Optimal boundary control of string oscillations by displacement at two ends with specified values of deflection function at intermediate moments of time

Abstract

We consider the problem of optimal boundary control for the equation of string vibrations with given initial, final conditions and given values of the string deflection function at intermediate moments of time and with a quality criterion specified over the entire time interval. Using the method of separation of variables and methods of optimal control theory with multipoint intermediate conditions, optimal boundary controls are constructed for arbitrary numbers of the first harmonics. As an application of the proposed constructive approach, a boundary optimal control is built with a given string deflection function at an intermediate moment of time.