About One Problem of Synthesis of Optimum Control by Thermal Conduction Process

Resumen

The formal procedure of obtaining Bellman equation in the problem of heat conductivity control is stated in [1]. Here we show how the problem of synthesis of optimum control with quadratic criterion of optimum is solved with the help of this equation. For simplification of formulas we used the simplest example whi.ch can be easily generalized. It should he noted, that during the solution the nonlinear boundary-value problem for integral-differential equation is derived, which is infinite dimensional analog of well-known Rikkati equation for finite dimensional systems.