  We study the minimum energy null-controllability problem for differential
equations with point-wise delays. For the equations of both neutral and
retarded type we reduce the problem of finding the optimal control to a
Volterra integral equation and solve it explicitly. We prove that for any
initial state and any controllability time the corresponding optimal control
belongs to the characteristic space generated by the equation's exponentials.
Besides, we show that the proposed approach can be applied to the systems of
retarded equations with one delay term.
