{"id":"https://openalex.org/W4296473399","doi":"https://doi.org/10.1109/tie.2022.3206750","title":"Adaptive Fractional-Order Backstepping Control for a General Class of Nonlinear Uncertain Integer-Order Systems","display_name":"Adaptive Fractional-Order Backstepping Control for a General Class of Nonlinear Uncertain Integer-Order Systems","publication_year":2022,"publication_date":"2022-09-20","ids":{"openalex":"https://openalex.org/W4296473399","doi":"https://doi.org/10.1109/tie.2022.3206750"},"language":"en","primary_location":{"id":"doi:10.1109/tie.2022.3206750","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tie.2022.3206750","pdf_url":null,"source":{"id":"https://openalex.org/S58031724","display_name":"IEEE Transactions on Industrial Electronics","issn_l":"0278-0046","issn":["0278-0046","1557-9948"],"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 Industrial Electronics","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/A5011833760","display_name":"Xinyao Li","orcid":"https://orcid.org/0000-0001-8683-3019"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]},{"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","SG"],"is_corresponding":false,"raw_author_name":"Xinyao Li","raw_affiliation_strings":["School of Electrical Engineering, Yanshan University, Qinhuangdao, China","School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore"],"raw_orcid":"https://orcid.org/0000-0001-8683-3019","affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, Yanshan University, Qinhuangdao, China","institution_ids":["https://openalex.org/I39333907"]},{"raw_affiliation_string":"School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100344158","display_name":"Changyun Wen","orcid":"https://orcid.org/0000-0001-9530-360X"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Changyun Wen","raw_affiliation_strings":["School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore"],"raw_orcid":"https://orcid.org/0000-0001-9530-360X","affiliations":[{"raw_affiliation_string":"School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100366459","display_name":"Xiaolei Li","orcid":"https://orcid.org/0000-0002-5527-6042"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]},{"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","SG"],"is_corresponding":false,"raw_author_name":"Xiaolei Li","raw_affiliation_strings":["School of Electrical Engineering, Yanshan University, Qinhuangdao, China","School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore"],"raw_orcid":"https://orcid.org/0000-0002-5527-6042","affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, Yanshan University, Qinhuangdao, China","institution_ids":["https://openalex.org/I39333907"]},{"raw_affiliation_string":"School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052909822","display_name":"Jinsong He","orcid":"https://orcid.org/0000-0002-5602-4103"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]},{"id":"https://openalex.org/I74872605","display_name":"China Southern Power Grid (China)","ror":"https://ror.org/03hkh9419","country_code":"CN","type":"company","lineage":["https://openalex.org/I74872605"]}],"countries":["CN","SG"],"is_corresponding":false,"raw_author_name":"Jinsong He","raw_affiliation_strings":["Power Dispatching and Control Center of China Southern Power Grid, Guangzhou, China","School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore"],"raw_orcid":"https://orcid.org/0000-0002-5602-4103","affiliations":[{"raw_affiliation_string":"Power Dispatching and Control Center of China Southern Power Grid, Guangzhou, China","institution_ids":["https://openalex.org/I74872605"]},{"raw_affiliation_string":"School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.3458,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.8836259,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"70","issue":"7","first_page":"7246","last_page":"7256"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11081","display_name":"Advanced Control Systems Design","score":0.9998000264167786,"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/T11081","display_name":"Advanced Control Systems Design","score":0.9998000264167786,"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/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9994999766349792,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9940000176429749,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/backstepping","display_name":"Backstepping","score":0.9696338772773743},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.8159102201461792},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5660386681556702},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5615808963775635},{"id":"https://openalex.org/keywords/lyapunov-stability","display_name":"Lyapunov stability","score":0.5614867210388184},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.542080283164978},{"id":"https://openalex.org/keywords/adaptive-control","display_name":"Adaptive control","score":0.5416306853294373},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5356155633926392},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4913391172885895},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.48156288266181946},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.46884286403656006},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.46131467819213867},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3387962579727173},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.322797954082489},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.20564493536949158},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.17564520239830017},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06655168533325195}],"concepts":[{"id":"https://openalex.org/C72218879","wikidata":"https://www.wikidata.org/wiki/Q4839759","display_name":"Backstepping","level":4,"score":0.9696338772773743},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.8159102201461792},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5660386681556702},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5615808963775635},{"id":"https://openalex.org/C2776829284","wikidata":"https://www.wikidata.org/wiki/Q1341651","display_name":"Lyapunov