On the optimal control for the elastic plate's vibrations in the conflict situations

It is discussed the problem of an optimal control for the plate's linear vibrations, when the distributive disposed forces influence on it. The problem is solved by the method of Fourie 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. In the end of the article a numerical example is given.