{"id":"https://openalex.org/W4287733503","doi":"https://doi.org/10.1109/tcsii.2022.3162611","title":"Continuous Higher-Order Sliding Mode Control for a Class of <i>n</i>-th Order Perturbed Systems","display_name":"Continuous Higher-Order Sliding Mode Control for a Class of <i>n</i>-th Order Perturbed Systems","publication_year":2022,"publication_date":"2022-03-28","ids":{"openalex":"https://openalex.org/W4287733503","doi":"https://doi.org/10.1109/tcsii.2022.3162611"},"language":"en","primary_location":{"id":"doi:10.1109/tcsii.2022.3162611","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsii.2022.3162611","pdf_url":null,"source":{"id":"https://openalex.org/S93916849","display_name":"IEEE Transactions on Circuits & Systems II Express Briefs","issn_l":"1549-7747","issn":["1549-7747","1558-3791"],"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 Circuits and Systems II: Express Briefs","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":"https://openalex.org/A5100759593","display_name":"Jianxiong Li","orcid":"https://orcid.org/0000-0003-3983-7679"},"institutions":[{"id":"https://openalex.org/I39333907","display_name":"Yanshan University","ror":"https://ror.org/02txfnf15","country_code":"CN","type":"education","lineage":["https://openalex.org/I39333907"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jianxiong Li","raw_affiliation_strings":["Department of Automation, School of Electrical Engineering, Yanshan University (West Campus), Qinhuangdao, China","Research Center of the Ministry of Education for Intelligent Control System and Intelligent Equipment and the Key Laboratory of Industrial Computer Control Engineering of Hebei Province, Yanshan University, Qinhuangdao, China"],"affiliations":[{"raw_affiliation_string":"Department of Automation, School of Electrical Engineering, Yanshan University (West Campus), Qinhuangdao, China","institution_ids":["https://openalex.org/I39333907"]},{"raw_affiliation_string":"Research Center of the Ministry of Education for Intelligent Control System and Intelligent Equipment and the Key Laboratory of Industrial Computer Control Engineering of Hebei Province, Yanshan University, Qinhuangdao, China","institution_ids":["https://openalex.org/I39333907"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103013056","display_name":"Xinjian Liu","orcid":"https://orcid.org/0000-0002-3322-5121"},"institutions":[{"id":"https://openalex.org/I39333907","display_name":"Yanshan University","ror":"https://ror.org/02txfnf15","country_code":"CN","type":"education","lineage":["https://openalex.org/I39333907"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xinjian Liu","raw_affiliation_strings":["Research Center of the Ministry of Education for Intelligent Control System and Intelligent Equipment and the Key Laboratory of Industrial Computer Control Engineering of Hebei Province, Yanshan University, Qinhuangdao, China"],"affiliations":[{"raw_affiliation_string":"Research Center of the Ministry of Education for Intelligent Control System and Intelligent Equipment and the Key Laboratory of Industrial Computer Control Engineering of Hebei Province, Yanshan University, Qinhuangdao, China","institution_ids":["https://openalex.org/I39333907"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016620131","display_name":"Miao Xu","orcid":"https://orcid.org/0000-0001-9409-6960"},"institutions":[{"id":"https://openalex.org/I39333907","display_name":"Yanshan University","ror":"https://ror.org/02txfnf15","country_code":"CN","type":"education","lineage":["https://openalex.org/I39333907"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Miao Xu","raw_affiliation_strings":["Research Center of the Ministry of Education for Intelligent Control System and Intelligent Equipment and the Key Laboratory of Industrial Computer Control Engineering of Hebei Province, Yanshan University, Qinhuangdao, China"],"affiliations":[{"raw_affiliation_string":"Research Center of the Ministry of Education for Intelligent Control System and Intelligent Equipment and the Key Laboratory of Industrial Computer Control Engineering of Hebei Province, Yanshan University, Qinhuangdao, China","institution_ids":["https://openalex.org/I39333907"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100759430","display_name":"Yiming Fang","orcid":"https://orcid.org/0000-0002-8363-8207"},"institutions":[{"id":"https://openalex.org/I39333907","display_name":"Yanshan University","ror":"https://ror.org/02txfnf15","country_code":"CN","type":"education","lineage":["https://openalex.org/I39333907"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yiming Fang","raw_affiliation_strings":["Research Center of the Ministry of Education for Intelligent Control System and Intelligent Equipment and the Key Laboratory of Industrial Computer Control Engineering of Hebei Province, Yanshan University, Qinhuangdao, China"],"affiliations":[{"raw_affiliation_string":"Research Center of the Ministry of Education for Intelligent Control System and Intelligent Equipment and the Key Laboratory of Industrial Computer Control Engineering of Hebei Province, Yanshan University, Qinhuangdao, China","institution_ids":["https://openalex.org/I39333907"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100759593"],"corresponding_institution_ids":["https://openalex.org/I39333907"],"apc_list":null,"apc_paid":null,"fwci":0.482,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.61315959,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"69","issue":"7","first_page":"3179","last_page":"3183"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9995999932289124,"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":0.9995999932289124,"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/T11394","display_name":"Dynamics and Control of Mechanical Systems","score":0.9794999957084656,"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/T10244","display_name":"Chaos control