HOMOGENIZATION OF CONSTRAINED OPTIMAL CONTROL PROBLEMS FOR ONE-DIMENSIONAL ELLIPTIC EQUATIONS ON PERIODIC GRAPHS
Kogut PI, Leugering G (2009)
Publication Language: English
Publication Status: Published
Publication Type: Journal article
Publication year: 2009
Journal
Publisher: EDP Sciences
Book Volume: 15
Pages Range: 471-498
Journal Issue: 2
URI: http://www.esaim-cocv.org/articles/cocv/abs/2009/02/cocv0505/cocv0505.html
DOI: 10.1051/cocv:2008037
Open Access Link: http://www.esaim-cocv.org/articles/cocv/pdf/2009/02/cocv0505.pdf
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.
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APA:
Kogut, P.I., & Leugering, G. (2009). HOMOGENIZATION OF CONSTRAINED OPTIMAL CONTROL PROBLEMS FOR ONE-DIMENSIONAL ELLIPTIC EQUATIONS ON PERIODIC GRAPHS. Esaim-Control Optimisation and Calculus of Variations, 15(2), 471-498. https://doi.org/10.1051/cocv:2008037
MLA:
Kogut, Peter I., and Günter Leugering. "HOMOGENIZATION OF CONSTRAINED OPTIMAL CONTROL PROBLEMS FOR ONE-DIMENSIONAL ELLIPTIC EQUATIONS ON PERIODIC GRAPHS." Esaim-Control Optimisation and Calculus of Variations 15.2 (2009): 471-498.
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