{"id":"https://openalex.org/W2039606278","doi":"https://doi.org/10.1137/s0363012904441684","title":"Controller Design via Nonsmooth Multidirectional Search","display_name":"Controller Design via Nonsmooth Multidirectional Search","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2039606278","doi":"https://doi.org/10.1137/s0363012904441684","mag":"2039606278"},"language":"en","primary_location":{"id":"doi:10.1137/s0363012904441684","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012904441684","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","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/A5033569810","display_name":"Pierre Apkarian","orcid":"https://orcid.org/0000-0003-1122-9153"},"institutions":[{"id":"https://openalex.org/I2801658355","display_name":"Office National d'\u00c9tudes et de Recherches A\u00e9rospatiales","ror":"https://ror.org/005y2ap84","country_code":"FR","type":"facility","lineage":["https://openalex.org/I2801658355"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Pierre Apkarian","raw_affiliation_strings":["ONERA - The French Aerospace Lab [Toulouse] (F-31055 Toulouse - France)"],"affiliations":[{"raw_affiliation_string":"ONERA - The French Aerospace Lab [Toulouse] (F-31055 Toulouse - France)","institution_ids":["https://openalex.org/I2801658355"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030567369","display_name":"Dominikus Noll","orcid":"https://orcid.org/0000-0002-8638-2438"},"institutions":[{"id":"https://openalex.org/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555","https://openalex.org/I4405258862"]},{"id":"https://openalex.org/I84500057","display_name":"Institut de Math\u00e9matiques de Toulouse","ror":"https://ror.org/014vp6c30","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I134560555","https://openalex.org/I196454796","https://openalex.org/I4210141950","https://openalex.org/I4210152422","https://openalex.org/I4405258862","https://openalex.org/I4405258862","https://openalex.org/I4405258862","https://openalex.org/I4405258862","https://openalex.org/I4405259414","https://openalex.org/I84500057"]},{"id":"https://openalex.org/I196454796","display_name":"Institut National des Sciences Appliqu\u00e9es de Toulouse","ror":"https://ror.org/01h8pf755","country_code":"FR","type":"education","lineage":["https://openalex.org/I196454796","https://openalex.org/I4405258862"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Dominikus Noll","raw_affiliation_strings":["IMT - Institut de Math\u00e9matiques de Toulouse UMR5219 (UPS IMT, F-31062 Toulouse Cedex 9, \r\nINSA Toulouse, F-31077 Toulouse,\r\nFrance UT1, F-31042 Toulouse, \r\nFrance UT2, F-31058 Toulouse,\r\n\r\nT\u00e9l\u00e9phone : 05.61.55.67.90 - France)"],"affiliations":[{"raw_affiliation_string":"IMT - Institut de Math\u00e9matiques de Toulouse UMR5219 (UPS IMT, F-31062 Toulouse Cedex 9, \r\nINSA Toulouse, F-31077 Toulouse,\r\nFrance UT1, F-31042 Toulouse, \r\nFrance UT2, F-31058 Toulouse,\r\n\r\nT\u00e9l\u00e9phone : 05.61.55.67.90 - France)","institution_ids":["https://openalex.org/I84500057","https://openalex.org/I134560555","https://openalex.org/I196454796"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5033569810"],"corresponding_institution_ids":["https://openalex.org/I2801658355"],"apc_list":null,"apc_paid":null,"fwci":24.7721,"has_fulltext":false,"cited_by_count":66,"citation_normalized_percentile":{"value":0.99583836,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"44","issue":"6","first_page":"1923","last_page":"1949"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9994000196456909,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9994000196456909,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9987999796867371,"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/benchmark","display_name":"Benchmark (surveying)","score":0.8546937704086304},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.6919605731964111},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6813531517982483},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6222066879272461},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6199547052383423},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5089476108551025},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5050919651985168},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.446056604385376},{"id":"https://openalex.org/keywords/descent","display_name":"Descent (aeronautics)","score":0.43407142162323},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.39525043964385986},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3560125231742859},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2614292800426483},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.18670061230659485},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12143033742904663}],"concepts":[{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.8546937704086304},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.6919605731964111},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6813531517982483},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6222066879272461},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6199547052383423},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5089476108551025},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5050919651985168},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.446056604385376},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.43407142162323},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.39525043964385986},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3560125231742859},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2614292800426483},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.18670061230659485},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12143033742904663},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","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},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"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/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/s0363012904441684","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012904441684","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.141.6570","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.141.6570","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://mip.ups-tlse.fr/~noll/PAPERS/POLYTOPE.