Synthesis of distributed optimal control in the tracking problem at the optimization of thermal processes described by integro-differential equations

In this paper, we examine the synthesis problem for a distributed thermal control system in the case where a Fredholm integral operator is involved in the boundary-value problem. We use the method proposed by A. I. Egorov and develop it based on the Bellman scheme. Using the notions of a generalized solution of a boundary-value problem and the Frechet differential for the Bellman functional, we obtain a partial integro-differential equation. For synthesizing a distributed optimal control, we propose a numerical algorithm.