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dc.contributor.author
Costanza, Vicente
dc.contributor.author
Rivadeneira Paz, Pablo Santiago
dc.date.available
2019-05-15T17:47:24Z
dc.date.issued
2011-02
dc.identifier.citation
Costanza, Vicente; Rivadeneira Paz, Pablo Santiago; Initial values for Riccati ODEs from variational PDEs; Sociedade Brasileira de Matemática Aplicada e Computacional; Matematica Aplicada E Computacional; 30; 2; 2-2011; 331-347
dc.identifier.issn
0101-8205
dc.identifier.uri
http://hdl.handle.net/11336/76394
dc.description.abstract
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.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Sociedade Brasileira de Matemática Aplicada e Computacional
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
First-Order Pdes
dc.subject
Hamiltonian Equations
dc.subject
Nonlinear Systems
dc.subject
Optimal Control
dc.subject
Riccati Equations
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
Initial values for Riccati ODEs from variational PDEs
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2019-05-14T14:06:39Z
dc.journal.volume
30
dc.journal.number
2
dc.journal.pagination
331-347
dc.journal.pais
Brasil
dc.journal.ciudad
Sao Carlos, Brasil
dc.description.fil
Fil: Costanza, Vicente. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentina
dc.description.fil
Fil: Rivadeneira Paz, Pablo Santiago. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentina
dc.journal.title
Matematica Aplicada E Computacional
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1590/S1807-03022011000200005
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