Delaying control of non-homogeneous string forced vibrations under mixed boundary conditions

Optimal control problem on finite time-interval is considered for non-homogeneous wave equation with variable coefficients and mixed boundary conditions. It is assumed that control process is carried out by delaying impacts with arbitrary distribution. Functionals describing the summary momentum and total energy of control impacts in considered time-interval are taken as control process optimality criterias. Using Fourier generalized integral transformation the problem is firstly reduced to interpolation problem with respect to unknown function Fourier transform, and then to truncated system of moments problem with respect to required function. Solution of the problem is obtained explicitly by means of generalized functions. Necessary and sufficient conditions on existence of optimal control function in terms of space of measurable functions are obtained using existence theorems of general moments theory. Numerical calculations are done and optimal resolving control function is plotted for piecewise non-homogeneous string, consisting of two heterogeneous strings.