  The aim of this article is to study the asymptotic behaviour of some low-cost
control problems. These problems motivate the study of H-convergence with
weakly convergingdata. An improved lower bound for the limit of energy
functionals correspondingto weak data is established, in the periodic case.
This fact is used to prove the Gamma-convergence of a low-cost problem with
Dirichlet-type integral. Finally, we study the asymptotic behaviour of a
low-cost problem with controls converging to measures.
