Control Problem of String Vibrations with Inseparable Multipoint Conditions at Intermediate Points in Time

Abstract

The problem of controlling the vibrations of a string with given inseparable values of the deflection function and velocities at intermediate times is considered. By the method of separation of variables, the problem reduces to the problem of controlling ordinary differential equations with given initial, final, and unseparated multipoint intermediate conditions. The problem is solved using methods of the theory of control of finite-dimensional systems with multipoint intermediate conditions. As an application of the proposed approach, a control action is constructed for the control problem of string vibrations with specified unseparated conditions on the values of the deflection function and string velocities at two intermediate points in time.