Boundary control of some distributed inhomogeneous oscillatory system with intermediate conditions

We consider boundary-control problems for a distributed inhomogeneous oscillatory system described by a one-dimensional wave equation with piecewise constant characteristics. We assume that the propagation times for all homogeneous sections are the same. The control is performed by shifting one end with the other end fixed. The initial, intermediate, and final conditions on the deflection function and the velocities of the points of the system are given. An approach to the analytical construction of the boundary control is proposed. The results obtained are illustrated by a specific example. A computational experiment and a comparative analysis were performed.