On the problems of boundary control and optimal control of a distributed inhomogeneous oscillatory system with specified intermediate conditions on the state function

We discuss the problems of boundary control and optimal boundary control of a distributed inhomogeneous (piecewise homogeneous) oscillatory system with specified different states at intermediate time points. The control is carried out both by shifting one end with the other end fixed, and by shifting at the two ends with specified initial and final conditions and set values of the state function and the velocities of the points at different intermediate points in time. For optimal boundary control problems, the quality criterion is set over the entire time interval.