Boundary control of forced string vibrations by first directional derivatives on a short time interval

We solve a problem on the boundary control of forced vibrations of a homogeneous string by two first directional derivatives with time-dependent coefficients and noncharacteristic directions in the boundary conditions on a short time interval in the set of classical solutions. We obtain smoothness, coordination, and controllability conditions on the right-hand side of the equation and the initial and terminal data necessary and sufficient for the unique boundary control of the wave process.