The amplification of perturbations near the leading-edge of swept wings is known to play a major role in boundary layer transition. Optimal perturbations and their optimal control in swept attachment-line boundary layers are addressed in the context of the swept Hiemenz base flow, under the G\ortler-H\ammerlin assumption. An adjoint formulation is used to determine the initial condition that experiences the strongest energy growth over a given time interval ; amplification as high as one thousand is observed at high Reynolds numbers. The optimal control sequence of wall-normal blowing and suction leading to the lowest energy at a given time is then computed by implementing an analogous adjoint method. Optimal control leads to a drastic reduction of the maximum energy by several orders of magnitude. Two-dimensional mechanisms are found to be responsible for most of the transient energy amplification. Control inhibits energy amplification at a given time by accelerating these processes.