# Integro-Differential Riccati Equation in the Optimal Control Problem by the Process of Heat Conductivity

Riccati equations occur when solving the problems of dynamics of processes in continuous environments, problems of the theory of heat conductivity and diffusion, problems of the theory of optimal control. In case of systems with lumped parameters it is necessary to investigate the usual matrix differential Riccati equations. There are integro-differential Riccati equations for mathematical models of systems with the distributed parameters. In the majority of monographs devoted to the theory of optimum control by systems with distributed parameters, the differential Riccati equations are not considered at all. In the given article the linear-quadratic problem of optimal control is investigated by heat conductivity process. By means of the method of Lagrange multipliers we obtain necessary optimality conditions. The uniqueness of optimal control is proved. Firstly for such problem we use Dirac delta-function and obtain the integro-differential Riccati equations. The formula for calculating the solution of this equation is proposed. By means of the given formula the optimum control is presented in the closed form.

Publication year:
2013
Issue:
2
УДК:
517.977.56
С. 59–63. Бібліогр.: 7 назв.
References:

1. Бутковский А.Г. Теория оптимального управления системами с распределенными параметрами. — М.: Наука, 1965. — 476 с.
2. Бутковский А.Г. Методы управления системами с ра- спределенными параметрами. — М.: Наука, 1975. — 568 с.
3. Сиразетдинов Т.К. Оптимизация систем с распределенными параметрами. — М.: Наука, 1977. — 480 с.
4. Ройтенберг Я.Н. Автоматическое управление. — М.: Наука, 1971. — 396 с.
5. D.S. Naidu, Optimal control systems (Electrical engineering textbook series). — Boka Raton—London—New York—Washington: CRC PRESS, D.C. — 2003. — 434 p.

References [transliteration]:

1. Butkovskiĭ A.G. Teorii͡a optimal'nogo upravlenii͡a sistemami s raspredelennymi parametrami. – M.: Nauka, 1965. – 476 s.
2. Butkovskiĭ A.G. Metody upravlenii͡a sistemami s raspredelennymi parametrami. – M.: Nauka, 1975. – 568 s.
3. Sirazetdinov T.K. Optimizat͡sii͡a sistem s raspredelennymi parametrami. – M.: Nauka, 1977. – 480 s.
4. Roĭtenberg I͡A.N. Avtomaticheskoe upravlenie. – M.: Nauka, 1971. – 396 s.
5. D.S. Naidu, Optimal control systems (Electrical engineering textbook series). – Boka Raton–London–New York–Washington: CRC PRESS, D.C. – 2003. – 434 p.

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