**On the Optimal Control of the Circular Plate's Vibrations
in the Conflict Situations**

It is discussed the problem of an optimal
control for the circular plate's linear vibrations, when the distributive
disposed forces influence on it. The problem is solved by the method of variable
division and it is brought to the differential game, which is described by the
infinitesimal differential equations of second order. The extremal strategies
are constructed by the extreme targeting method. It is shown that if the
resources of the first player are more than the resources of the second player
and the influencing forces belong to class L_{2}, then the problem of
damping of plate's vibrations is solved.