INTEC 05402
INSTITUTO DE DESARROLLO TECNOLOGICO PARA LA INDUSTRIA QUIMICA
Unidad Ejecutora - UE
congresos y reuniones científicas
Título:
Partial Differential Equations for Missing Boundary Conditions in the Linear-Quadratic Optimal Control Problem
Autor/es:
V. COSTANZA; C. E. NEUMAN
Lugar:
Río Gallegos, Santa Cruz, Argentina
Reunión:
Congreso; XII Reunión de Trabajo en Procesamiento de la Información y Control, RPIC 2007; 2007
Institución organizadora:
U.N.P.A. y RPIC
Resumen:
A procedure for obtaining the reachable
nal states and the initial values of the costates
corresponding to a family of nite-horizon, linearquadratic
problems is devised. The optimal control
can then be constructed in each case from the solution
to the Hamiltonian equations, integrated on-line.
The missing boundary conditions are found by solving
rst-order, quasi-linear, partial differential equations
for two auxiliary nn matrices, whose independent
variables are the time-horizon duration T and
the nal-penalty matrix S: These PDEs need to be integrated
off-line, the solution rendering information
on the boundary values of the whole two-parameter
family of control problems, that can be used for design
purposes. The mathematical foundations of
the solution take advange of the simplectic structure
of the Hamiltonian formalism, which allows to re-
ne a conjecture suggested by Bellman when developing
his .invariant-imbedding. methodology. Results
are tested against solutions of the differential Riccati
equations associated with these problems.nn matrices, whose independent
variables are the time-horizon duration T and
the nal-penalty matrix S: These PDEs need to be integrated
off-line, the solution rendering information
on the boundary values of the whole two-parameter
family of control problems, that can be used for design
purposes. The mathematical foundations of
the solution take advange of the simplectic structure
of the Hamiltonian formalism, which allows to re-
ne a conjecture suggested by Bellman when developing
his .invariant-imbedding. methodology. Results
are tested against solutions of the differential Riccati
equations associated with these problems.T and
the nal-penalty matrix S: These PDEs need to be integrated
off-line, the solution rendering information
on the boundary values of the whole two-parameter
family of control problems, that can be used for design
purposes. The mathematical foundations of
the solution take advange of the simplectic structure
of the Hamiltonian formalism, which allows to re-
ne a conjecture suggested by Bellman when developing
his .invariant-imbedding. methodology. Results
are tested against solutions of the differential Riccati
equations associated with these problems.S: These PDEs need to be integrated
off-line, the solution rendering information
on the boundary values of the whole two-parameter
family of control problems, that can be used for design
purposes. The mathematical foundations of
the solution take advange of the simplectic structure
of the Hamiltonian formalism, which allows to re-
ne a conjecture suggested by Bellman when developing
his .invariant-imbedding. methodology. Results
are tested against solutions of the differential Riccati
equations associated with these problems.
