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

In this work, we examine a distributed inhomogeneous oscillatory system, in which various states are specified at intermediate times. Problems of boundary control and optimal boundary control of this system are considered. The dynamics of this object is modeled by a one-dimensional wave equation with piecewise constant characteristics; the oscillations propagate in homogeneous domains areas in the same time. The quality criterion for optimal boundary control problems is specified over the entire time interval. A constructive approach to constructing a boundary control function and optimal control of one-dimensional oscillatory inhomogeneous processes is proposed. The research approach is based on methods of separation of variables, control theory, and optimal control of finite-dimensional systems with multipoint intermediate conditions. Under the influence of the constructed control law, wave oscillations from a given initial state pass into a given terminal state through multipoint intermediate states.