The Problem of Boundary Control of Displacement at Two Ends by the Process of Oscillation of a Rod Consisting of Two Sections of Different Density and Elasticity

Abstract

The problem of boundary control for a one-dimensional wave equation with piecewise constant characteristics is considered. In this case, it is assumed that the time of passage of the wave through each homogeneous section is the same. The control is carried out by displacement at both ends. A constructive approach to constructing a control action with given initial and final conditions is proposed. The construction scheme is as follows: the original problem is reduced to the problem of controlling distributed influences with zero boundary conditions. Further, the method of separation of variables and methods of control theory for finite-dimensional systems are used. The results obtained are illustrated by a specific example.