{"id":"https://openalex.org/W3020679343","doi":"https://doi.org/10.1109/tac.2021.3110895","title":"Nonlinear Dynamic Systems Parameterization Using Interval-Based Global Optimization: Computing Lipschitz Constants and Beyond","display_name":"Nonlinear Dynamic Systems Parameterization Using Interval-Based Global Optimization: Computing Lipschitz Constants and Beyond","publication_year":2021,"publication_date":"2021-09-08","ids":{"openalex":"https://openalex.org/W3020679343","doi":"https://doi.org/10.1109/tac.2021.3110895","mag":"3020679343"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2021.3110895","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2021.3110895","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","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2004.12061","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058844843","display_name":"Sebastian A. Nugroho","orcid":"https://orcid.org/0000-0001-7555-687X"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sebastian Adi Nugroho","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, USA","\u2020University of Michigan"],"raw_orcid":"https://orcid.org/0000-0001-7555-687X","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, USA","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"\u2020University of Michigan","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027125753","display_name":"Ahmad F. Taha","orcid":"https://orcid.org/0000-0003-0486-2794"},"institutions":[{"id":"https://openalex.org/I200719446","display_name":"Vanderbilt University","ror":"https://ror.org/02vm5rt34","country_code":"US","type":"education","lineage":["https://openalex.org/I200719446"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ahmad F. Taha","raw_affiliation_strings":["Department of Civil and Environmental Engineering, Vanderbilt University, Nashville, TN, USA","Vanderbilt University,#TAB#"],"raw_orcid":"https://orcid.org/0000-0003-0486-2794","affiliations":[{"raw_affiliation_string":"Department of Civil and Environmental Engineering, Vanderbilt University, Nashville, TN, USA","institution_ids":["https://openalex.org/I200719446"]},{"raw_affiliation_string":"Vanderbilt University,#TAB#","institution_ids":["https://openalex.org/I200719446"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013306127","display_name":"and Vu Hoang","orcid":null},"institutions":[{"id":"https://openalex.org/I45438204","display_name":"The University of Texas at San Antonio","ror":"https://ror.org/01kd65564","country_code":"US","type":"education","lineage":["https://openalex.org/I45438204"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Vu Hoang","raw_affiliation_strings":["Department of Mathematics, The University of Texas at San Antonio, San Antonio, TX, USA","University of Texas at San Antonio,#TAB#"],"raw_orcid":"https://orcid.org/0000-0003-3246-7548","affiliations":[{"raw_affiliation_string":"Department of Mathematics, The University of Texas at San Antonio, San Antonio, TX, USA","institution_ids":["https://openalex.org/I45438204"]},{"raw_affiliation_string":"University of Texas at San Antonio,#TAB#","institution_ids":["https://openalex.org/I45438204"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2034,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.48363,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":95},"biblio":{"volume":"67","issue":"8","first_page":"3836","last_page":"3850"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10305","display_name":"Power System Optimization and Stability","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T10305","display_name":"Power System Optimization and Stability","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9957000017166138,"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":0.9954000115394592,"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/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.8036148548126221},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.5749467611312866},{"id":"https://openalex.org/keywords/bounding-overwatch","display_name":"Bounding overwatch","score":0.5123904347419739},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5088491439819336},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5061284899711609},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5025684833526611},{"id":"https://openalex.org/keywords/observer","display_name":"Observer (physics)","score":0.5004971027374268},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.49303266406059265},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47682374715805054},{"id":"https://openalex.org/keywords/global-optimization","display_name":"Global