We study the optimal control problem of a second order linear evolution equation defined in two-component composites with ε -periodic disconnected inclusions of size ε in presence of a jump of the solution on the interface that varies according to a parameter γ . In particular here the case γ < 1 is analyzed. The optimal control theory, introduced by Lions (Optimal Control of System Governed by Partial Differential Equations, 1971), leads us to characterize the control as the solution of a set of equations, called optimality conditions. The main result of this paper proves that the optimal control of the ε -problem, which is the unique minimum point of a quadratic cost functional J ε , converges to the optimal control of the homogenized problem with respect to a suitable limit cost functional J ∞ . The main difficulties are to find the appropriate limit functional for the control of the homogenized system and to identify the limit of the controls.