stability","level":3,"score":0.5614867210388184},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.542080283164978},{"id":"https://openalex.org/C107464732","wikidata":"https://www.wikidata.org/wiki/Q235781","display_name":"Adaptive control","level":3,"score":0.5416306853294373},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5356155633926392},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4913391172885895},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.48156288266181946},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.46884286403656006},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.46131467819213867},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3387962579727173},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.322797954082489},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.20564493536949158},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.17564520239830017},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06655168533325195},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tie.2022.3206750","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tie.2022.3206750","pdf_url":null,"source":{"id":"https://openalex.org/S58031724","display_name":"IEEE Transactions on Industrial Electronics","issn_l":"0278-0046","issn":["0278-0046","1557-9948"],"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 Industrial Electronics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3975214020","display_name":null,"funder_award_id":"OE2020-T1-1-067","funder_id":"https://openalex.org/F4320320751","funder_display_name":"Ministry of Education - Singapore"},{"id":"https://openalex.org/G6616309162","display_name":null,"funder_award_id":"61903319","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7022389823","display_name":null,"funder_award_id":"62103352","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320320751","display_name":"Ministry of Education - Singapore","ror":"https://ror.org/01kcva023"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W148919764","https://openalex.org/W1605182429","https://openalex.org/W1969313263","https://openalex.org/W1975684972","https://openalex.org/W2029057284","https://openalex.org/W2051671655","https://openalex.org/W2054949701","https://openalex.org/W2063133641","https://openalex.org/W2084213262","https://openalex.org/W2090167557","https://openalex.org/W2093275073","https://openalex.org/W2110968795","https://openalex.org/W2130640606","https://openalex.org/W2143121414","https://openalex.org/W2148475246","https://openalex.org/W2150284897","https://openalex.org/W2151015649","https://openalex.org/W2157347895","https://openalex.org/W2167040191","https://openalex.org/W2259227674","https://openalex.org/W2395392600","https://openalex.org/W2415733029","https://openalex.org/W2477921776","https://openalex.org/W2576168630","https://openalex.org/W2595884034","https://openalex.org/W2733667913","https://openalex.org/W2759069897","https://openalex.org/W2761636223","https://openalex.org/W2766540366","https://openalex.org/W2807358671","https://openalex.org/W2906699276","https://openalex.org/W2963791186","https://openalex.org/W3003302312","https://openalex.org/W3035839639","https://openalex.org/W3111876756","https://openalex.org/W3152800280","https://openalex.org/W3186524116"],"related_works":["https://openalex.org/W1847613412","https://openalex.org/W2972367213","https://openalex.org/W4382203996","https://openalex.org/W3177256865","https://openalex.org/W2378628179","https://openalex.org/W2382713386","https://openalex.org/W1973298112","https://openalex.org/W2392266503","https://openalex.org/W1934622834","https://openalex.org/W2372856383"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"we":[3],"consider":[4],"the":[5,34,46,52,56,60,64,72,99,102],"adaptive":[6,104],"fractional-order":[7,29,105],"backstepping":[8,36,106],"control":[9,27,107],"problem":[10],"for":[11],"a":[12,77],"class":[13],"of":[14,55,101],"high-order":[15],"integer-order":[16],"systems":[17],"with":[18],"uncertainties":[19],"and":[20,71,95],"unknown":[21],"external":[22],"disturbance.":[23],"To":[24],"obtain":[25],"enhanced":[26],"performance,":[28],"calculus":[30],"is":[31,42],"integrated":[32],"within":[33],"conventional":[35],"controller":[37],"design":[38,90],"procedure.":[39],"Theoretical":[40],"proof":[41],"provided":[43],"based":[44],"on":[45],"Lyapunov":[47],"stability":[48,54],"theorem":[49],"to":[50,76,81],"ensure":[51],"global":[53],"closed-loop":[57,65],"system":[58],"in":[59],"sense":[61],"that":[62],"all":[63],"signals":[66],"are":[67],"uniformly":[68],"ultimately":[69],"bounded":[70],"output":[73],"tracking":[74],"error":[75],"reference":[78],"signal":[79],"converges":[80],"an":[82],"adjustable":[83],"arbitrarily":[84],"small":[85],"range":[86],"by":[87],"tuning":[88],"certain":[89],"parameters.":[91],"Both":[92],"numerical":[93],"simulation":[94],"experimental":[96],"results":[97],"verify":[98],"efficacy":[100],"proposed":[103],"scheme.":[108]},"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}