and synchronization","score":0.9721999764442444,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.6609861850738525},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5437719225883484},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5327003002166748},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4849858283996582},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4698673188686371},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.46271273493766785},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.43442967534065247},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4303388297557831},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40982499718666077},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3910180330276489},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.37055253982543945},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3595088720321655},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24806317687034607},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2420540750026703},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09678810834884644}],"concepts":[{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.6609861850738525},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5437719225883484},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5327003002166748},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4849858283996582},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4698673188686371},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.46271273493766785},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.43442967534065247},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4303388297557831},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40982499718666077},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3910180330276489},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37055253982543945},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3595088720321655},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24806317687034607},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2420540750026703},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09678810834884644},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcsii.2022.3162611","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsii.2022.3162611","pdf_url":null,"source":{"id":"https://openalex.org/S93916849","display_name":"IEEE Transactions on Circuits & Systems II Express Briefs","issn_l":"1549-7747","issn":["1549-7747","1558-3791"],"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 Circuits and Systems II: Express Briefs","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6360770410","display_name":null,"funder_award_id":"F2019203090","funder_id":"https://openalex.org/F4320322163","funder_display_name":"Natural Science Foundation of Hebei Province"},{"id":"https://openalex.org/G6800415243","display_name":null,"funder_award_id":"61873226","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/F4320322163","display_name":"Natural Science Foundation of Hebei Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1999558720","https://openalex.org/W2018851823","https://openalex.org/W2031945217","https://openalex.org/W2035116146","https://openalex.org/W2091198516","https://openalex.org/W2113766349","https://openalex.org/W2154608673","https://openalex.org/W2164812525","https://openalex.org/W2305138675","https://openalex.org/W2420367108","https://openalex.org/W2587895662","https://openalex.org/W2599070313","https://openalex.org/W2600696923","https://openalex.org/W2758225856","https://openalex.org/W2784008933","https://openalex.org/W2964941559","https://openalex.org/W2991551040","https://openalex.org/W3025822866","https://openalex.org/W4293078920","https://openalex.org/W4293738473"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W3185235544","https://openalex.org/W4297791327","https://openalex.org/W2897842840","https://openalex.org/W2911623553","https://openalex.org/W2397777611","https://openalex.org/W1502031429","https://openalex.org/W2318923278","https://openalex.org/W2417585376","https://openalex.org/W1994157709"],"abstract_inverted_index":{"In":[0],"this":[1],"brief,":[2],"a":[3,15,34,84,89,99],"general":[4],"continuous":[5,38,90],"higher-order":[6],"sliding":[7,100],"mode":[8,101],"(HOSM)":[9],"control":[10,52,92],"algorithm":[11,40,53],"is":[12,117],"proposed":[13,51,138],"for":[14,41],"class":[16],"of":[17,36,58,102,113,136],"<inline-formula":[18,68,104],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[19,69,105],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[20,70,106],"<tex-math":[21,71,107],"notation=\"LaTeX\">$n$":[22],"</tex-math></inline-formula>":[23,73,109],"-order":[24],"systems":[25],"with":[26,45,142],"Lipschitz":[27,79],"disturbance,":[28],"which":[29],"can":[30,76],"be":[31],"regarded":[32],"as":[33],"generalization":[35],"the":[37,48,56,59,66,78,114,134,137,143],"super-twisting":[39],"arbitrary":[42],"relative":[43],"degree":[44],"respect":[46],"to":[47,65,98],"output.":[49],"The":[50,111,130],"only":[54],"requires":[55],"information":[57],"output":[60],"and":[61,75,94,124],"its":[62],"derivatives":[63],"up":[64],"order":[67,103],"notation=\"LaTeX\">$n-1$":[72],",":[74],"compensate":[77],"disturbance":[80],"exactly":[81],"by":[82,120,140],"using":[83],"discontinuous":[85],"integral":[86],"term,":[87],"generating":[88],"homogeneous":[91,127],"signal":[93],"achieving":[95],"finite-time":[96],"convergence":[97,112],"notation=\"LaTeX\">$n+1$":[108],".":[110],"closed-loop":[115],"system":[116],"proved":[118],"rigorously":[119],"employing":[121],"an":[122],"explicit":[123],"directly":[125],"constructed":[126],"Lyapunov":[128],"function.":[129],"simulation":[131],"results":[132],"validate":[133],"effectiveness":[135],"method":[139],"comparing":[141],"existing":[144],"results.":[145]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
