The problem of boundary control of string vibrationsby displacement of the left end when the right end is fixedwith the given values of the deflection functionat intermediate times

We consider the boundary control problem for the homogeneous string vibrationequation with given the classical boundary (initial and final) conditions and with given valuesof the deflection function at intermediate times. The control is performed by displacementof the left end of the string when the right end is fixed. The problem is reduced to thecontrol problem with zero boundary conditions. We propose the constructive method forconstructing the boundary control of the process of string vibrations with given values ofthe deflection function at intermediate times.We present the results of numerical experimentsand the corresponding graphs confirm the validity of the results.