Homogenization of boundary optimal control problem in a domain with highly oscillating boundary via periodic unfolding method
We study the asymptotic behavior of boundary optimal control problems in this paper. We apply the controls through Neumann as well as Dirichlet data on the smooth part of the boundary where as homogeneous Neumann data is considered on the oscillating part of the boundary of the domain. We consider two cost functionals namely L^2-cost functional and Dirichlet-cost functional. We apply periodic unfolding operator tools to establish corresponding limit optimal control problems. In the process we introduce interior and boundary unfolding operators to achieve the limit problems which consist two parts, namely in the lower part and the upper part with appropriate interface conditions.