Synthesis of the Control of the Temperature Maintaining Process in a Heat Supply Problem

Abstract

We consider a problem of controlling a heating appliance used for heating a heattransfer agent, which delivers heat into a closed system. To control the process, we use feedback, under which information on the process state is continuously or discretely received from individual points of the appliance with installed temperature sensors. The mathematical model of the controlled process is described in both cases by a pointwise loaded first-order hyperbolic equation. We have obtained formulas for the gradient of the functional of the problem. These formulas allow us to use numerical first-order optimization methods for solving the problems. Numerical experiments have been carried out by the example of solving several test problems.