Optimal control over the process of heating of a thin core

Authors

  • M.M. Kopets

DOI:

https://doi.org/10.15407/dopovidi2014.07.048

Keywords:

control, core, heating

Abstract

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.

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References

Roitenberg Ya. N. Automatic control. Moscow: Nauka, 1978 (in Russian).

Naidu D. S. Optimal control systems. Boca Raton: CRC Press, 2003.

Zhukovsiky V. I., Chikriy A. A. Linear quadratic differential games. Kyiv: Nauk. dumka, 1994 (in Russian).

Krylov N. A. On some differential equations of mathematical physics having application in technical matters. Leningrad: Izd-vo AN USSR, 1933 (in Russian).

Sirazetdinov T. K. Optimizing systems with distributed parameters. Moscow: Nauka, 1977 (in Russian).

Published

28.02.2025

How to Cite

Kopets, M. (2025). Optimal control over the process of heating of a thin core . Reports of the National Academy of Sciences of Ukraine, (7), 48–52. https://doi.org/10.15407/dopovidi2014.07.048

Issue

Section

Information Science and Cybernetics