Average reachability of continuous-time Markov jump linear systems and the linear minimum mean square estimator
. In this paper we study the average reachability gramian for continuous-time linear systems with additive noise and jump parameters driven by a general Markov chain. We define a rather natural reachability concept by requiring that the average reachability gramian be positive definite. Aiming at a...
- Autores:
-
Roa Narvaez, Alfredo Rafael
Fontoura Costa, Eduardo
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2016
- Institución:
- Corporación Universidad de la Costa
- Repositorio:
- REDICUC - Repositorio CUC
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.cuc.edu.co:11323/1286
- Acceso en línea:
- https://hdl.handle.net/11323/1286
https://repositorio.cuc.edu.co/
- Palabra clave:
- Continuous-time systems
Filtering
Markov jump linear systems
Reachability of stochastic systems
Stochastic systems
- Rights
- openAccess
- License
- Atribución – No comercial – Compartir igual
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dc.title.eng.fl_str_mv |
Average reachability of continuous-time Markov jump linear systems and the linear minimum mean square estimator |
title |
Average reachability of continuous-time Markov jump linear systems and the linear minimum mean square estimator |
spellingShingle |
Average reachability of continuous-time Markov jump linear systems and the linear minimum mean square estimator Continuous-time systems Filtering Markov jump linear systems Reachability of stochastic systems Stochastic systems |
title_short |
Average reachability of continuous-time Markov jump linear systems and the linear minimum mean square estimator |
title_full |
Average reachability of continuous-time Markov jump linear systems and the linear minimum mean square estimator |
title_fullStr |
Average reachability of continuous-time Markov jump linear systems and the linear minimum mean square estimator |
title_full_unstemmed |
Average reachability of continuous-time Markov jump linear systems and the linear minimum mean square estimator |
title_sort |
Average reachability of continuous-time Markov jump linear systems and the linear minimum mean square estimator |
dc.creator.fl_str_mv |
Roa Narvaez, Alfredo Rafael Fontoura Costa, Eduardo |
dc.contributor.author.spa.fl_str_mv |
Roa Narvaez, Alfredo Rafael Fontoura Costa, Eduardo |
dc.subject.eng.fl_str_mv |
Continuous-time systems Filtering Markov jump linear systems Reachability of stochastic systems Stochastic systems |
topic |
Continuous-time systems Filtering Markov jump linear systems Reachability of stochastic systems Stochastic systems |
description |
. In this paper we study the average reachability gramian for continuous-time linear systems with additive noise and jump parameters driven by a general Markov chain. We define a rather natural reachability concept by requiring that the average reachability gramian be positive definite. Aiming at a testable condition, we introduce a set of reachability matrices for this class of systems and employ invariance properties of the null space of the noise coefficient matrices to show that the system is reachable if and only if these matrices are of full rank. We also show for reachable systems that the state second moment is positive definite. One consequence of this result in the context of linear minimum mean square state estimation for reachable systems is that the expectation of the error covariance matrix is positive definite. Moreover, the average boundedness of the error covariance matrix is invariant to a type of perturbation in the noise model, meaning that the estimates are not overly sensitive, which consists in a property that is desirable in applications and sometimes referred to as stability of the estimator. |
