Optimal control of the location of the hinge point of rigid inclusions in an equilibrium problem of a Timoshenko plate

We consider a family of contact problems on the equilibrium of a Timoshenko composite plate containing two thin rigid inclusions, which are connected in a hinged manner. The family's problems depends on a parameter specifying the coordinate of a connection point of the inclusions. An optimal control problem is formulated with a quality functional defined using an arbitrary continuous functional given on a suitable Sobolev space. In this case, control is specified by the coordinate parameter of the connection point of the inclusions. The continuity of solutions of the family's problems on this parameter is proved. The solvability of the optimal control problem is established.