Artículo
An efficient cost reduction procedure for bounded-control LQR problems
Fecha de publicación:
10/2016
Editorial:
Springer
Revista:
Computational And Applied Mathematics
ISSN:
2238-3603
e-ISSN:
1807-0302
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
A novel approach has been developed for approximating the solution to the constrained LQR problem, based on updating the final state and costate of a related regular problem, and on slightly shifting the switching times (the instants when the control meets the constraints). The main result is the expression of a suboptimal control in feedback form using the solution of some compatible Riccati equation. The gradient method is applied to reduce the cost via explicit algebraic formula for its partial derivatives with respect to the hidden final state/costate of the related regular problem and to the switching times. The numerical methodis termed efficient because it does not involve integrations of states or cost trajectories, and reduces to its minimum the dimension of the unknown parameters at the final condition. All the relevant objects are calculated from a few auxiliary matrices, which are computed onlyonce. The scheme is here applied to two case studies whose optimal solutions are known. The first example is a two-dimensional model of the "cheapest stop of a train" problem. The second one refers to the temperature control of a metallic strip leaving a multi-stand rollingmill, a problem with a high-dimensional state.
Palabras clave:
Optimal Control
,
Restricted Controls
,
Lqr Problem
,
Gradient Methods
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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; Gómez Múnera, John Anderson; An efficient cost reduction procedure for bounded-control LQR problems; Springer; Computational And Applied Mathematics; 10-2016; 1-22
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