We study the asymptotic behavior of an optimal boundary control vε and a solution uε to the parabolic state problem specified in a domain Ωε ⊂ \({\mathbb{R}}^{n}\) , n ⩾ 3, ε-periodically perforated by tiny balls along a part of its boundary as ε → 0. On the boundary of inclusion, we impose the dynamic condition with a large growth coefficient at the time derivative. The critical relation between the period of structure, diameter of balls, and the growth coefficient is considered. This relation leads to the emergence of the nonlocal “strange” term given by some ordinary differential equation, in the effective state equation. We establish the weak convergence of the optimal control to the optimal control associated with the limit cost functional containing the new “strange” term.
