{"id":"https://openalex.org/W2100297845","doi":"https://doi.org/10.1109/cdc.2007.4434286","title":"A semidefinite relaxation for the quadratic minimax problem with application to H&lt;inf&gt;&amp;#x221E;&lt;/inf&gt; model predictive control","display_name":"A semidefinite relaxation for the quadratic minimax problem with application to H&lt;inf&gt;&amp;#x221E;&lt;/inf&gt; model predictive control","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2100297845","doi":"https://doi.org/10.1109/cdc.2007.4434286","mag":"2100297845"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2007.4434286","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2007.4434286","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 46th IEEE Conference on Decision and Control","raw_type":"proceedings-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/A5017365903","display_name":"Patience E. Orukpe","orcid":"https://orcid.org/0000-0003-1317-7924"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Patience E. Orukpe","raw_affiliation_strings":["Control and Power Research Group, Department of Electrical and Electronic Engineering, Imperial College London, London, UK","Imperial College London, #N#London"],"affiliations":[{"raw_affiliation_string":"Control and Power Research Group, Department of Electrical and Electronic Engineering, Imperial College London, London, UK","institution_ids":["https://openalex.org/I47508984"]},{"raw_affiliation_string":"Imperial College London, #N#London","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083334628","display_name":"Imad M. Jaimoukha","orcid":"https://orcid.org/0000-0002-2971-3149"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Imad M. Jaimoukha","raw_affiliation_strings":["Control and Power Research Group, Department of Electrical and Electronic Engineering, Imperial College London, London, UK","Imperial College London, #N#London"],"affiliations":[{"raw_affiliation_string":"Control and Power Research Group, Department of Electrical and Electronic Engineering, Imperial College London, London, UK","institution_ids":["https://openalex.org/I47508984"]},{"raw_affiliation_string":"Imperial College London, #N#London","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5017365903"],"corresponding_institution_ids":["https://openalex.org/I47508984"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.08936742,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"39","issue":null,"first_page":"177","last_page":"181"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":1.0,"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":1.0,"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/T10876","display_name":"Fault Detection and Control Systems","score":0.9975000023841858,"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":0.9950000047683716,"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/minimax","display_name":"Minimax","score":0.7749416828155518},{"id":"https://openalex.org/keywords/quadratic-growth","display_name":"Quadratic growth","score":0.6777764558792114},{"id":"https://openalex.org/keywords/quadratically-constrained-quadratic-program","display_name":"Quadratically constrained quadratic program","score":0.6703741550445557},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.6032376885414124},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5679199695587158},{"id":"https://openalex.org/keywords/model-predictive-control","display_name":"Model predictive control","score":0.5350950956344604},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5274543762207031},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4999361038208008},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.4931025207042694},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.48818808794021606},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.4657628834247589},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4477244019508362},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3619588017463684},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3477817177772522},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2784755825996399},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.16690999269485474},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.148759126663208},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08135181665420532}],"concepts":[{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.7749416828155518},{"id":"https://openalex.org/C195956108","wikidata":"https://www.wikidata.org/wiki/Q7268362","display_name":"Quadratic growth","level":2,"score":0.6777764558792114},{"id":"https://openalex.org/C65148998","wikidata":"https://www.wikidata.org/wiki/Q7268373","display_name":"Quadratically constrained quadratic program","level":3,"score":0.6703741550445557},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.6032376885414124},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5679199695587158},{"id":"https://openalex.org/C172205157","wikidata":"https://www.wikidata.org/wiki/Q1782962","display_name":"Model predictive control","level":3,"score":0.5350950956344604},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5274543762207031},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4999361038208008},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.4931025207042694},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.48818808794021606},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.4657628834247589},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4477244019508362},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3619588017463684},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3477817177772522},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2784755825996399},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.16690999269485474},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.148759126663208},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08135181665420532},{"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/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"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/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2007.4434286","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2007.4434286","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 46th IEEE Conference on Decision and Control","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W572922989","https://openalex.org/W1545969632","https://openalex.org/W1548917674","https://openalex.org/W1594682877","https://openalex.org/W1608758704","https://openalex.org/W1968511016","https://openalex.org/W1976410223","https://openalex.org/W1978956894","https://openalex.org/W2006296914","https://openalex.org/W2020352231","https://openalex.org/W2020562473","https://openalex.org/W2032173185","https://openalex.org/W2035400420","https://openalex.org/W2037768031","https://openalex.org/W2064091343","https://openalex.org/W2103530631","https://openalex.org/W2115922137","https://openalex.org/W2125976962","https://openalex.org/W2130281847","https://openalex.org/W2162805088","https://openalex.org/W2164639906","https://openalex.org/W2164957979","https://openalex.org/W2170377759","https://openalex.org/W2201185988","https://openalex.org/W2495457432","https://openalex.org/W2498694880","https://openalex.org/W3210839039","https://openalex.org/W4254785040","https://openalex.org/W6684599098"],"related_works":["https://openalex.org/W4293088966","https://openalex.org/W2233303476","https://openalex.org/W2112847829","https://openalex.org/W1878408459","https://openalex.org/W4297407962","https://openalex.org/W2352839224","https://openalex.org/W2097504558","https://openalex.org/W2371590971","https://openalex.org/W1653317167","https://openalex.org/W2022619808"],"abstract_inverted_index":{"We":[0,49,145],"derive":[1,105],"a":[2,6,12,18,30,106,164],"semidefinite":[3],"relaxation":[4],"for":[5,122],"minimax":[7,77,166],"problem":[8,167],"with":[9,23],"two":[10],"players:":[11],"quadratically":[13,19],"bounded":[14],"disturbance":[15,45,59],"signal":[16],"and":[17,29,46,60,86,94,127,135],"constrained":[20],"control":[21,47,65,102,161],"signal,":[22,103],"quadratic":[24,31,133],"constraints":[25,35,42,56,83,126,134],"on":[26,36,43,57,63,71,84],"the":[27,37,44,51,55,58,64,72,76,82,88,91,95,101,124,128,143,147,150],"state":[28,38],"cost":[32,92],"function.":[33],"The":[34,116],"result":[39],"in":[40,100,119],"mixed":[41,125],"signals.":[48],"use":[50],"S-Procedure":[52],"to":[53,66],"relax":[54],"tighten":[61],"those":[62],"obtain":[67],"an":[68,154],"upper":[69,108],"bound":[70],"optimum":[73],"value":[74],"of":[75,149],"problem.":[78],"By":[79],"further":[80],"relaxing":[81],"disturbance,":[85],"under":[87],"assumption":[89],"that":[90,130,136],"function":[93],"constraint":[96],"sets":[97],"are":[98],"convex":[99],"we":[104,131,137],"second":[107],"bound,":[109],"computable":[110],"using":[111],"linear":[112],"matrix":[113],"inequality":[114],"techniques.":[115],"novelty":[117],"is":[118,168],"our":[120],"procedure":[121],"separating":[123],"facts":[129],"handle":[132],"make":[138],"no":[139],"convexity":[140],"assumptions":[141],"concerning":[142],"disturbance.":[144],"illustrate":[146],"effectiveness":[148],"proposed":[151],"scheme":[152],"through":[153],"Hscr":[155],"<sub":[156],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[157],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">infin</sub>":[158],"model":[159],"predictive":[160],"simulation,":[162],"where":[163],"finite-horizon":[165],"solved":[169],"at":[170],"each":[171],"time":[172],"step.":[173]},"counts_by_year":[{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
