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":null,"display_name":"G. Narayanan","orcid":"https://orcid.org/0000-0002-4225-6835"},"institutions":[{"id":"https://openalex.org/I31419693","display_name":"Kyungpook National University","ror":"https://ror.org/040c17130","country_code":"KR","type":"education","lineage":["https://openalex.org/I31419693"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"G. Narayanan","raw_affiliation_strings":["School of Electronic and Electrical Engineering, Kyungpook National University, Daegu, South Korea"],"raw_orcid":"https://orcid.org/0000-0002-4225-6835","affiliations":[{"raw_affiliation_string":"School of Electronic and Electrical Engineering, Kyungpook National University, Daegu, South Korea","institution_ids":["https://openalex.org/I31419693"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Sangmoon Lee","orcid":"https://orcid.org/0000-0001-8252-952X"},"institutions":[{"id":"https://openalex.org/I31419693","display_name":"Kyungpook National University","ror":"https://ror.org/040c17130","country_code":"KR","type":"education","lineage":["https://openalex.org/I31419693"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Sangmoon Lee","raw_affiliation_strings":["School of Electronic and Electrical Engineering, Kyungpook National University, Daegu, South Korea"],"raw_orcid":"https://orcid.org/0000-0001-8252-952X","affiliations":[{"raw_affiliation_string":"School of Electronic and Electrical Engineering, Kyungpook National University, Daegu, South Korea","institution_ids":["https://openalex.org/I31419693"]}]},{"author_position":"last","author":{"id":null,"display_name":"Sangtae Ahn","orcid":"https://orcid.org/0000-0001-9487-5649"},"institutions":[{"id":"https://openalex.org/I31419693","display_name":"Kyungpook National University","ror":"https://ror.org/040c17130","country_code":"KR","type":"education","lineage":["https://openalex.org/I31419693"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Sangtae Ahn","raw_affiliation_strings":["School of Electronic and Electrical Engineering, Kyungpook National University, Daegu, South Korea"],"raw_orcid":"https://orcid.org/0000-0001-9487-5649","affiliations":[{"raw_affiliation_string":"School of Electronic and Electrical Engineering, Kyungpook National University, Daegu, South Korea","institution_ids":["https://openalex.org/I31419693"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I31419693"],"apc_list":null,"apc_paid":null,"fwci":0.9389,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.83180937,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"34","issue":"2","first_page":"503","last_page":"516"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.6340000033378601,"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.6340000033378601,"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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.16120000183582306,"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/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.06750000268220901,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/control-theory","display_name":"Control theory (sociology)","score":0.7646999955177307},{"id":"https://openalex.org/keywords/backstepping","display_name":"Backstepping","score":0.6797999739646912},{"id":"https://openalex.org/keywords/tracking-error","display_name":"Tracking error","score":0.6419000029563904},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5615000128746033},{"id":"https://openalex.org/keywords/reinforcement-learning","display_name":"Reinforcement learning","score":0.5475000143051147},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5378000140190125},{"id":"https://openalex.org/keywords/sliding-mode-control","display_name":"Sliding mode control","score":0.47269999980926514},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.4717000126838684},{"id":"https://openalex.org/keywords/tracking","display_name":"Tracking (education)","score":0.4690000116825104}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.7646999955177307},{"id":"https://openalex.org/C72218879","wikidata":"https://www.wikidata.org/wiki/Q4839759","display_name":"Backstepping","level":4,"score":0.6797999739646912},{"id":"https://openalex.org/C183356978","wikidata":"https://www.wikidata.org/wiki/Q1779213","display_name":"Tracking error","level":3,"score":0.6419000029563904},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6340000033378601},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5615000128746033},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.5475000143051147},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5378000140190125},{"id":"https://openalex.org/C36662352","wikidata":"https://www.wikidata.org/wiki/Q6008560","display_name":"Sliding mode control","level":3,"score":0.47269999980926514},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.4717000126838684},{"id":"https://openalex.org/C2775936607","wikidata":"https://www.wikidata.org/wiki/Q466845","display_name":"Tracking (education)","level":2,"score":0.4690000116825104},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.45579999685287476},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4074000120162964},{"id":"https://openalex.org/C2776829284","wikidata":"https://www.wikidata.org/wiki/Q1341651","display_name":"Lyapunov stability","level":3,"score":0.3946000039577484},{"id":"https://openalex.org/C195975749","wikidata":"https://www.wikidata.org/wiki/Q1475705","display_name":"Fuzzy control