# 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

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topKogut, 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 -

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