Control of a parabolic system with disturbances and a convex goal

Abstract

The problem of controlling the heating process of a given number of rods by changing the temperatures at their left ends is considered. Temperatures at the right ends of the rods are formed by disturbances. The density functions of the internal heat sources of the rods are not known exactly, and only the boundaries of the range of their possible values are given. The goal of the choice of a control is to lead the vector of average temperatures of the rods at a fixed time to a convex terminal set. For this problem, necessary and sufficient conditions have been found that must be satisfied by the initial temperatures of the rods so that the goal can be achieved under any admissible realization of disturbances and density functions of internal heat sources. The case of a problem with a possible change in the dynamics of the controlled system is considered.