system","level":3,"score":0.3901999890804291},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.3517000079154968},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.34470000863075256},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.3321000039577484},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.3276999890804291},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.3246999979019165},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.32420000433921814},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.28929999470710754},{"id":"https://openalex.org/C202286095","wikidata":"https://www.wikidata.org/wiki/Q579262","display_name":"Error function","level":2,"score":0.28029999136924744},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.2777999937534332},{"id":"https://openalex.org/C107464732","wikidata":"https://www.wikidata.org/wiki/Q235781","display_name":"Adaptive control","level":3,"score":0.2734000086784363},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.26269999146461487},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.2578999996185303},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.25600001215934753},{"id":"https://openalex.org/C48677424","wikidata":"https://www.wikidata.org/wiki/Q6888088","display_name":"Mode (computer interface)","level":2,"score":0.2547000050544739}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tfuzz.2025.3639438","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2025.3639438","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"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 Fuzzy Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322120","display_name":"National Research Foundation of Korea","ror":"https://ror.org/013aysd81"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W2770878849","https://openalex.org/W2780814805","https://openalex.org/W2895632869","https://openalex.org/W2904446620","https://openalex.org/W2999849856","https://openalex.org/W3004863268","https://openalex.org/W3012901298","https://openalex.org/W3033814782","https://openalex.org/W3193905726","https://openalex.org/W3199908702","https://openalex.org/W3207351513","https://openalex.org/W3217020828","https://openalex.org/W4298137341","https://openalex.org/W4312345920","https://openalex.org/W4312836399","https://openalex.org/W4313144554","https://openalex.org/W4319459190","https://openalex.org/W4327703283","https://openalex.org/W4366503956","https://openalex.org/W4385381673","https://openalex.org/W4385693193","https://openalex.org/W4385863366","https://openalex.org/W4386002882","https://openalex.org/W4390575658","https://openalex.org/W4391421629","https://openalex.org/W4391883198","https://openalex.org/W4392246994","https://openalex.org/W4393340506","https://openalex.org/W4399039388","https://openalex.org/W4401537233","https://openalex.org/W4402626611","https://openalex.org/W4402808976","https://openalex.org/W4406028161","https://openalex.org/W4406770373","https://openalex.org/W4408235904","https://openalex.org/W4409602180"],"related_works":[],"abstract_inverted_index":{"This":[0],"study":[1],"presents":[2],"a":[3,74,108,122,149],"reinforcement":[4,150],"learning-based":[5],"interval":[6],"type-2":[7],"(IT-2)":[8],"fuzzy":[9,58],"formation":[10,79,101,130,172,217],"tracking":[11,46,80,102,173,199],"control":[12,38,133],"strategy":[13],"for":[14,77,113,167,193],"leader-follower":[15],"flexible":[16],"joint":[17],"robots":[18],"(FJRs),":[19],"addressing":[20],"challenges":[21],"arising":[22],"from":[23],"nonlinearities,":[24],"unmodeled":[25],"dynamics,":[26],"and":[27,64,88,129,170,219],"unknown":[28],"external":[29],"disturbances.":[30,65],"The":[31,125],"proposed":[32,211],"approach":[33],"employs":[34],"fractional-order":[35],"sliding":[36,131],"mode":[37,132],"(FOSMC)":[39],"to":[40,137,165,204],"guarantee":[41],"finite-time":[42],"convergence":[43,203],"of":[44,71,99],"the":[45,56,68,78,97,100,114,175,187,210],"error":[47,103,200],"with":[48,174,197],"rigorously":[49],"proven":[50],"stability.":[51],"Unlike":[52],"conventional":[53],"backstepping":[54],"methods,":[55],"IT-2":[57],"FOSMC":[59],"framework":[60],"effectively":[61],"addresses":[62],"uncertainties":[63,169],"By":[66],"considering":[67],"memory":[69],"effect":[70],"fractional":[72],"calculus,":[73],"Hamilton-Jacobi-Bellman":[75],"equation":[76],"dynamics":[81],"is":[82,104,160],"derived":[83],"using":[84,189],"an":[85,155],"auxiliary":[86],"system":[87,168],"equivalent":[89],"transformation.":[90],"A":[91],"novel":[92],"cost":[93,110,127],"function":[94,128],"based":[95,153],"on":[96,154],"derivative":[98],"introduced,":[105],"resulting":[106],"in":[107],"discounted":[109],"that":[111,181],"accounts":[112],"Laplacian":[115],"matrix":[116],"<inline-formula":[117],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[118],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex-math":[119],"notation=\"LaTeX\">$\\widehat{L}$</tex-math></inline-formula>":[120],"under":[121],"performance":[123],"constraint.":[124],"optimal":[126,205],"policy":[134,142],"are":[135],"shown":[136],"be":[138],"gradually":[139],"approximable":[140],"via":[141],"iteration.":[143],"To":[144],"achieve":[145],"intelligent":[146],"near-optimal":[147],"control,":[148],"learning":[151],"algorithm":[152],"actor-critic":[156,190],"neural":[157,194],"network":[158,195],"architecture":[159],"implemented,":[161],"enabling":[162],"all":[163,182],"agents":[164],"compensate":[166],"maintain":[171],"leader.":[176],"Lyapunov":[177],"stability":[178],"analysis":[179],"confirms":[180],"follower":[183],"FJRs":[184],"can":[185],"track":[186],"leader":[188],"update":[191],"laws":[192],"weights,":[196],"distributed":[198],"designs":[201],"ensuring":[202],"values.":[206],"Simulation":[207],"results":[208],"validate":[209],"approach,":[212],"demonstrating":[213],"reduced":[214],"chattering,":[215],"improved":[216],"tracking,":[218],"enhanced":[220],"robustness.":[221]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-12-03T00:00:00"}