{"id":"https://openalex.org/W2125147507","doi":"https://doi.org/10.1109/cdc.2007.4434504","title":"Using semiconvex duality and max-plus analysis to obtain a new fundamental solution for the differential riccati equation","display_name":"Using semiconvex duality and max-plus analysis to obtain a new fundamental solution for the differential riccati equation","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2125147507","doi":"https://doi.org/10.1109/cdc.2007.4434504","mag":"2125147507"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2007.4434504","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2007.4434504","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/A5069202152","display_name":"William M. McEneaney","orcid":"https://orcid.org/0000-0002-0576-9949"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"William M. McEneaney","raw_affiliation_strings":["Department of Mechanical and Aerospace Eng, University of California, San Diego, USA","University of California, San Diego, La Jolla,"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Aerospace Eng, University of California, San Diego, USA","institution_ids":["https://openalex.org/I36258959"]},{"raw_affiliation_string":"University of California, San Diego, La Jolla,","institution_ids":["https://openalex.org/I36258959"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5069202152"],"corresponding_institution_ids":["https://openalex.org/I36258959"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.18371768,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"166","issue":null,"first_page":"4761","last_page":"4766"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7595694065093994},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.6722717881202698},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5819015502929688},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.5724835395812988},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.524837076663971},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.524476945400238},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.523581862449646},{"id":"https://openalex.org/keywords/fundamental-matrix","display_name":"Fundamental matrix (linear differential equation)","score":0.5054605007171631},{"id":"https://openalex.org/keywords/algebraic-riccati-equation","display_name":"Algebraic Riccati equation","score":0.46671149134635925},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.4640435576438904},{"id":"https://openalex.org/keywords/linear-quadratic-regulator","display_name":"Linear-quadratic regulator","score":0.44670236110687256},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.37656357884407043},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37434813380241394},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.31887632608413696},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.30993229150772095},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.1993848979473114}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7595694065093994},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.6722717881202698},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5819015502929688},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.5724835395812988},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.524837076663971},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.524476945400238},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.523581862449646},{"id":"https://openalex.org/C2780427248","wikidata":"https://www.wikidata.org/wiki/Q17014996","display_name":"Fundamental matrix (linear differential equation)","level":2,"score":0.5054605007171631},{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.46671149134635925},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4640435576438904},{"id":"https://openalex.org/C98779006","wikidata":"https://www.wikidata.org/wiki/Q2520550","display_name":"Linear-quadratic regulator","level":3,"score":0.44670236110687256},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.37656357884407043},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37434813380241394},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.31887632608413696},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.30993229150772095},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.1993848979473114},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2007.4434504","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2007.4434504","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":13,"referenced_works":["https://openalex.org/W586948577","https://openalex.org/W644523282","https://openalex.org/W1493342205","https://openalex.org/W1988565074","https://openalex.org/W2008455282","https://openalex.org/W2034750182","https://openalex.org/W2043228814","https://openalex.org/W2046972933","https://openalex.org/W2106758919","https://openalex.org/W2127154761","https://openalex.org/W2154089215","https://openalex.org/W2187175807","https://openalex.org/W3102323183"],"related_works":["https://openalex.org/W2005019312","https://openalex.org/W2018296362","https://openalex.org/W2547959172","https://openalex.org/W2727200542","https://openalex.org/W2002357820","https://openalex.org/W2334216590","https://openalex.org/W2997206142","https://openalex.org/W2027962246","https://openalex.org/W2244442793","https://openalex.org/W2107449083"],"abstract_inverted_index":{"Semiconvex":[0],"duality":[1],"and":[2,124],"max-plus":[3,51],"analysis":[4],"are":[5],"used":[6],"to":[7,30],"obtain":[8],"a":[9,27,31,50,63,75,84,101,116,132],"surprising":[10],"new":[11,102],"fundamental":[12,103,122,129],"solution":[13,29,47,104,123,130],"for":[14,105,109],"the":[15,24,37,41,46,66,70,79,106,121,125],"ubiquitous":[16],"matrix":[17,76,81,93,118],"differential":[18],"Riccati":[19],"equation":[20],"(DRE).":[21],"We":[22],"consider":[23],"DRE":[25],"as":[26,49,62,83],"finite-dimensional":[28],"deterministic":[32],"linear/quadratic":[33],"control":[34,135],"problem.":[35],"Taking":[36],"semiconvex":[38],"dual":[39,71],"of":[40,69,98],"associated":[42],"semigroup,":[43],"one":[44,73],"obtains":[45,74],"operator":[48,53],"integral":[52],"with":[54],"quadratic":[55],"kernel.":[56],"The":[57,86],"kernel":[58,80],"is":[59,89,113],"equivalently":[60],"represented":[61],"matrix.":[64],"Using":[65],"semigroup":[67],"property":[68],"operator,":[72],"operation":[77],"whereby":[78],"propagates":[82],"semigroup.":[85],"propagation":[87],"forward":[88],"through":[90],"some":[91],"simple":[92],"operations.":[94],"This":[95,128],"time-indexed":[96],"family":[97],"matrices":[99],"forms":[100],"DRE.":[107],"Solution":[108],"any":[110],"initial":[111,126],"condition":[112],"obtained":[114],"by":[115],"few":[117],"operations":[119],"on":[120],"condition.":[127],"has":[131],"particularly":[133],"nice":[134],"interpretation.":[136]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}