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

Published online by Cambridge University Press:  24 June 2008

Peter I. Kogut  and
Günter Leugering
Peter I. Kogut
Affiliation:
Department of Differential Equations, Dnipropetrovsk National University, Naukova str., 13, 49050 Dnipropetrovsk, Ukraine. p.kogut@i.ua
Günter Leugering
Affiliation:
Institüt für Angewandte Mathematik Lehrstuhl II, Universität Erlangen-Nürnberg Martensstr.3, 91058 Erlangen, Germany. Guenter.Leugering@am.uni-erlangen.de
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Abstract

We are concerned with the asymptotic analysis of optimal controlproblems for 1-D partial differential equations defined on aperiodic planar graph, as the period of the graph tends to zero. Wefocus on optimal control problems for elliptic equations withdistributed and boundary controls. Using approaches of the theory ofhomogenization we show that the original problem on the periodicgraph tends to a standard linear quadratic optimal control problemfor a two-dimensional homogenized system, and its solution can beused as suboptimal controls for the original problem.

Keywords

Optimal controlhomogenizationelliptic equationperiodic graph

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Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 15 , Issue 2 , April 2009 , pp. 471 - 498
Copyright
© EDP Sciences, SMAI, 2008

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