Optimal control over the process of heating of a thin core

TitleOptimal control over the process of heating of a thin core
Publication TypeJournal Article
Year of Publication2014
AuthorsKopets, MM
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
SectionInformation Science and Cybernetics
Date Published7/2014

The paper is devoted to the linear-quadratic optimal control problem for the process of heating of a thin core. The simultaneous use of distributed and boundary controls is supposed. A method of Lagrange multipliers is proposed, and the Lagrange function includes not only a partial differential equation, but also boundary conditions. For the considered optimization problem, the necessary conditions of optimality are obtained. Their analysis has given chance to deduce the Riccati integro-differential equation.

Keywordscontrol, core, heating

1. Roitenberg Ya. N. Automatic control. Moscow: Nauka, 1978 (in Russian).
2. Naidu D. S. Optimal control systems. Boca Raton: CRC Press, 2003.
3. Zhukovsiky V. I., Chikriy A. A. Linear quadratic differential games. Kyiv: Nauk. dumka, 1994 (in Russian).
4. Krylov N. A. On some differential equations of mathematical physics having application in technical matters. Leningrad: Izd-vo AN USSR, 1933 (in Russian).
5. Sirazetdinov T. K. Optimizing systems with distributed parameters. Moscow: Nauka, 1977 (in Russian).