{"id":"https://openalex.org/W4254508741","doi":"https://doi.org/10.1109/cdc.2008.4738777","title":"An iterative algorithm to solve periodic Riccati differential equations with an indefinite quadratic term","display_name":"An iterative algorithm to solve periodic Riccati differential equations with an indefinite quadratic term","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W4254508741","doi":"https://doi.org/10.1109/cdc.2008.4738777"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2008.4738777","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2008.4738777","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 47th 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/A5063804648","display_name":"Yantao Feng","orcid":null},"institutions":[{"id":"https://openalex.org/I118347636","display_name":"Australian National University","ror":"https://ror.org/019wvm592","country_code":"AU","type":"education","lineage":["https://openalex.org/I118347636"]},{"id":"https://openalex.org/I42894916","display_name":"Data61","ror":"https://ror.org/03q397159","country_code":"AU","type":"other","lineage":["https://openalex.org/I1292875679","https://openalex.org/I2801453606","https://openalex.org/I42894916","https://openalex.org/I4387156119"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Yantao Feng","raw_affiliation_strings":["NICTA, Canberra, ACT, Australia","Research School of Information Sciences and Engineering, Australian National University, Canberra, ACT, Australia"],"affiliations":[{"raw_affiliation_string":"NICTA, Canberra, ACT, Australia","institution_ids":["https://openalex.org/I42894916"]},{"raw_affiliation_string":"Research School of Information Sciences and Engineering, Australian National University, Canberra, ACT, Australia","institution_ids":["https://openalex.org/I118347636"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015736743","display_name":"Brian D. O. Anderson","orcid":"https://orcid.org/0000-0002-1493-4774"},"institutions":[{"id":"https://openalex.org/I118347636","display_name":"Australian National University","ror":"https://ror.org/019wvm592","country_code":"AU","type":"education","lineage":["https://openalex.org/I118347636"]},{"id":"https://openalex.org/I42894916","display_name":"Data61","ror":"https://ror.org/03q397159","country_code":"AU","type":"other","lineage":["https://openalex.org/I1292875679","https://openalex.org/I2801453606","https://openalex.org/I42894916","https://openalex.org/I4387156119"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Brian D. O. Anderson","raw_affiliation_strings":["NICTA, Canberra, ACT, Australia","Research School of Information Sciences and Engineering, Australian National University, Canberra, ACT, Australia"],"affiliations":[{"raw_affiliation_string":"NICTA, Canberra, ACT, Australia","institution_ids":["https://openalex.org/I42894916"]},{"raw_affiliation_string":"Research School of Information Sciences and Engineering, Australian National University, Canberra, ACT, Australia","institution_ids":["https://openalex.org/I118347636"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5063804648"],"corresponding_institution_ids":["https://openalex.org/I118347636","https://openalex.org/I42894916"],"apc_list":null,"apc_paid":null,"fwci":1.0309,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.79777576,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"36","issue":null,"first_page":"339","last_page":"344"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9998999834060669,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9994000196456909,"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"}},{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9991999864578247,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.7121996879577637},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6766148805618286},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6410250663757324},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.6264248490333557},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6051949262619019},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.5740599632263184},{"id":"https://openalex.org/keywords/linear-quadratic-regulator","display_name":"Linear-quadratic regulator","score":0.5554693937301636},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.4893421530723572},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.45303237438201904},{"id":"https://openalex.org/keywords/algebraic-riccati-equation","display_name":"Algebraic Riccati equation","score":0.4500744640827179},{"id":"https://openalex.org/keywords/quadratically-constrained-quadratic-program","display_name":"Quadratically constrained quadratic program","score":0.4313161075115204},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42853233218193054},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4247710406780243},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39536920189857483},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3816732168197632},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.25104203820228577},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11299672722816467}],"concepts":[{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.7121996879577637},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6766148805618286},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6410250663757324},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6264248490333557},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6051949262619019},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.5740599632263184},{"id":"https://openalex.org/C98779006","wikidata":"https://www.wikidata.org/wiki/Q2520550","display_name":"Linear-quadratic regulator","level":3,"score":0.5554693937301636},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.4893421530723572},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.45303237438201904},{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.4500744640827179},{"id":"https://openalex.org/C65148998","wikidata":"https://www.wikidata.org/wiki/Q7268373","display_name":"Quadratically constrained quadratic program","level":3,"score":0.4313161075115204},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42853233218193054},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4247710406780243},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39536920189857483},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3816732168197632},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.25104203820228577},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11299672722816467},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"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/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/cdc.2008.4738777","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2008.4738777","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 47th IEEE Conference on Decision and Control","raw_type":"proceedings-article"},{"id":"pmh:oai:openresearch-repository.anu.edu.au:1885/733798638","is_oa":false,"landing_page_url":"https://hdl.handle.net/1885/733798638","pdf_url":null,"source":{"id":"https://openalex.org/S4306402539","display_name":"ANU Open Research (Australian National University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I118347636","host_organization_name":"Australian National University","host_organization_lineage":["https://openalex.org/I118347636"],"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":"Conference paper"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1559958010","https://openalex.org/W1976169918","https://openalex.org/W1988565074","https://openalex.org/W2006008863","https://openalex.org/W2006365015","https://openalex.org/W2037025184","https://openalex.org/W2053110557","https://openalex.org/W2057231818","https://openalex.org/W2068245533","https://openalex.org/W2079902511","https://openalex.org/W2134582887","https://openalex.org/W2170133674","https://openalex.org/W2468740297","https://openalex.org/W4231011685","https://openalex.org/W6633623442","https://openalex.org/W6652066393","https://openalex.org/W6670564238","https://openalex.org/W6719863994"],"related_works":["https://openalex.org/W2005019312","https://openalex.org/W2547959172","https://openalex.org/W2018296362","https://openalex.org/W2727200542","https://openalex.org/W2002357820","https://openalex.org/W197349956","https://openalex.org/W2997206142","https://openalex.org/W2027962246","https://openalex.org/W2804494800","https://openalex.org/W2116228702"],"abstract_inverted_index":{"An":[0],"iterative":[1],"algorithm":[2],"to":[3],"solve":[4],"periodic":[5],"Riccati":[6],"differential":[7],"equations":[8],"(PRDE)":[9],"with":[10,28,42],"an":[11,29],"indefinite":[12,30],"quadratic":[13,31,46],"term":[14,32,47],"is":[15,58,63],"proposed.":[16],"In":[17],"our":[18],"algorithm,":[19],"we":[20],"replace":[21],"the":[22,34],"problem":[23,35],"of":[24,36,40],"solving":[25,37],"a":[26,38,43,61],"PRDE":[27],"by":[33,52],"sequence":[39],"PRDEs":[41],"negative":[44],"semidefinite":[45],"which":[48],"can":[49],"be":[50],"solved":[51],"existing":[53],"methods.":[54],"The":[55],"global":[56],"convergence":[57],"guaranteed":[59],"and":[60],"proof":[62],"given.":[64]},"counts_by_year":[],"updated_date":"2026-03-17T09:09:15.849793","created_date":"2025-10-10T00:00:00"}
