The LQ control problem for Markovian jumps linear systems with horizon defined by stopping times
Autor(a) principal: | |
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Data de Publicação: | 2004 |
Outros Autores: | , |
Tipo de documento: | Artigo de conferência |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1383686 http://hdl.handle.net/11449/67955 |
Resumo: | This paper deals with a stochastic optimal control problem involving discrete-time jump Markov linear systems. The jumps or changes between the system operation modes evolve according to an underlying Markov chain. In the model studied, the problem horizon is defined by a stopping time τ which represents either, the occurrence of a fix number N of failures or repairs (TN), or the occurrence of a crucial failure event (τΔ), after which the system is brought to a halt for maintenance. In addition, an intermediary mixed case for which T represents the minimum between TN and τΔ is also considered. These stopping times coincide with some of the jump times of the Markov state and the information available allows the reconfiguration of the control action at each jump time, in the form of a linear feedback gain. The solution for the linear quadratic problem with complete Markov state observation is presented. The solution is given in terms of recursions of a set of algebraic Riccati equations (ARE) or a coupled set of algebraic Riccati equation (CARE). |
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Repositório Institucional da UNESP |
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The LQ control problem for Markovian jumps linear systems with horizon defined by stopping timesDiscrete time control systemsFeedbackMarkov processesMatrix algebraOptimal control systemsProbabilityRiccati equationsSet theoryJump linear quadratic (JLQ) controlMarkov statesMarkovian jump linear systems (MJLS)Linear control systemsThis paper deals with a stochastic optimal control problem involving discrete-time jump Markov linear systems. The jumps or changes between the system operation modes evolve according to an underlying Markov chain. In the model studied, the problem horizon is defined by a stopping time τ which represents either, the occurrence of a fix number N of failures or repairs (TN), or the occurrence of a crucial failure event (τΔ), after which the system is brought to a halt for maintenance. In addition, an intermediary mixed case for which T represents the minimum between TN and τΔ is also considered. These stopping times coincide with some of the jump times of the Markov state and the information available allows the reconfiguration of the control action at each jump time, in the form of a linear feedback gain. The solution for the linear quadratic problem with complete Markov state observation is presented. The solution is given in terms of recursions of a set of algebraic Riccati equations (ARE) or a coupled set of algebraic Riccati equation (CARE).UNESP Univ. Est. Paulista Fac. de Ciências e Tecnologia, C.P. 467, 19060-900 Pres. Prudente, SPUNICAMP Univ. Est. de Campinas Depto. de Telemática, C.P. 6101, 13081-970 Campinas, SPUNESP Univ. Est. Paulista Fac. de Ciências e Tecnologia, C.P. 467, 19060-900 Pres. Prudente, SPUniversidade Estadual Paulista (Unesp)Universidade Estadual de Campinas (UNICAMP)Nespoli, Cristiane [UNESP]Do Val, João B. R.Cáceres, Yusef2014-05-27T11:21:11Z2014-05-27T11:21:11Z2004-11-29info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/conferenceObject703-707http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1383686Proceedings of the American Control Conference, v. 1, p. 703-707.0743-1619http://hdl.handle.net/11449/67955WOS:0002246883001162-s2.0-874427044069482537989528810000-0002-0690-0857Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengProceedings of the American Control Conference0,500info:eu-repo/semantics/openAccess2022-03-14T20:13:21Zoai:repositorio.unesp.br:11449/67955Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462022-03-14T20:13:21Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
The LQ control problem for Markovian jumps linear systems with horizon defined by stopping times |
title |
The LQ control problem for Markovian jumps linear systems with horizon defined by stopping times |
spellingShingle |
The LQ control problem for Markovian jumps linear systems with horizon defined by stopping times Nespoli, Cristiane [UNESP] Discrete time control systems Feedback Markov processes Matrix algebra Optimal control systems Probability Riccati equations Set theory Jump linear quadratic (JLQ) control Markov states Markovian jump linear systems (MJLS) Linear control systems |
title_short |
The LQ control problem for Markovian jumps linear systems with horizon defined by stopping times |
title_full |
The LQ control problem for Markovian jumps linear systems with horizon defined by stopping times |
title_fullStr |
The LQ control problem for Markovian jumps linear systems with horizon defined by stopping times |
title_full_unstemmed |
The LQ control problem for Markovian jumps linear systems with horizon defined by stopping times |
title_sort |
The LQ control problem for Markovian jumps linear systems with horizon defined by stopping times |
author |
Nespoli, Cristiane [UNESP] |
author_facet |
Nespoli, Cristiane [UNESP] Do Val, João B. R. Cáceres, Yusef |
author_role |
author |
author2 |
Do Val, João B. R. Cáceres, Yusef |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) Universidade Estadual de Campinas (UNICAMP) |
dc.contributor.author.fl_str_mv |
Nespoli, Cristiane [UNESP] Do Val, João B. R. Cáceres, Yusef |
dc.subject.por.fl_str_mv |
Discrete time control systems Feedback Markov processes Matrix algebra Optimal control systems Probability Riccati equations Set theory Jump linear quadratic (JLQ) control Markov states Markovian jump linear systems (MJLS) Linear control systems |
topic |
Discrete time control systems Feedback Markov processes Matrix algebra Optimal control systems Probability Riccati equations Set theory Jump linear quadratic (JLQ) control Markov states Markovian jump linear systems (MJLS) Linear control systems |
description |
This paper deals with a stochastic optimal control problem involving discrete-time jump Markov linear systems. The jumps or changes between the system operation modes evolve according to an underlying Markov chain. In the model studied, the problem horizon is defined by a stopping time τ which represents either, the occurrence of a fix number N of failures or repairs (TN), or the occurrence of a crucial failure event (τΔ), after which the system is brought to a halt for maintenance. In addition, an intermediary mixed case for which T represents the minimum between TN and τΔ is also considered. These stopping times coincide with some of the jump times of the Markov state and the information available allows the reconfiguration of the control action at each jump time, in the form of a linear feedback gain. The solution for the linear quadratic problem with complete Markov state observation is presented. The solution is given in terms of recursions of a set of algebraic Riccati equations (ARE) or a coupled set of algebraic Riccati equation (CARE). |
publishDate |
2004 |
dc.date.none.fl_str_mv |
2004-11-29 2014-05-27T11:21:11Z 2014-05-27T11:21:11Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/conferenceObject |
format |
conferenceObject |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1383686 Proceedings of the American Control Conference, v. 1, p. 703-707. 0743-1619 http://hdl.handle.net/11449/67955 WOS:000224688300116 2-s2.0-8744270440 6948253798952881 0000-0002-0690-0857 |
url |
http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1383686 http://hdl.handle.net/11449/67955 |
identifier_str_mv |
Proceedings of the American Control Conference, v. 1, p. 703-707. 0743-1619 WOS:000224688300116 2-s2.0-8744270440 6948253798952881 0000-0002-0690-0857 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Proceedings of the American Control Conference 0,500 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
703-707 |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1803046632549253120 |