Estimation of the Reachable Set for the Problem of Vibrating Kirchhoff Plate

Abstract

We consider a dynamical system with distributed parameters for the description of controlled vibrations of a Kirchhoff plate without polar moment of inertia. A class of optimal controls corresponding to finite-dimensional approximations is used to study the reachable set. Analytic estimates for the norm of these control functions are obtained depending on the boundary conditions. These estimates are used to study the reachable set for the infinite-dimensional system. For a model with incommensurable frequencies, an estimate of the reachable set is obtained under the condition of power decay of the amplitudes o generalized coordinates.