Method of straight lines in the boundary control and observation problems for a hyperbolic equation with boundary conditions of the second and third kind (Q1281219)

The problem of the boundary control and observations for equations of vibrations of unhomogeneous string is investigated by the method of straight lines. The purpose of control is the transfer of the system from an initial state to the assigned finite state. The dynamics of the controlled process is described by a hyperbolic equation of second order with positive coefficients and with the boundary values of the second and the third kind. The equation of vibrations with variable coefficients is also investigated. The finite dimensional approximations are given by the method of straight lines with difference discretization with respect to the space variable. The convergence of the finite dimensional approximations is established taking into account the conditions of control and observations of the initial continuous systems. The convergence was proved analogically as for equations of vibrations of homogeneous systems.