Artículo
Approximating the Solution to LQR Problems with Bounded Controls
Fecha de publicación:
08/2011
Editorial:
Planta Piloto de Ingeniería Química
Revista:
Latin American Applied Research
ISSN:
0327-0793
e-ISSN:
1851-8796
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
New equations involving the unknown final states and initial costates corresponding to families of LQR problems are shown to be useful in calculating optimal strategies when bounded control restrictions are present, and in approximating the solution to fixed-end problems. The missing boundary values of the Hamiltonian equations are obtained by (off-line) solving two uncoupled, first-order, linear partial differential equations for two auxiliary n×n matrices, whose independent variables are the time-horizon duration T and the eigenvalues of the final-penalty matrix S. The solutions to these PDEs give information on the behavior of the whole (T,S)-family of control problems. Illustrations of numerical results are provided and checked against analytical solutions of ´the cheapest stop of a train´ problem.
Palabras clave:
Optimal Control
,
Constrained Control
,
Lqr
,
First Order Pdes
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Articulos(INTEC)
Articulos de INST.DE DES.TECNOL.PARA LA IND.QUIMICA (I)
Articulos de INST.DE DES.TECNOL.PARA LA IND.QUIMICA (I)
Citación
Costanza, Vicente; Rivadeneira Paz, Pablo Santiago; Approximating the Solution to LQR Problems with Bounded Controls; Planta Piloto de Ingeniería Química; Latin American Applied Research; 41; 4; 8-2011; 339-351
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