Initial values for Riccati ODEs from variational PDEs
Autor(a) principal: | |
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Data de Publicação: | 2011 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Computational & Applied Mathematics |
Texto Completo: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022011000200005 |
Resumo: | The recently discovered variational PDEs (partial differential equations) for finding missing boundary conditions in Hamilton equations of optimal control are applied to the extended-space transformation of time-variant linear-quadratic regulator (LQR) problems. These problems become autonomous but with nonlinear dynamics and costs. The numerical solutions to the PDEs are checked against the analytical solutions to the original LQR problem. This is the first validation of the PDEs in the literature for a nonlinear context. It is also found that the initial value of the Riccati matrix can be obtained from the spatial derivative of the Hamiltonian flow, which satisfies the variational equation. This last result has practical implications when implementing two-degrees-of freedom control strategies for nonlinear systems with generalized costs. |
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Computational & Applied Mathematics |
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Initial values for Riccati ODEs from variational PDEsoptimal controlnonlinear systemsRiccati equationsHamiltonian equationsfirst-order PDEsThe recently discovered variational PDEs (partial differential equations) for finding missing boundary conditions in Hamilton equations of optimal control are applied to the extended-space transformation of time-variant linear-quadratic regulator (LQR) problems. These problems become autonomous but with nonlinear dynamics and costs. The numerical solutions to the PDEs are checked against the analytical solutions to the original LQR problem. This is the first validation of the PDEs in the literature for a nonlinear context. It is also found that the initial value of the Riccati matrix can be obtained from the spatial derivative of the Hamiltonian flow, which satisfies the variational equation. This last result has practical implications when implementing two-degrees-of freedom control strategies for nonlinear systems with generalized costs.Sociedade Brasileira de Matemática Aplicada e Computacional2011-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022011000200005Computational & Applied Mathematics v.30 n.2 2011reponame:Computational & Applied Mathematicsinstname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)instacron:SBMAC10.1590/S1807-03022011000200005info:eu-repo/semantics/openAccessCostanza,VicenteRivadeneira,Pablo S.eng2011-07-27T00:00:00Zoai:scielo:S1807-03022011000200005Revistahttps://www.scielo.br/j/cam/ONGhttps://old.scielo.br/oai/scielo-oai.php||sbmac@sbmac.org.br1807-03022238-3603opendoar:2011-07-27T00:00Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)false |
dc.title.none.fl_str_mv |
Initial values for Riccati ODEs from variational PDEs |
title |
Initial values for Riccati ODEs from variational PDEs |
spellingShingle |
Initial values for Riccati ODEs from variational PDEs Costanza,Vicente optimal control nonlinear systems Riccati equations Hamiltonian equations first-order PDEs |
title_short |
Initial values for Riccati ODEs from variational PDEs |
title_full |
Initial values for Riccati ODEs from variational PDEs |
title_fullStr |
Initial values for Riccati ODEs from variational PDEs |
title_full_unstemmed |
Initial values for Riccati ODEs from variational PDEs |
title_sort |
Initial values for Riccati ODEs from variational PDEs |
author |
Costanza,Vicente |
author_facet |
Costanza,Vicente Rivadeneira,Pablo S. |
author_role |
author |
author2 |
Rivadeneira,Pablo S. |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Costanza,Vicente Rivadeneira,Pablo S. |
dc.subject.por.fl_str_mv |
optimal control nonlinear systems Riccati equations Hamiltonian equations first-order PDEs |
topic |
optimal control nonlinear systems Riccati equations Hamiltonian equations first-order PDEs |
description |
The recently discovered variational PDEs (partial differential equations) for finding missing boundary conditions in Hamilton equations of optimal control are applied to the extended-space transformation of time-variant linear-quadratic regulator (LQR) problems. These problems become autonomous but with nonlinear dynamics and costs. The numerical solutions to the PDEs are checked against the analytical solutions to the original LQR problem. This is the first validation of the PDEs in the literature for a nonlinear context. It is also found that the initial value of the Riccati matrix can be obtained from the spatial derivative of the Hamiltonian flow, which satisfies the variational equation. This last result has practical implications when implementing two-degrees-of freedom control strategies for nonlinear systems with generalized costs. |
publishDate |
2011 |
dc.date.none.fl_str_mv |
2011-01-01 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022011000200005 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022011000200005 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1590/S1807-03022011000200005 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
text/html |
dc.publisher.none.fl_str_mv |
Sociedade Brasileira de Matemática Aplicada e Computacional |
publisher.none.fl_str_mv |
Sociedade Brasileira de Matemática Aplicada e Computacional |
dc.source.none.fl_str_mv |
Computational & Applied Mathematics v.30 n.2 2011 reponame:Computational & Applied Mathematics instname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC) instacron:SBMAC |
instname_str |
Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC) |
instacron_str |
SBMAC |
institution |
SBMAC |
reponame_str |
Computational & Applied Mathematics |
collection |
Computational & Applied Mathematics |
repository.name.fl_str_mv |
Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC) |
repository.mail.fl_str_mv |
||sbmac@sbmac.org.br |
_version_ |
1754734890246471680 |