Feedback Control of the Power of Moving Sources in Bar Heating

The authors consider the problem of synthesis of power control of the sources moving according to the given rules along certain trajectories when the bar is heated. The current values of the controls are determined depending on bar’s temperature at the points of measurement. Formulas for the components of the gradient of the objective functional are obtained with respect to the feedback parameters and coordinates of the measurement points, which are used to numerically solve the test problem using first-order numerical optimization methods. The results of computer experiments are presented.