{"id":"https://openalex.org/W4393248217","doi":"https://doi.org/10.1109/tac.2025.3538775","title":"Chattering Phenomena in Time-Optimal Control for High-Order Chain-of-Integrator Systems With Full State Constraints","display_name":"Chattering Phenomena in Time-Optimal Control for High-Order Chain-of-Integrator Systems With Full State Constraints","publication_year":2025,"publication_date":"2025-02-05","ids":{"openalex":"https://openalex.org/W4393248217","doi":"https://doi.org/10.1109/tac.2025.3538775"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2025.3538775","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2025.3538775","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2403.17675","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045375278","display_name":"Yunan Wang","orcid":"https://orcid.org/0000-0002-9812-7709"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yunan Wang","raw_affiliation_strings":["State Key Laboratory of Tribology in Advanced Equipment, Department of Mechanical Engineering, Tsinghua University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-9812-7709","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Tribology in Advanced Equipment, Department of Mechanical Engineering, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079033650","display_name":"Chuxiong Hu","orcid":"https://orcid.org/0000-0002-3504-3065"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chuxiong Hu","raw_affiliation_strings":["State Key Laboratory of Tribology in Advanced Equipment, Department of Mechanical Engineering, Tsinghua University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-3504-3065","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Tribology in Advanced Equipment, Department of Mechanical Engineering, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Zeyang Li","orcid":"https://orcid.org/0009-0006-2868-1153"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zeyang Li","raw_affiliation_strings":["State Key Laboratory of Tribology in Advanced Equipment, Department of Mechanical Engineering, Tsinghua University, Beijing, China"],"raw_orcid":"https://orcid.org/0009-0006-2868-1153","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Tribology in Advanced Equipment, Department of Mechanical Engineering, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Yujie Lin","orcid":"https://orcid.org/0009-0007-1059-7954"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yujie Lin","raw_affiliation_strings":["Qiuzhen College, Tsinghua University, Beijing, China"],"raw_orcid":"https://orcid.org/0009-0007-1059-7954","affiliations":[{"raw_affiliation_string":"Qiuzhen College, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031907990","display_name":"Shize Lin","orcid":"https://orcid.org/0000-0002-2424-8129"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shize Lin","raw_affiliation_strings":["State Key Laboratory of Tribology in Advanced Equipment, Department of Mechanical Engineering, Tsinghua University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-2424-8129","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Tribology in Advanced Equipment, Department of Mechanical Engineering, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006031631","display_name":"Suqin He","orcid":"https://orcid.org/0000-0001-9070-2126"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Suqin He","raw_affiliation_strings":["State Key Laboratory of Tribology in Advanced Equipment, Department of Mechanical Engineering, Tsinghua University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0001-9070-2126","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Tribology in Advanced Equipment, Department of Mechanical Engineering, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I99065089"],"apc_list":null,"apc_paid":null,"fwci":4.0106,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.92723859,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":98},"biblio":{"volume":"70","issue":"8","first_page":"5365","last_page":"5380"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.8925999999046326,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.8925999999046326,"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":0.8615999817848206,"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":0.8119999766349792,"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/integrator","display_name":"Integrator","score":0.8943934440612793},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.6874271631240845},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6343995332717896},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5855833292007446},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.5603978633880615},{"id":"https://openalex.org/keywords/chain","display_name":"Chain (unit)","score":0.5518520474433899},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4879409968852997},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15867584943771362},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.15690824389457703},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11107966303825378},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06536978483200073},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.03976520895957947}],"concepts":[{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.8943934440612793},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.6874271631240845},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6343995332717896},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5855833292007446},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.5603978633880615},{"id":"https://openalex.org/C199185054","wikidata":"https://www.wikidata.org/wiki/Q552299","display_name":"Chain (unit)","level":2,"score":0.5518520474433899},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4879409968852997},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15867584943771362},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.15690824389457703},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11107966303825378},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06536978483200073},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.03976520895957947},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tac.2025.3538775","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2025.3538775","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2403.17675","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2403.17675","pdf_url":"https://arxiv.org/pdf/2403.17675","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2403.17675","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2403.17675","pdf_url":"https://arxiv.org/pdf/2403.17675","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2866013771","display_name":null,"funder_award_id":"624B2077","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6719335952","display_name":null,"funder_award_id":"2023YFB4302003","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program 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/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4393248217.pdf","grobid_xml":"https://content.openalex.org/works/W4393248217.grobid-xml"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W20802081","https://openalex.org/W148202061","https://openalex.org/W150313508","https://openalex.org/W1595765050","https://openalex.org/W1662965174","https://openalex.org/W1964673114","https://openalex.org/W1982019931","https://openalex.org/W2005143756","https://openalex.org/W2015764599","https://openalex.org/W2039354617","https://openalex.org/W2056653303","https://openalex.org/W2056823730","https://openalex.org/W2076020921","https://openalex.org/W2092711598","https://openalex.org/W2110307800","https://openalex.org/W2119224729","https://openalex.org/W2130980192","https://openalex.org/W2160032004","https://openalex.org/W2164784865","https://openalex.org/W2242835355","https://openalex.org/W2480459371","https://openalex.org/W2544386679","https://openalex.org/W2963774831","https://openalex.org/W3087909510","https://openalex.org/W3089331246","https://openalex.org/W3174299515","https://openalex.org/W4236201940","https://openalex.org/W4246313583","https://openalex.org/W4312572987","https://openalex.org/W4393248217","https://openalex.org/W4400487643","https://openalex.org/W4401608518","https://openalex.org/W4402300723","https://openalex.org/W4402733117","https://openalex.org/W6606460134"],"related_works":["https://openalex.org/W2366352762","https://openalex.org/W2613964090","https://openalex.org/W2081322886","https://openalex.org/W2380425739","https://openalex.org/W2349324463","https://openalex.org/W1988313539","https://openalex.org/W2027541371","https://openalex.org/W2380535488","https://openalex.org/W2371144154","https://openalex.org/W2029980887"],"abstract_inverted_index":{"Time-optimal":[0],"control":[1,26,42,117],"for":[2,59,118],"high-order":[3,28],"chain-of-integrator":[4],"systems":[5],"with":[6,121,165],"full":[7],"state":[8,71],"constraints":[9,72,123],"remains":[10,51],"an":[11,82,128],"open":[12],"and":[13,87,92],"challenging":[14],"problem":[15],"within":[16],"the":[17,34,37,41,62,68,75,88,95,100,106,111,157,160],"discipline":[18],"of":[19,24,36,70,78,90,108,137,162],"optimal":[20,25,116],"control.":[21],"The":[22,114,150],"behavior":[23],"in":[27,61,81,110,156],"problems":[29,120],"lacks":[30],"precise":[31],"characterization.":[32],"Even":[33],"existence":[35,107],"chattering":[38,60,96,109,115],"phenomenon,":[39],"i.e.,":[40],"switches":[43],"infinitely":[44],"many":[45],"times":[46,80],"over":[47],"a":[48,56,153],"finite":[49,166],"period,":[50],"unknown.":[52],"This":[53],"article":[54,104],"establishes":[55],"theoretical":[57],"framework":[58],"problem,":[63],"providing":[64,127],"novel":[65],"findings":[66],"on":[67],"uniqueness":[69],"inducing":[73],"chattering,":[74,86],"upper":[76],"bound":[77],"switching":[79,167],"unconstrained":[83],"arc":[84],"during":[85],"convergence":[89],"states":[91],"costates":[93],"to":[94,130,147],"limit":[97],"point.":[98],"For":[99],"first":[101],"time,":[102],"this":[103],"proves":[105],"considered":[112],"problem.":[113],"fourth-order":[119],"velocity":[122],"is":[124],"precisely":[125],"solved,":[126],"approach":[129],"plan":[131],"time-optimal":[132],"snap-limited":[133],"trajectories.":[134],"Other":[135],"cases":[136],"order":[138],"<inline-formula":[139],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[140],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex-math":[141],"notation=\"LaTeX\">$n\\leq":[142],"4$</tex-math></inline-formula>":[143],"are":[144],"proved":[145],"not":[146],"allow":[148],"chattering.":[149],"conclusions":[151],"challenge":[152],"prevalent":[154],"conception":[155],"industry":[158],"concerning":[159],"time-optimality":[161],"S-shaped":[163],"trajectories":[164],"times.":[168]},"counts_by_year":[{"year":2025,"cited_by_count":5}],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2025-10-10T00:00:00"}