Optimization of Placement of Heating Sources of Plate and Synthesis of Their Power Control at Moving Measurement Points

The paper presents a method for controlling lumped sources in systems with distributed parameters, using the example of heat source control in the heating of a thin plate. Both the locations and power of these control sources are optimized. The current control values are determined depending on temperature on the value of the plate temperature at the measurement points moving according to the given rules. Formulas for calculating the gradient components of a functional within the space of feedback parameters, enabling the use of first-order optimization methods for solving the problem numerically.