On the optimal stabilization of the orthotropic rectangular plate

The optimal stabilization problem of the oscillations of an orthotropic rectangular plate, which is fixed at the edges by hinges has been considered. The plate becomes stable by means of supplementary control action on its upper plane. The problem has been solved by Fourier’s method, after which an infinite system of a second-order ordinary differential equations was received with separable variables. The optimal control action for each equation was formed in $L_2$ field.