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dc.contributor.author
Costanza, Vicente
dc.contributor.author
Neuman, C. E.
dc.date.available
2017-05-30T14:10:12Z
dc.date.issued
2009-12
dc.identifier.citation
Costanza, Vicente; Neuman, C. E.; Partial Differential Equations for Missing Boundary Conditions in the Linear-Quadratic Optimal Control Problem; Planta Piloto de Ingeniería Química; Latin American Applied Research; 39; 3; 12-2009; 207-212
dc.identifier.issn
0327-0793
dc.identifier.uri
http://hdl.handle.net/11336/17096
dc.description.abstract
New equations involving the unknown final states and initial costates corresponding to families of LQR problems are found, and their solutions are computed and validated. Having the initial values of the costates, the optimal control can then be constructed, for each particular problem, from the solution to the Hamiltonian equations, now achievable through on-line integration. The missing boundary conditions are obtained by solving (offline) two uncoupled, first-order, quasi-linear, partial differential equations for two auxiliary n × n matrices, whose independent variables are the timehorizon duration T and the final-penalty matrix S. The solutions to these PDEs give information on the behavior of the whole two-parameter family of control problems, which can be used for design purposes. The mathematical treatment takes advantage of the symplectic structure of the Hamiltonian formalism, which allows to reformulate one of Bellman's conjectures related to the “invariantimbedding” methodology. Results are tested against solutions of the differential Riccati equations associated with these problems, and the attributes of the two approaches are illustrated and discussed.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Planta Piloto de Ingeniería Química
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Optimal Control
dc.subject
Linear-Quadratic Problem
dc.subject
First-Order Pdes
dc.subject
Boundary-Value Problems
dc.subject.classification
Ingeniería Química
dc.subject.classification
Ingeniería Química
dc.subject.classification
INGENIERÍAS Y TECNOLOGÍAS
dc.title
Partial Differential Equations for Missing Boundary Conditions in the Linear-Quadratic Optimal Control Problem
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2017-05-22T14:04:05Z
dc.identifier.eissn
1851-8796
dc.journal.volume
39
dc.journal.number
3
dc.journal.pagination
207-212
dc.journal.pais
Argentina
dc.journal.ciudad
Bahía Blanca
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: Neuman, C. E.. Universidad Nacional del Litoral; Argentina
dc.journal.title
Latin American Applied Research
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/http://www.laar.uns.edu.ar/indexes/artic_v3903/Vol39_3_207.pdf
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