optimization","score":0.46812406182289124},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.43858417868614197},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.438438355922699},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4368399977684021},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.419355571269989},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3622552752494812},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3488233983516693},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18054234981536865},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08239051699638367}],"concepts":[{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.8036148548126221},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.5749467611312866},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.5123904347419739},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5088491439819336},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5061284899711609},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5025684833526611},{"id":"https://openalex.org/C2780704645","wikidata":"https://www.wikidata.org/wiki/Q9251458","display_name":"Observer (physics)","level":2,"score":0.5004971027374268},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.49303266406059265},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47682374715805054},{"id":"https://openalex.org/C164752517","wikidata":"https://www.wikidata.org/wiki/Q5570875","display_name":"Global optimization","level":2,"score":0.46812406182289124},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.43858417868614197},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.438438355922699},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4368399977684021},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.419355571269989},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3622552752494812},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3488233983516693},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18054234981536865},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08239051699638367},{"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/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tac.2021.3110895","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2021.3110895","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:2004.12061","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2004.12061","pdf_url":"https://arxiv.org/pdf/2004.12061","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:3020679343","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/2004.12061","pdf_url":null,"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2004.12061","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2004.12061","pdf_url":null,"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2004.12061","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2004.12061","pdf_url":"https://arxiv.org/pdf/2004.12061","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2290344242","display_name":null,"funder_award_id":"DMS-1614797","funder_id":"https://openalex.org/F4320335353","funder_display_name":"National Science Foundation of Sri Lanka"},{"id":"https://openalex.org/G337674814","display_name":null,"funder_award_id":"DMS-1810687","funder_id":"https://openalex.org/F4320335353","funder_display_name":"National Science Foundation of Sri Lanka"},{"id":"https://openalex.org/G405294037","display_name":null,"funder_award_id":"CMMI-1728629","funder_id":"https://openalex.org/F4320335353","funder_display_name":"National Science Foundation of Sri Lanka"},{"id":"https://openalex.org/G8146254768","display_name":null,"funder_award_id":"ECCS-2013786","funder_id":"https://openalex.org/F4320335353","funder_display_name":"National Science Foundation of Sri Lanka"},{"id":"https://openalex.org/G985643917","display_name":null,"funder_award_id":"CMMI-2044430","funder_id":"https://openalex.org/F4320335353","funder_display_name":"National Science Foundation of Sri Lanka"},{"id":"https://openalex.org/G989473546","display_name":null,"funder_award_id":"CMMI-1917164","funder_id":"https://openalex.org/F4320335353","funder_display_name":"National Science Foundation of Sri Lanka"}],"funders":[{"id":"https://openalex.org/F4320335353","display_name":"National Science Foundation of Sri