Filtering for Nonlinear and Linear Markov Jump Systems
Autor(a) principal: | |
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Data de Publicação: | 2023 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNIFESP |
Texto Completo: | https://hdl.handle.net/11600/70880 https://ieeexplore.ieee.org/document/10273597 |
Resumo: | In this paper we consider the finite horizon filtering problem of discrete-time Markov jump systems (MJS). In the first part we consider a MJS satisfying some general nonlinear conditions. It is obtained, for a fixed set of auxiliary constants, filter gains, based on a set of coupled Riccati like difference equations, that yield a minimum upper bound for the estimation error covariance matrix. When the nonlinear parameters are set to zero the MJS becomes a Markov jump linear system (MJLS) and, in the second part of the paper, it is shown that the obtained filter gains derived from a set of coupled Riccati like difference equations provide the optimal “prediction-correction” Markovian filter for the nominal MJLS (which reduces to the standard Kalman filter for the no jump case). The paper is concluded with some numerical examples © 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. |
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Costa, Oswaldo Luiz do ValleOliveira, André Marcorin dehttp://lattes.cnpq.br/18648361145268182024-03-20T18:06:59Z2024-03-20T18:06:59Z2023-10-06In this paper we consider the finite horizon filtering problem of discrete-time Markov jump systems (MJS). In the first part we consider a MJS satisfying some general nonlinear conditions. It is obtained, for a fixed set of auxiliary constants, filter gains, based on a set of coupled Riccati like difference equations, that yield a minimum upper bound for the estimation error covariance matrix. When the nonlinear parameters are set to zero the MJS becomes a Markov jump linear system (MJLS) and, in the second part of the paper, it is shown that the obtained filter gains derived from a set of coupled Riccati like difference equations provide the optimal “prediction-correction” Markovian filter for the nominal MJLS (which reduces to the standard Kalman filter for the no jump case). The paper is concluded with some numerical examples © 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)FAPESP 2021/13338-6FAPESP 2014/50851−0CNPq 304149/2019CNPq 465755/2014−3CAPES 88887.136349/2017-00O. L. V. Costa and A. M. de Oliveira, "Filtering for Nonlinear and Linear Markov Jump Systems," in IEEE Transactions on Automatic Control, doi: 10.1109/TAC.2023.3322379.10.1109/TAC.2023.33223791558-25230018-9286https://hdl.handle.net/11600/70880https://ieeexplore.ieee.org/document/10273597engAlessandro Astolfi, Zhan Shu, David CastanonIEEE Transactions on Automatic ControlNonlinear systemsDiscrete-timeMarkovian jump systems“prediction-correction” formulaFinite horizonRiccati equationsFiltering for Nonlinear and Linear Markov Jump Systemsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UNIFESPinstname:Universidade Federal de São Paulo (UNIFESP)instacron:UNIFESPInstituto de Ciência e Tecnologia (ICT)Ciência e TecnologiaEngenharia de ComputaçãoCiência da ComputaçãoCiência da computaçãoFiltragemLICENSElicense.txtlicense.txttext/plain; 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 |
dc.title.none.fl_str_mv |
Filtering for Nonlinear and Linear Markov Jump Systems |
title |
Filtering for Nonlinear and Linear Markov Jump Systems |
spellingShingle |
Filtering for Nonlinear and Linear Markov Jump Systems Costa, Oswaldo Luiz do Valle Nonlinear systems Discrete-time Markovian jump systems “prediction-correction” formula Finite horizon Riccati equations |
title_short |
Filtering for Nonlinear and Linear Markov Jump Systems |
title_full |
Filtering for Nonlinear and Linear Markov Jump Systems |
title_fullStr |
Filtering for Nonlinear and Linear Markov Jump Systems |
title_full_unstemmed |
Filtering for Nonlinear and Linear Markov Jump Systems |
title_sort |
Filtering for Nonlinear and Linear Markov Jump Systems |
author |
Costa, Oswaldo Luiz do Valle |
author_facet |
Costa, Oswaldo Luiz do Valle Oliveira, André Marcorin de |
author_role |
author |
author2 |
Oliveira, André Marcorin de |
author2_role |
author |
dc.contributor.authorLattes.none.fl_str_mv |
http://lattes.cnpq.br/1864836114526818 |
dc.contributor.author.fl_str_mv |
Costa, Oswaldo Luiz do Valle Oliveira, André Marcorin de |
dc.subject.por.fl_str_mv |
Nonlinear systems Discrete-time Markovian jump systems “prediction-correction” formula Finite horizon Riccati equations |
topic |
Nonlinear systems Discrete-time Markovian jump systems “prediction-correction” formula Finite horizon Riccati equations |
description |
In this paper we consider the finite horizon filtering problem of discrete-time Markov jump systems (MJS). In the first part we consider a MJS satisfying some general nonlinear conditions. It is obtained, for a fixed set of auxiliary constants, filter gains, based on a set of coupled Riccati like difference equations, that yield a minimum upper bound for the estimation error covariance matrix. When the nonlinear parameters are set to zero the MJS becomes a Markov jump linear system (MJLS) and, in the second part of the paper, it is shown that the obtained filter gains derived from a set of coupled Riccati like difference equations provide the optimal “prediction-correction” Markovian filter for the nominal MJLS (which reduces to the standard Kalman filter for the no jump case). The paper is concluded with some numerical examples © 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. |
publishDate |
2023 |
dc.date.issued.fl_str_mv |
2023-10-06 |
dc.date.accessioned.fl_str_mv |
2024-03-20T18:06:59Z |
dc.date.available.fl_str_mv |
2024-03-20T18:06:59Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
O. L. V. Costa and A. M. de Oliveira, "Filtering for Nonlinear and Linear Markov Jump Systems," in IEEE Transactions on Automatic Control, doi: 10.1109/TAC.2023.3322379. |
dc.identifier.uri.fl_str_mv |
https://hdl.handle.net/11600/70880 https://ieeexplore.ieee.org/document/10273597 |
dc.identifier.doi.none.fl_str_mv |
10.1109/TAC.2023.3322379 |
dc.identifier.issn.none.fl_str_mv |
1558-2523 0018-9286 |
identifier_str_mv |
O. L. V. Costa and A. M. de Oliveira, "Filtering for Nonlinear and Linear Markov Jump Systems," in IEEE Transactions on Automatic Control, doi: 10.1109/TAC.2023.3322379. 10.1109/TAC.2023.3322379 1558-2523 0018-9286 |
url |
https://hdl.handle.net/11600/70880 https://ieeexplore.ieee.org/document/10273597 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.ispartof.none.fl_str_mv |
IEEE Transactions on Automatic Control |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Alessandro Astolfi, Zhan Shu, David Castanon |
publisher.none.fl_str_mv |
Alessandro Astolfi, Zhan Shu, David Castanon |
dc.source.none.fl_str_mv |
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Universidade Federal de São Paulo (UNIFESP) |
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UNIFESP |
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UNIFESP |
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Repositório Institucional da UNIFESP |
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Repositório Institucional da UNIFESP |
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https://repositorio.unifesp.br/bitstreams/114b0973-2b26-4ff2-9e3a-310f18842f36/download |
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MD5 |
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Repositório Institucional da UNIFESP - Universidade Federal de São Paulo (UNIFESP) |
repository.mail.fl_str_mv |
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1803210220863750144 |