{"id":"https://openalex.org/W2061053321","doi":"https://doi.org/10.1093/imamci/dnp001","title":"Optimal control for linear discrete-time systems with Markov perturbations in Hilbert spaces","display_name":"Optimal control for linear discrete-time systems with Markov perturbations in Hilbert spaces","publication_year":2008,"publication_date":"2008-12-19","ids":{"openalex":"https://openalex.org/W2061053321","doi":"https://doi.org/10.1093/imamci/dnp001","mag":"2061053321"},"language":"en","primary_location":{"id":"doi:10.1093/imamci/dnp001","is_oa":false,"landing_page_url":"https://doi.org/10.1093/imamci/dnp001","pdf_url":null,"source":{"id":"https://openalex.org/S162756791","display_name":"IMA Journal of Mathematical Control and Information","issn_l":"0265-0754","issn":["0265-0754","1471-6887"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IMA Journal of Mathematical Control and Information","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/A5065300080","display_name":"Viorica Mariela Ungureanu","orcid":"https://orcid.org/0000-0002-3356-086X"},"institutions":[{"id":"https://openalex.org/I4210088362","display_name":"Constantin Br\u00e2ncu\u0219i University of Targu Jiu","ror":"https://ror.org/0058xhs49","country_code":"RO","type":"education","lineage":["https://openalex.org/I4210088362","https://openalex.org/I97553796"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"V. M. Ungureanu","raw_affiliation_strings":["\u201cConstantin Brancusi\u201d University of Tirgu-Jiu, Bulevardul Republicii nr.1, Tg-Jiu, Gorj, Romania"],"affiliations":[{"raw_affiliation_string":"\u201cConstantin Brancusi\u201d University of Tirgu-Jiu, Bulevardul Republicii nr.1, Tg-Jiu, Gorj, Romania","institution_ids":["https://openalex.org/I4210088362"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5065300080"],"corresponding_institution_ids":["https://openalex.org/I4210088362"],"apc_list":{"value":2582,"currency":"GBP","value_usd":3167},"apc_paid":null,"fwci":1.645,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.86350713,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"26","issue":"1","first_page":"105","last_page":"127"},"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":0.9248999953269958,"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":0.9248999953269958,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9203000068664551,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9106000065803528,"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/hilbert-space","display_name":"Hilbert space","score":0.7797783017158508},{"id":"https://openalex.org/keywords/observability","display_name":"Observability","score":0.7575178742408752},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7262051105499268},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.6980404257774353},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.6829479932785034},{"id":"https://openalex.org/keywords/algebraic-riccati-equation","display_name":"Algebraic Riccati equation","score":0.6015777587890625},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.5704566240310669},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.5626543760299683},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5428304076194763},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5266989469528198},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5059947371482849},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.42950883507728577},{"id":"https://openalex.org/keywords/linear-quadratic-gaussian-control","display_name":"Linear-quadratic-Gaussian control","score":0.4195978045463562},{"id":"https://openalex.org/keywords/linear-quadratic-regulator","display_name":"Linear-quadratic regulator","score":0.41285771131515503},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3023250997066498},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.263300359249115},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.25249260663986206},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.09802833199501038}],"concepts":[{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.7797783017158508},{"id":"https://openalex.org/C36299963","wikidata":"https://www.wikidata.org/wiki/Q1369844","display_name":"Observability","level":2,"score":0.7575178742408752},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7262051105499268},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.6980404257774353},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.6829479932785034},{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.6015777587890625},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.5704566240310669},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.5626543760299683},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5428304076194763},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5266989469528198},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5059947371482849},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.42950883507728577},{"id":"https://openalex.org/C204495892","wikidata":"https://www.wikidata.org/wiki/Q1798304","display_name":"Linear-quadratic-Gaussian control","level":3,"score":0.4195978045463562},{"id":"https://openalex.org/C98779006","wikidata":"https://www.wikidata.org/wiki/Q2520550","display_name":"Linear-quadratic regulator","level":3,"score":0.41285771131515503},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3023250997066498},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.263300359249115},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.25249260663986206},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.09802833199501038},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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":1,"locations":[{"id":"doi:10.1093/imamci/dnp001","is_oa":false,"landing_page_url":"https://doi.org/10.1093/imamci/dnp001","pdf_url":null,"source":{"id":"https://openalex.org/S162756791","display_name":"IMA Journal of Mathematical Control and Information","issn_l":"0265-0754","issn":["0265-0754","1471-6887"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IMA Journal of Mathematical Control and Information","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2005019312","https://openalex.org/W2547959172","https://openalex.org/W2018296362","https://openalex.org/W2107449083","https://openalex.org/W2726381554","https://openalex.org/W2002357820","https://openalex.org/W1737855854","https://openalex.org/W197349956","https://openalex.org/W2997206142","https://openalex.org/W2804494800"],"abstract_inverted_index":{"In":[0],"this":[1,60],"article,":[2],"we":[3,62],"discuss":[4],"a":[5,23,48],"quadratic":[6],"control":[7,67],"problem":[8],"for":[9],"linear":[10],"discrete-time":[11,24],"systems":[12],"with":[13],"Markov":[14],"perturbations":[15],"in":[16],"Hilbert":[17],"spaces,":[18],"which":[19],"is":[20],"linked":[21],"to":[22],"Riccati":[25,45],"equation":[26,46],"defined":[27],"on":[28,53,59],"certain":[29],"infinite-dimensional":[30],"ordered":[31],"Banach":[32],"space.":[33],"We":[34],"prove":[35],"that":[36],"under":[37],"stabilizability":[38],"and":[39,55],"stochastic":[40],"uniform":[41],"observability":[42],"conditions,":[43],"the":[44,64,72],"has":[47],"unique,":[49],"uniformly":[50],"positive,":[51],"bounded":[52],"N":[54],"stabilizing":[56],"solution.":[57],"Based":[58],"result,":[61],"solve":[63],"proposed":[65],"optimal":[66],"problem.":[68],"An":[69],"example":[70],"illustrates":[71],"theory.":[73]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":5}],"updated_date":"2026-02-25T21:11:00.739837","created_date":"2025-10-10T00:00:00"}