{"id":"https://openalex.org/W2803500012","doi":"https://doi.org/10.1109/access.2018.2838127","title":"Double Hyperbolic Reaching Law With Chattering-Free and Fast Convergence","display_name":"Double Hyperbolic Reaching Law With Chattering-Free and Fast Convergence","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2803500012","doi":"https://doi.org/10.1109/access.2018.2838127","mag":"2803500012"},"language":"en","primary_location":{"id":"doi:10.1109/access.2018.2838127","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2018.2838127","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1109/access.2018.2838127","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101917317","display_name":"Liang Tao","orcid":"https://orcid.org/0000-0003-2834-5548"},"institutions":[{"id":"https://openalex.org/I55712492","display_name":"Zhejiang University of Technology","ror":"https://ror.org/02djqfd08","country_code":"CN","type":"education","lineage":["https://openalex.org/I55712492"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liang Tao","raw_affiliation_strings":["Zhejiang University of Technology, Hangzhou, Zhejiang, CN","ORCiD","College of Information Engineering, Zhejiang University of Technology, Hangzhou, China"],"raw_orcid":"https://orcid.org/0000-0003-2834-5548","affiliations":[{"raw_affiliation_string":"Zhejiang University of Technology, Hangzhou, Zhejiang, CN","institution_ids":["https://openalex.org/I55712492"]},{"raw_affiliation_string":"ORCiD","institution_ids":[]},{"raw_affiliation_string":"College of Information Engineering, Zhejiang University of Technology, Hangzhou, China","institution_ids":["https://openalex.org/I55712492"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071166741","display_name":"Qiang Chen","orcid":"https://orcid.org/0000-0001-5869-0436"},"institutions":[{"id":"https://openalex.org/I55712492","display_name":"Zhejiang University of Technology","ror":"https://ror.org/02djqfd08","country_code":"CN","type":"education","lineage":["https://openalex.org/I55712492"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qiang Chen","raw_affiliation_strings":["Zhejiang University of Technology, Hangzhou, Zhejiang, CN","College of Information Engineering, Zhejiang University of Technology, Hangzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Zhejiang University of Technology, Hangzhou, Zhejiang, CN","institution_ids":["https://openalex.org/I55712492"]},{"raw_affiliation_string":"College of Information Engineering, Zhejiang University of Technology, Hangzhou, China","institution_ids":["https://openalex.org/I55712492"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044387376","display_name":"Yurong Nan","orcid":"https://orcid.org/0000-0002-3728-986X"},"institutions":[{"id":"https://openalex.org/I55712492","display_name":"Zhejiang University of Technology","ror":"https://ror.org/02djqfd08","country_code":"CN","type":"education","lineage":["https://openalex.org/I55712492"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yurong Nan","raw_affiliation_strings":["Zhejiang University of Technology, Hangzhou, Zhejiang, CN","College of Information Engineering, Zhejiang University of Technology, Hangzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Zhejiang University of Technology, Hangzhou, Zhejiang, CN","institution_ids":["https://openalex.org/I55712492"]},{"raw_affiliation_string":"College of Information Engineering, Zhejiang University of Technology, Hangzhou, China","institution_ids":["https://openalex.org/I55712492"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016523393","display_name":"Chun Wu","orcid":"https://orcid.org/0000-0002-2444-9430"},"institutions":[{"id":"https://openalex.org/I55712492","display_name":"Zhejiang University of Technology","ror":"https://ror.org/02djqfd08","country_code":"CN","type":"education","lineage":["https://openalex.org/I55712492"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chun Wu","raw_affiliation_strings":["Zhejiang University of Technology, Hangzhou, Zhejiang, CN","College of Information Engineering, Zhejiang University of Technology, Hangzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Zhejiang University of Technology, Hangzhou, Zhejiang, CN","institution_ids":["https://openalex.org/I55712492"]},{"raw_affiliation_string":"College of Information Engineering, Zhejiang University of Technology, Hangzhou, China","institution_ids":["https://openalex.org/I55712492"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I55712492"],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":2.6359,"has_fulltext":false,"cited_by_count":38,"citation_normalized_percentile":{"value":0.89842711,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"6","issue":null,"first_page":"27717","last_page":"27725"},"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/T11615","display_name":"Control and Dynamics of Mobile Robots","score":0.9991999864578247,"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/T11687","display_name":"Teleoperation and Haptic Systems","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/hyperbolic-function","display_name":"Hyperbolic function","score":0.8099637627601624},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6071649193763733},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5719108581542969},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5534166693687439},{"id":"https://openalex.org/keywords/inverse-hyperbolic-function","display_name":"Inverse hyperbolic function","score":0.5450799465179443},{"id":"https://openalex.org/keywords/inverse-trigonometric-functions","display_name":"Inverse trigonometric functions","score":0.529512882232666},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5081686973571777},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5009984970092773},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.4603549838066101},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.43887633085250854},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.43804487586021423},{"id":"https://openalex.org/keywords/sliding-mode-control","display_name":"Sliding mode control","score":0.42362499237060547},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4015120267868042},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.29748010635375977},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2108331024646759},{"id":"https://openalex.org/keywords/hyperbolic-manifold","display_name":"Hyperbolic