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dc.contributor.author
Costanza, Vicente
dc.contributor.author
Rivadeneira Paz, Pablo Santiago
dc.contributor.author
Spies, Ruben Daniel
dc.date.available
2019-05-15T17:21:53Z
dc.date.issued
2011-02
dc.identifier.citation
Costanza, Vicente; Rivadeneira Paz, Pablo Santiago; Spies, Ruben Daniel; Equations for the Missing Boundary Values in the Hamiltonian Formulation of Optimal Control Problems; Springer/Plenum Publishers; Journal Of Optimization Theory And Applications; 149; 1; 2-2011; 26-46
dc.identifier.issn
0022-3239
dc.identifier.uri
http://hdl.handle.net/11336/76390
dc.description.abstract
Partial differential equations for the unknown final state and initial costate arising in the Hamiltonian formulation of regular optimal control problems with a quadratic final penalty are found. It is shown that the missing boundary conditions for Hamilton's canonical ordinary differential equations satisfy a system of first-order quasilinear vector partial differential equations (PDEs), when the functional dependence of the H-optimal control in phase-space variables is explicitly known. Their solutions are computed in the context of nonlinear systems with ℝn-valued states. No special restrictions are imposed on the form of the Lagrangian cost term. Having calculated the initial values of the costates, the optimal control can then be constructed from on-line integration of the corresponding 2n-dimensional Hamilton ordinary differential equations (ODEs). The off-line procedure requires finding two auxiliary n×n matrices that generalize those appearing in the solution of the differential Riccati equation (DRE) associated with the linear-quadratic regulator (LQR) problem. In all equations, the independent variables are the finite time-horizon duration T and the final-penalty matrix coefficient S, so their solutions give information on a whole two-parameter family of control problems, which can be used for design purposes. The mathematical treatment takes advantage from the symplectic structure of the Hamiltonian formalism, which allows one to reformulate Bellman's conjectures concerning the "invariant-embedding" methodology for two-point boundary-value problems. Results for LQR problems are tested against solutions of the associated differential Riccati equation, and the attributes of the two approaches are illustrated and discussed. Also, nonlinear problems are numerically solved and compared against those obtained by using shooting techniques.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Springer/Plenum Publishers
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Boundary-Value Problems
dc.subject
First Order Pdes
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Hamilton Equations
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Optimal Control
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Riccati Equations
dc.subject.classification
Matemática Pura
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Matemáticas
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CIENCIAS NATURALES Y EXACTAS
dc.title
Equations for the Missing Boundary Values in the Hamiltonian Formulation of Optimal Control Problems
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2019-05-14T14:05:27Z
dc.journal.volume
149
dc.journal.number
1
dc.journal.pagination
26-46
dc.journal.pais
Estados Unidos
dc.journal.ciudad
New York
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.description.fil
Fil: Spies, Ruben Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
dc.journal.title
Journal Of Optimization Theory And Applications
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/http://www.springerlink.com/content/yvg3451g55530q21/
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1007/s10957-010-9773-3
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