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

Kogut, Peter I.; Leugering, Günter

ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 2, pp. 471-498.

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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