manifold","score":0.16106262803077698},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12200850248336792},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0921345055103302},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.08981260657310486}],"concepts":[{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.8099637627601624},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6071649193763733},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5719108581542969},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5534166693687439},{"id":"https://openalex.org/C163016742","wikidata":"https://www.wikidata.org/wiki/Q640600","display_name":"Inverse hyperbolic function","level":4,"score":0.5450799465179443},{"id":"https://openalex.org/C68827188","wikidata":"https://www.wikidata.org/wiki/Q674533","display_name":"Inverse trigonometric functions","level":2,"score":0.529512882232666},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5081686973571777},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5009984970092773},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.4603549838066101},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.43887633085250854},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.43804487586021423},{"id":"https://openalex.org/C36662352","wikidata":"https://www.wikidata.org/wiki/Q6008560","display_name":"Sliding mode control","level":3,"score":0.42362499237060547},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4015120267868042},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.29748010635375977},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2108331024646759},{"id":"https://openalex.org/C70984080","wikidata":"https://www.wikidata.org/wiki/Q2619102","display_name":"Hyperbolic manifold","level":3,"score":0.16106262803077698},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12200850248336792},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0921345055103302},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.08981260657310486},{"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/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2018.2838127","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2018.2838127","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:673c5acd815f4eccb28eacfa74d58044","is_oa":true,"landing_page_url":"https://doaj.org/article/673c5acd815f4eccb28eacfa74d58044","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":"IEEE Access, Vol 6, Pp 27717-27725 (2018)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2018.2838127","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2018.2838127","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.8299999833106995,"display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G1957722113","display_name":null,"funder_award_id":"LQ18E070005","funder_id":"https://openalex.org/F4320338464","funder_display_name":"Natural Science Foundation of Zhejiang Province"},{"id":"https://openalex.org/G5495531604","display_name":null,"funder_award_id":"LY17F030018","funder_id":"https://openalex.org/F4320338464","funder_display_name":"Natural Science Foundation of Zhejiang Province"},{"id":"https://openalex.org/G5648046468","display_name":null,"funder_award_id":"61403343","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/F4320338464","display_name":"Natural Science Foundation of Zhejiang Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W193758602","https://openalex.org/W1597554859","https://openalex.org/W1621133376","https://openalex.org/W1981392343","https://openalex.org/W2000201135","https://openalex.org/W2011823101","https://openalex.org/W2012890691","https://openalex.org/W2040575761","https://openalex.org/W2041966368","https://openalex.org/W2051570364","https://openalex.org/W2061556785","https://openalex.org/W2062763880","https://openalex.org/W2077003942","https://openalex.org/W2084279695","https://openalex.org/W2088552730","https://openalex.org/W2113766349","https://openalex.org/W2146356627","https://openalex.org/W2157540237","https://openalex.org/W2177697177","https://openalex.org/W2334750579","https://openalex.org/W2343693428","https://openalex.org/W2394735311","https://openalex.org/W2395228928","https://openalex.org/W2421558842","https://openalex.org/W2462438590","https://openalex.org/W2548642014","https://openalex.org/W2572974507","https://openalex.org/W6636601489"],"related_works":["https://openalex.org/W4318472270","https://openalex.org/W2930333407","https://openalex.org/W3012344327","https://openalex.org/W2554670270","https://openalex.org/W2510075261","https://openalex.org/W3176193352","https://openalex.org/W1559834326","https://openalex.org/W4390958324","https://openalex.org/W3006811425","https://openalex.org/W3093821283"],"abstract_inverted_index":{"This":[0],"paper":[1],"proposes":[2],"a":[3],"novel":[4],"continuous":[5],"reaching":[6,89,108],"law":[7],"for":[8],"chattering-free":[9,95],"sliding":[10,47,58,73],"mode":[11,48,59,74],"control":[12],"by":[13],"using":[14],"two":[15],"hyperbolic":[16,32,67],"functions":[17],"with":[18,112],"similar":[19],"changing":[20],"rate":[21],"and":[22,94,101],"opposite":[23],"amplitude":[24],"characteristics.":[25],"The":[26],"first":[27],"function":[28,69],"is":[29,50,61,110,122,133],"an":[30,113],"inverse":[31],"sine":[33],"function,":[34],"which":[35],"can":[36,70,97],"guarantee":[37],"the":[38,42,46,54,57,65,72,84,87,91,102,107,117,137,140],"fast":[39,92],"convergence":[40,93,104],"as":[41],"initial":[43],"value":[44],"of":[45,106,139],"variable":[49,60,75],"far":[51],"away":[52],"from":[53],"equilibrium.":[55],"When":[56],"approaching":[62],"to":[63,79,135],"zero,":[64],"second":[66],"tangent":[68],"ensure":[71],"be":[76,98],"infinitely":[77],"close":[78],"zero":[80],"rather":[81],"than":[82],"cross":[83],"zero.":[85],"With":[86],"proposed":[88,141],"law,":[90],"property":[96],"both":[99],"guaranteed,":[100],"satisfactory":[103],"performance":[105],"phase":[109],"achieved":[111],"approximation":[114],"method.":[115,142],"Moreover,":[116],"steady":[118],"state":[119],"error":[120],"bound":[121],"analyzed":[123],"in":[124],"details":[125],"when":[126],"considering":[127],"external":[128],"disturbances.":[129],"A":[130],"simple":[131],"example":[132],"provided":[134],"demonstrate":[136],"effectiveness":[138]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2026-07-21T08:15:58.654021","created_date":"2025-10-10T00:00:00"}
