Optimal control of external loads in the equilibrium problem for a composite body contacting with a rigid inclusion with a sharp edge

In this paper, we consider a nonclassical mathematical model that describes the mechanical point contact of a composite body with an obstacle of special geometry. The nonlinearity of the model is due to inequality-type conditions within the framework of the corresponding variational problem. An optimal control problem is formulated in which the controls are functions of external loads, and the cost functional is specified using a weakly upper semi-continuous functional defined on the Sobolev space. The solvability of the optimal control problem is proved. For the sequence of solutions corresponding to the maximizing sequence, the strong convergence in the corresponding Sobolev space is proved.