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.154.5873","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.154.5873","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://mip.ups-tlse.fr/~noll/PAPERS/multidirectional.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.331.3960","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.331.3960","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.univ-toulouse.fr/Archive-MIP/publis/files/04.30.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-01868783v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01868783","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Control and Optimization, 2006, 44 (6), pp.1923 - 1949. &#x27E8;10.1137/S0363012904441684&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":60,"referenced_works":["https://openalex.org/W786514019","https://openalex.org/W1420250989","https://openalex.org/W1551360398","https://openalex.org/W1553702074","https://openalex.org/W1597990070","https://openalex.org/W1601741115","https://openalex.org/W1601803999","https://openalex.org/W1964092554","https://openalex.org/W1965748532","https://openalex.org/W1967969202","https://openalex.org/W1968778183","https://openalex.org/W1971200627","https://openalex.org/W1993433915","https://openalex.org/W1998855065","https://openalex.org/W1998990712","https://openalex.org/W1999563762","https://openalex.org/W2005197166","https://openalex.org/W2008829493","https://openalex.org/W2013621063","https://openalex.org/W2022931449","https://openalex.org/W2025051282","https://openalex.org/W2029251835","https://openalex.org/W2032173185","https://openalex.org/W2033864828","https://openalex.org/W2036808929","https://openalex.org/W2039867272","https://openalex.org/W2051306216","https://openalex.org/W2054428029","https://openalex.org/W2054875385","https://openalex.org/W2059706201","https://openalex.org/W2064558818","https://openalex.org/W2064942524","https://openalex.org/W2069665540","https://openalex.org/W2079629485","https://openalex.org/W2079688774","https://openalex.org/W2085822045","https://openalex.org/W2086155756","https://openalex.org/W2090839010","https://openalex.org/W2092810212","https://openalex.org/W2106929622","https://openalex.org/W2107543637","https://openalex.org/W2111946256","https://openalex.org/W2120267268","https://openalex.org/W2123556725","https://openalex.org/W2132385139","https://openalex.org/W2140691217","https://openalex.org/W2145546299","https://openalex.org/W2147228817","https://openalex.org/W2152710595","https://openalex.org/W2161496432","https://openalex.org/W2162737890","https://openalex.org/W2171074980","https://openalex.org/W2499340036","https://openalex.org/W2617474297","https://openalex.org/W2724565893","https://openalex.org/W2801034590","https://openalex.org/W2911911537","https://openalex.org/W3161055505","https://openalex.org/W3210839039","https://openalex.org/W4212912562"],"related_works":["https://openalex.org/W2486267010","https://openalex.org/W2378211422","https://openalex.org/W4298096494","https://openalex.org/W4321353415","https://openalex.org/W2745001401","https://openalex.org/W1678820847","https://openalex.org/W2130974462","https://openalex.org/W2028665553","https://openalex.org/W2086519370","https://openalex.org/W972276598"],"abstract_inverted_index":{"We":[0,35],"propose":[1],"an":[2],"algorithm":[3,86],"which":[4],"combines":[5],"multidirectional":[6],"search":[7,41],"(MDS)":[8],"with":[9,43,70,118],"nonsmooth":[10,44],"optimization":[11],"techniques":[12,42],"to":[13,38,49,89],"solve":[14],"difficult":[15],"problems":[16],"in":[17,47,53,133],"automatic":[18],"control.":[19],"Applications":[20],"include":[21],"static":[22,92,123],"and":[23,32,64,138],"fixed-order":[24],"output":[25,93],"feedback":[26,94],"controller":[27,96,124],"design,":[28],"simultaneous":[29],"stabilization,":[30],"$H_2/H_\\infty$-synthesis,":[31],"much":[33],"else.":[34],"show":[36],"how":[37],"combine":[39],"direct":[40],"descent":[45],"steps":[46],"order":[48],"obtain":[50],"convergence":[51],"certificates":[52],"the":[54,98],"presence":[55],"of":[56],"nonsmoothness.":[57],"Our":[58,76],"technique":[59],"is":[60],"efficient":[61],"when":[62],"small":[63],"medium":[65],"size":[66],"controllers":[67],"for":[68,97,128],"plants":[69],"large":[71],"state":[72],"dimension":[73],"are":[74],"sought.":[75],"numerical":[77],"testing":[78],"includes":[79],"several":[80],"benchmark":[81,102],"examples.":[82],"For":[83],"instance,":[84],"our":[85],"needs":[87],"0.41\\,s":[88],"compute":[90],"a":[91,116],"stabilizing":[95],"Boeing":[99],"767":[100],"flutter":[101],"problem":[103],"[E.":[104],"E.":[105],"J.":[106,142],"Davison,":[107],"IFAC":[108],"Technical":[109],"Committee":[110],"Reports,":[111],"Pergamon":[112],"Press,":[113],"Oxford,":[114],"1990],":[115],"system":[117,130],"55":[119],"states.":[120],"The":[121],"first":[122],"without":[125],"performance":[126],"specifications":[127],"this":[129],"was":[131],"obtained":[132],"[J.":[134],"Burke,":[135],"A.":[136],"Lewis,":[137],"M.":[139],"Overton,":[140],"SIAM":[141],"Optim.,":[143],"15":[144],"(2003),":[145],"pp.":[146],"751-779].":[147]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
