  We consider the homogenization of an optimal control problem in which the
control is placed on a part of the boundary and the spatial domain contains a
thin layer of "small particles", very close to the controlling boundary, and a
Robin boundary condition is assumed on the boundary of those "small particles".
This problem can be associated with the climatization modeling of Bioclimatic
Double Skin Fa\c{c}ades which was developed in modern architecture as a tool
for energy optimization. We assume that the size of the particles and the
parameters involved in the Robin boundary condition are critical (and so they
justify the occurrence of some "strange terms" in the homogenized problem). The
cost functional is given by a weighted balance of the distance (in a H^1-type
metric) to a prescribed target internal temperature u_{T} and the proper cost
of the control (given by its L^2 norm). We prove the (weak) convergence of
states u_{{\epsilon}} and of the controls v_{{\epsilon}} to some functions
which are completely identified: u_0 satisfies an artificial boundary condition
on the control boundary and v_0 is the optimal control associated to a limit
cost functional J_0 in which the "boundary strange term" on the control
boundary arises. This information on the limit problem makes much more
manageable the study of the optimal climatization of such double skin
structures.
