Advanced Mathematical Models & Applications

The paper considers the inverse problem of determining the right side of the linear equation of vibrations of plate structures. Dynamics of plate-like constructions, for example of bridges, roof coverings and of other structural elements can be controlled by the resistance to seismic loads and optimal displacement equation. This time an optimal control method is used to optimize the behavior of the construction, i.e. with the aim of achieving maximum stability with minimum energy consumption. In the paper first, the considered problem is reduced to the corresponding optimal control problem. Further, using the standard procedures the existence theorem for the optimal control is proved. Then the differentiability of the constructed functional is investigated, and the necessary and sufficient optimality conditions are derived.