Some optimal control problems with boundary conditions of Robin type and singular cost functionals

We are concerned with the study of a class of linear boundary optimal control systems associated to the Laplace operator on a regular bounded domain in the n dimensional Euclidean space obtained by perturbing a singular system. The sets of admissible controls, taken here, are closed convex subsets of the Hilbert space of all square integrable functions on the boundary, verifying some natural conditions. The cost functional, used here, is singular. For these systems, we prove the existence of the (perturbed) states and optimal controls, and study their convergence.