Optimal Control with Nonlinear Feedback of the Power of Sources During Heating of the Rod

An approach to the optimal synthesis of control of lumped sources for objects with distributed parameters is investigated. It is proposed to use a class of nonlinear dependencies that implement feedback. As an example, we study the problem of nonlinear synthesis of controlling the power and speed of motion of lumped sources for heating a thin rod. To assign the speed of movement and power of the sources, their quadratic dependence on the difference between the desired and current measured temperature values at the measurement points was used. In the space of parameters involved in these dependencies, formulas for the gradient of the objective functional are obtained. These formulas are used in gradient methods for minimizing the objective functional. Numerical experiments were carried out on the test problem. An analysis of the obtained results was carried out, including the condition that measurements at control points are carried out with errors.