Optimizing placement of the control points at synthesis of the heating process control

Abstract

Consideration was given to the problem of optimizing the locations of the control points over the object state within the framework of the optimal feedback control problems of the distributed parameter objects. For certainty, considered was heating of a rod in furnace where the temperature of controlled vs. the temperature measured at certain points of the rod. The problem is reduced to that of parametric optimal control of an initial-boundary value problem where unknown current values of temperature at the measurement points occur at the right side of its equation and the boundary conditions. Formulas were derived for the components of the objective functional gradient with respect to the coordinates of the control point locations and the parameters of the measurement-dependent current control. The results of the carried out numerical experiments were given.