Optimal boundary control of oscillations of a string with given intermediate values of the speed for minimizing boundary energy

For the equation of oscillation of a string with given initial and terminal conditions, we consider optimal boundary control problems with given intermediate conditions on the values of the speed with criteria for the qualities of the integrals of the boundary energies. The control is perform by displacements of ends of the string. Boundary energy integrals are considered over the entire time interval. We propose a constructive approach to constructing optimal boundary controls for oscillations based on the methods of separation of variables and moment problems. A computational experiment was carried out and the results obtained were analysed.