Homogenization of an optimal control problem

We consider an optimal control problem in which both the state equation and the cost functional have rapidly oscillating coefficients (characterized respectively by matrices A<SUB>ε</SUB> and B<SUB>ε</SUB>, where ε is a small parameter). We make no periodicity assumption. We study the limit of the problem when ε → 0 and work in the framework of H-convergence. We prove that the limit satisfies a problem similar to the original one but with matrices A<SUB>0</SUB> (the H-limit of A<SUB>ε</SUB>) and B# (which is a perturbation of the H-limit B<SUB>0</SUB> of B<SUB>ε</SUB>). We also study some particular cases. This paper extends former results obtained by Kesavan and Vanninathan in the periodic case