publishDate |
2016 |
dc.date.issued.none.fl_str_mv |
2016 |
dc.date.accessioned.none.fl_str_mv |
2018-11-19T13:24:54Z |
dc.date.available.none.fl_str_mv |
2018-11-19T13:24:54Z |
dc.type.spa.fl_str_mv |
Artículo de revista |
dc.type.coar.fl_str_mv |
http://purl.org/coar/resource_type/c_2df8fbb1 |
dc.type.coar.spa.fl_str_mv |
http://purl.org/coar/resource_type/c_6501 |
dc.type.content.spa.fl_str_mv |
Text |
dc.type.driver.spa.fl_str_mv |
info:eu-repo/semantics/article |
dc.type.redcol.spa.fl_str_mv |
http://purl.org/redcol/resource_type/ART |
dc.type.version.spa.fl_str_mv |
info:eu-repo/semantics/acceptedVersion |
format |
http://purl.org/coar/resource_type/c_6501 |
status_str |
acceptedVersion |
dc.identifier.issn.spa.fl_str_mv |
03630129 |
dc.identifier.uri.spa.fl_str_mv |
https://hdl.handle.net/11323/1286 |
dc.identifier.instname.spa.fl_str_mv |
Corporación Universidad de la Costa |
dc.identifier.reponame.spa.fl_str_mv |
REDICUC - Repositorio CUC |
dc.identifier.repourl.spa.fl_str_mv |
https://repositorio.cuc.edu.co/ |
identifier_str_mv |
03630129 Corporación Universidad de la Costa REDICUC - Repositorio CUC |
url |
https://hdl.handle.net/11323/1286 https://repositorio.cuc.edu.co/ |
dc.language.iso.none.fl_str_mv |
eng |
language |
eng |
dc.rights.spa.fl_str_mv |
Atribución – No comercial – Compartir igual |
dc.rights.accessrights.spa.fl_str_mv |
info:eu-repo/semantics/openAccess |
dc.rights.coar.spa.fl_str_mv |
http://purl.org/coar/access_right/c_abf2 |
rights_invalid_str_mv |
Atribución – No comercial – Compartir igual http://purl.org/coar/access_right/c_abf2 |
eu_rights_str_mv |
openAccess |
dc.publisher.spa.fl_str_mv |
SIAM Journal on Control and Optimization |
institution |
Corporación Universidad de la Costa |
bitstream.url.fl_str_mv |
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spelling |
Roa Narvaez, Alfredo RafaelFontoura Costa, Eduardo2018-11-19T13:24:54Z2018-11-19T13:24:54Z201603630129https://hdl.handle.net/11323/1286Corporación Universidad de la CostaREDICUC - Repositorio CUChttps://repositorio.cuc.edu.co/. In this paper we study the average reachability gramian for continuous-time linear systems with additive noise and jump parameters driven by a general Markov chain. We define a rather natural reachability concept by requiring that the average reachability gramian be positive definite. Aiming at a testable condition, we introduce a set of reachability matrices for this class of systems and employ invariance properties of the null space of the noise coefficient matrices to show that the system is reachable if and only if these matrices are of full rank. We also show for reachable systems that the state second moment is positive definite. One consequence of this result in the context of linear minimum mean square state estimation for reachable systems is that the expectation of the error covariance matrix is positive definite. Moreover, the average boundedness of the error covariance matrix is invariant to a type of perturbation in the noise model, meaning that the estimates are not overly sensitive, which consists in a property that is desirable in applications and sometimes referred to as stability of the estimator.Roa Narvaez, Alfredo Rafael-a701a283-5910-4c8b-a74e-6554527e3b15-600Fontoura Costa, Eduardo-f549c51c-f93f-4815-9533-836811e280fa-600engSIAM Journal on Control and OptimizationAtribución – No comercial – Compartir igualinfo:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Continuous-time systemsFilteringMarkov jump linear systemsReachability of stochastic systemsStochastic systemsAverage