Optimization of the placement of measurement points and control of the power of moving sources in rod heating

Abstract

The problem of synthesis of power control of the sources moving according to the given rules and trajectories when the rod is heated is considered. The current values of the controls are determined depending on the values of the temperature of the bar 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 the 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.