Lanka","ror":"https://ror.org/010xaa060"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":67,"referenced_works":["https://openalex.org/W202693086","https://openalex.org/W296311487","https://openalex.org/W341561294","https://openalex.org/W643973177","https://openalex.org/W1480066506","https://openalex.org/W1496983606","https://openalex.org/W1507872748","https://openalex.org/W1596877211","https://openalex.org/W1763243278","https://openalex.org/W1917790556","https://openalex.org/W1971279595","https://openalex.org/W2009045999","https://openalex.org/W2022428792","https://openalex.org/W2024496631","https://openalex.org/W2037619805","https://openalex.org/W2052725501","https://openalex.org/W2058593815","https://openalex.org/W2063981310","https://openalex.org/W2067120253","https://openalex.org/W2072947288","https://openalex.org/W2079208522","https://openalex.org/W2082847490","https://openalex.org/W2097415784","https://openalex.org/W2116988405","https://openalex.org/W2118955756","https://openalex.org/W2127648965","https://openalex.org/W2132303335","https://openalex.org/W2144048072","https://openalex.org/W2166214758","https://openalex.org/W2166800714","https://openalex.org/W2168479567","https://openalex.org/W2171224795","https://openalex.org/W2284892594","https://openalex.org/W2291939691","https://openalex.org/W2296319761","https://openalex.org/W2346492432","https://openalex.org/W2500877924","https://openalex.org/W2518800336","https://openalex.org/W2536620281","https://openalex.org/W2610857016","https://openalex.org/W2737503212","https://openalex.org/W2744558223","https://openalex.org/W2760469938","https://openalex.org/W2769248238","https://openalex.org/W2802035633","https://openalex.org/W2887177611","https://openalex.org/W2897607160","https://openalex.org/W2917485204","https://openalex.org/W2963558573","https://openalex.org/W2964153729","https://openalex.org/W2964159750","https://openalex.org/W2972324952","https://openalex.org/W2973114205","https://openalex.org/W2982702658","https://openalex.org/W2989585496","https://openalex.org/W3004932145","https://openalex.org/W3011457441","https://openalex.org/W3045700193","https://openalex.org/W3146520007","https://openalex.org/W4229706427","https://openalex.org/W4242847488","https://openalex.org/W4250589301","https://openalex.org/W4298255709","https://openalex.org/W6600645789","https://openalex.org/W6637162671","https://openalex.org/W6639820860","https://openalex.org/W6776489125"],"related_works":["https://openalex.org/W3004932145","https://openalex.org/W2772465488","https://openalex.org/W2981787545","https://openalex.org/W2029926860","https://openalex.org/W2885196497","https://openalex.org/W2901087923","https://openalex.org/W1553335074","https://openalex.org/W3150838575","https://openalex.org/W1855336155","https://openalex.org/W1980562453","https://openalex.org/W2111485435","https://openalex.org/W3005623173","https://openalex.org/W3034983612","https://openalex.org/W109228798","https://openalex.org/W3135359894","https://openalex.org/W2137200960","https://openalex.org/W2997318655","https://openalex.org/W2884548887","https://openalex.org/W3038411884","https://openalex.org/W2508104519"],"abstract_inverted_index":{"Numerous":[0],"state-feedback":[1],"and":[2,42,70,72,98,164],"observer":[3],"designs":[4,19],"for":[5,106,115],"nonlinear":[6],"dynamic":[7],"systems":[8],"(NDS)":[9],"have":[10],"been":[11],"developed":[12],"in":[13],"the":[14,27,58,65,134,140,146,153],"past":[15],"three":[16],"decades.":[17],"These":[18,45,61],"assume":[20],"that":[21],"NDS":[22,158],"nonlinearities":[23],"satisfy":[24],"one":[25],"of":[26,85,148],"following":[28],"<italic":[29,51],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[30,52],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">function":[31],"set":[32,109],"classifications:</i>":[33],"bounded":[34],"Jacobian,":[35],"Lipschitz":[36],"continuity,":[37],"one-sided":[38],"Lipschitz,":[39],"quadratic":[40,43],"inner-boundedness,":[41],"boundedness.":[44],"function":[46,108],"sets":[47],"are":[48,73],"characterized":[49],"by":[50],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">constant</i>":[53],"scalars":[54],"or":[55],"matrices":[56],"bounding":[57,90,117,141],"NDS\u2019":[59,66],"nonlinearities.":[60],"constants":[62,118],"depend":[63],"on":[64,133,156],"operating":[67],"region,":[68],"topology,":[69],"parameters":[71,155],"utilized":[74],"to":[75,87,101,137,151],"synthesize":[76],"observer/controller":[77],"gains.":[78],"Unfortunately,":[79],"there":[80],"is":[81],"a":[82,126],"near-complete":[83],"absence":[84],"algorithms":[86],"compute":[88,102,152],"such":[89,103,159],"constants.":[91,104,142],"In":[92],"this":[93],"article,":[94],"we":[95,111,124,144],"develop":[96],"analytical":[97,113],"computational":[99],"methods":[100],"First,":[105],"every":[107],"classification,":[110],"derive":[112],"expressions":[114],"these":[116],"through":[119],"global":[120,129],"maximization":[121,130],"formulations.":[122],"Second,":[123],"utilize":[125],"derivative-free":[127],"interval-based":[128],"algorithm":[131],"based":[132],"branch-and-bound":[135],"framework":[136],"numerically":[138],"obtain":[139],"Third,":[143],"showcase":[145],"effectiveness":[147],"our":[149],"approaches":[150],"corresponding":[154],"some":[157],"as":[160],"highway":[161],"traffic":[162],"networks":[163],"synchronous":[165],"generator":[166],"models.":[167]},"counts_by_year":[{"year":2021,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2022-07-26T00:00:00"}
