Homogenization of constrained optimal control problems for one-dimensional elliptic equations on periodic graphs

Peter I. Kogut; Günter Leugering

ESAIM: Control, Optimisation and Calculus of Variations (2008)

  • Volume: 15, Issue: 2, page 471-498
  • ISSN: 1292-8119

Abstract

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We are concerned with the asymptotic analysis of optimal control problems for 1-D partial differential equations defined on a periodic planar graph, as the period of the graph tends to zero. We focus on optimal control problems for elliptic equations with distributed and boundary controls. Using approaches of the theory of homogenization we show that the original problem on the periodic graph tends to a standard linear quadratic optimal control problem for a two-dimensional homogenized system, and its solution can be used as suboptimal controls for the original problem.

How to cite

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Kogut, Peter I., and Leugering, Günter. "Homogenization of constrained optimal control problems for one-dimensional elliptic equations on periodic graphs." ESAIM: Control, Optimisation and Calculus of Variations 15.2 (2008): 471-498. <http://eudml.org/doc/90922>.

@article{Kogut2008,
abstract = { We are concerned with the asymptotic analysis of optimal control problems for 1-D partial differential equations defined on a periodic planar graph, as the period of the graph tends to zero. We focus on optimal control problems for elliptic equations with distributed and boundary controls. Using approaches of the theory of homogenization we show that the original problem on the periodic graph tends to a standard linear quadratic optimal control problem for a two-dimensional homogenized system, and its solution can be used as suboptimal controls for the original problem. },
author = {Kogut, Peter I., Leugering, Günter},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Optimal control; homogenization; elliptic equation; periodic graph; two-scale convergence; star-structure},
language = {eng},
month = {6},
number = {2},
pages = {471-498},
publisher = {EDP Sciences},
title = {Homogenization of constrained optimal control problems for one-dimensional elliptic equations on periodic graphs},
url = {http://eudml.org/doc/90922},
volume = {15},
year = {2008},
}

TY - JOUR
AU - Kogut, Peter I.
AU - Leugering, Günter
TI - Homogenization of constrained optimal control problems for one-dimensional elliptic equations on periodic graphs
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2008/6//
PB - EDP Sciences
VL - 15
IS - 2
SP - 471
EP - 498
AB - We are concerned with the asymptotic analysis of optimal control problems for 1-D partial differential equations defined on a periodic planar graph, as the period of the graph tends to zero. We focus on optimal control problems for elliptic equations with distributed and boundary controls. Using approaches of the theory of homogenization we show that the original problem on the periodic graph tends to a standard linear quadratic optimal control problem for a two-dimensional homogenized system, and its solution can be used as suboptimal controls for the original problem.
LA - eng
KW - Optimal control; homogenization; elliptic equation; periodic graph; two-scale convergence; star-structure
UR - http://eudml.org/doc/90922
ER -

References

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