On one problem of feedback control of a heating system

We consider a problem of controlling a heating device intended for heating a coolant supplying heat to a closed system is considered. Feedback is used to control the process, in which information about the process state is continuously or discretely received from individual points of the device, where temperature sensors are installed. The mathematical model of the controlled process in both cases is described by a point-loaded first-order hyperbolic equation. Formulas for the gradient of the objective functional of the problem are obtained, allowing the use of first-order numerical optimization methods for solving problems. Numerical experiments are carried out using the example of solving several test problems.