Approximating the Solution to LQR Problems with Bounded Controls

 

Autores
Costanza, Vicente; Rivadeneira Paz, Pablo Santiago
Tipo de recurso
artículo
Estado
Versión publicada
Año de publicación
2011
País
Argentina
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio
CONICET Digital (CONICET)
Descripción
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.
Idioma
inglés
OAI Identifier
oai:ri.conicet.gov.ar:11336/13105
Enlace del recurso
http://hdl.handle.net/11336/13105
Nivel de acceso
Acceso abierto
Materia
optimal control
constrained control
LQR
first order PDEs
Otras Ingenierías y Tecnologías
Otras Ingenierías y Tecnologías
INGENIERÍAS Y TECNOLOGÍAS