Approximating the Solution to LQR Problems with Bounded Controls

Authors
Costanza, Vicente; Rivadeneira Paz, Pablo Santiago
Publication Year
2011
Language
English
Format
article
Status
Published version
Description
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.
Fil: Costanza, Vicente. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); Argentina
Fil: Rivadeneira Paz, Pablo Santiago. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); Argentina
Subject
optimal control
constrained control
LQR
first order PDEs
Otras Ingenierías y Tecnologías
Otras Ingenierías y Tecnologías
INGENIERÍAS Y TECNOLOGÍAS
Access level
Open access
License
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repository
CONICET Digital (CONICET)
Institution
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identifier
oai:ri.conicet.gov.ar:11336/13105