reachability of continuous-time Markov jump linear systems and the linear minimum mean square estimatorArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/acceptedVersionPublicationORIGINALAverage reachability of continuous-time Markov jump linear.pdfAverage reachability of continuous-time Markov jump linear.pdfapplication/pdf735562https://repositorio.cuc.edu.co/bitstreams/737ea18e-a67b-4bb7-adf6-853ae4dc43d5/download2b88ec7fe0b9ddd2ad546e85b52cde07MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://repositorio.cuc.edu.co/bitstreams/f923ed2f-c7fd-495a-8dfd-9c67ef2ce6b5/download8a4605be74aa9ea9d79846c1fba20a33MD52THUMBNAILAverage reachability of continuous-time Markov jump linear.pdf.jpgAverage reachability of continuous-time Markov jump linear.pdf.jpgimage/jpeg56383https://repositorio.cuc.edu.co/bitstreams/71f97c81-8b91-4a7f-ad95-0195741bce5a/download10fc49325df07b973e488a175606b3a6MD54TEXTAverage reachability of continuous-time Markov jump linear.pdf.txtAverage reachability of continuous-time Markov jump linear.pdf.txttext/plain83059https://repositorio.cuc.edu.co/bitstreams/3ce7360c-0abf-4de9-aec1-9aa570ef3fe3/downloada93668353a63be7c085576b52e6635f6MD5511323/1286oai:repositorio.cuc.edu.co:11323/12862024-09-17 12:46:42.231open.accesshttps://repositorio.cuc.edu.coRepositorio de la Universidad de la Costa CUCrepdigital@cuc.edu.coTk9URTogUExBQ0UgWU9VUiBPV04gTElDRU5TRSBIRVJFClRoaXMgc2FtcGxlIGxpY2Vuc2UgaXMgcHJvdmlkZWQgZm9yIGluZm9ybWF0aW9uYWwgcHVycG9zZXMgb25seS4KCk5PTi1FWENMVVNJVkUgRElTVFJJQlVUSU9OIExJQ0VOU0UKCkJ5IHNpZ25pbmcgYW5kIHN1Ym1pdHRpbmcgdGhpcyBsaWNlbnNlLCB5b3UgKHRoZSBhdXRob3Iocykgb3IgY29weXJpZ2h0Cm93bmVyKSBncmFudHMgdG8gRFNwYWNlIFVuaXZlcnNpdHkgKERTVSkgdGhlIG5vbi1leGNsdXNpdmUgcmlnaHQgdG8gcmVwcm9kdWNlLAp0cmFuc2xhdGUgKGFzIGRlZmluZWQgYmVsb3cpLCBhbmQvb3IgZGlzdHJpYnV0ZSB5b3VyIHN1Ym1pc3Npb24gKGluY2x1ZGluZwp0aGUgYWJzdHJhY3QpIHdvcmxkd2lkZSBpbiBwcmludCBhbmQgZWxlY3Ryb25pYyBmb3JtYXQgYW5kIGluIGFueSBtZWRpdW0sCmluY2x1ZGluZyBidXQgbm90IGxpbWl0ZWQgdG8gYXVkaW8gb3IgdmlkZW8uCgpZb3UgYWdyZWUgdGhhdCBEU1UgbWF5LCB3aXRob3V0IGNoYW5naW5nIHRoZSBjb250ZW50LCB0cmFuc2xhdGUgdGhlCnN1Ym1pc3Npb24gdG8gYW55IG1lZGl1bSBvciBmb3JtYXQgZm9yIHRoZSBwdXJwb3NlIG9mIHByZXNlcnZhdGlvbi4KCllvdSBhbHNvIGFncmVlIHRoYXQgRFNVIG1heSBrZWVwIG1vcmUgdGhhbiBvbmUgY29weSBvZiB0aGlzIHN1Ym1pc3Npb24gZm9yCnB1cnBvc2VzIG9mIHNlY3VyaXR5LCBiYWNrLXVwIGFuZCBwcmVzZXJ2YXRpb24uCgpZb3UgcmVwcmVzZW50IHRoYXQgdGhlIHN1Ym1pc3Npb24gaXMgeW91ciBvcmlnaW5hbCB3b3JrLCBhbmQgdGhhdCB5b3UgaGF2ZQp0aGUgcmlnaHQgdG8gZ3JhbnQgdGhlIHJpZ2h0cyBjb250YWluZWQgaW4gdGhpcyBsaWNlbnNlLiBZb3UgYWxzbyByZXByZXNlbnQKdGhhdCB5b3VyIHN1Ym1pc3Npb24gZG9lcyBub3QsIHRvIHRoZSBiZXN0IG9mIHlvdXIga25vd2xlZGdlLCBpbmZyaW5nZSB1cG9uCmFueW9uZSdzIGNvcHlyaWdodC4KCklmIHRoZSBzdWJtaXNzaW9uIGNvbnRhaW5zIG1hdGVyaWFsIGZvciB3aGljaCB5b3UgZG8gbm90IGhvbGQgY29weXJpZ2h0LAp5b3UgcmVwcmVzZW50IHRoYXQgeW91IGhhdmUgb2J0YWluZWQgdGhlIHVucmVzdHJpY3RlZCBwZXJtaXNzaW9uIG9mIHRoZQpjb3B5cmlnaHQgb3duZXIgdG8gZ3JhbnQgRFNVIHRoZSByaWdodHMgcmVxdWlyZWQgYnkgdGhpcyBsaWNlbnNlLCBhbmQgdGhhdApzdWNoIHRoaXJkLXBhcnR5IG93bmVkIG1hdGVyaWFsIGlzIGNsZWFybHkgaWRlbnRpZmllZCBhbmQgYWNrbm93bGVkZ2VkCndpdGhpbiB0aGUgdGV4dCBvciBjb250ZW50IG9mIHRoZSBzdWJtaXNzaW9uLgoKSUYgVEhFIFNVQk1JU1NJT04gSVMgQkFTRUQgVVBPTiBXT1JLIFRIQVQgSEFTIEJFRU4gU1BPTlNPUkVEIE9SIFNVUFBPUlRFRApCWSBBTiBBR0VOQ1kgT1IgT1JHQU5JWkFUSU9OIE9USEVSIFRIQU4gRFNVLCBZT1UgUkVQUkVTRU5UIFRIQVQgWU9VIEhBVkUKRlVMRklMTEVEIEFOWSBSSUdIVCBPRiBSRVZJRVcgT1IgT1RIRVIgT0JMSUdBVElPTlMgUkVRVUlSRUQgQlkgU1VDSApDT05UUkFDVCBPUiBBR1JFRU1FTlQuCgpEU1Ugd2lsbCBjbGVhcmx5IGlkZW50aWZ5IHlvdXIgbmFtZShzKSBhcyB0aGUgYXV0aG9yKHMpIG9yIG93bmVyKHMpIG9mIHRoZQpzdWJtaXNzaW9uLCBhbmQgd2lsbCBub3QgbWFrZSBhbnkgYWx0ZXJhdGlvbiwgb3RoZXIgdGhhbiBhcyBhbGxvd2VkIGJ5IHRoaXMKbGljZW5zZSwgdG8geW91ciBzdWJtaXNzaW9uLgo= |