A linear-quadratic problem of optimal control over the heat conductivity process

1Kopets, MM
1National Technical University of Ukraine "Kyiv Polytechnic Institute"
Dopov. Nac. akad. nauk Ukr. 2014, 2:45-49
https://doi.org/10.15407/dopovidi2014.02.045
Section: Information Science and Cybernetics
Language: Ukrainian
Abstract: 

The problem of minimization of a quadratic functional on solutions of the second boundary-value problem for the heat equation is considered. The method of Lagrange multipliers is applied to research the formulated optimization problem. Such approach has given a chance to obtain the necessary conditions of optimality. On the basis of these conditions, the integro-differential Riccati equation with partial derivatives is deduced. The solution of this equation is presented in the closed form.

Keywords: heat conductivity, optimal control
References: 

1. Zhukovski V. I., Chikry A. A. Linear quadratic differential games. Kyiv: Nauk. dumka, 1994 (in Russian).
2. Bensoussan A., Da Prato G., Delfour M. C., Mitter S. K. Representation and control of infinite dimensional systems. Boston; Basel; Berlin: Birkhäuser, 2007. https://doi.org/10.1007/978-0-8176-4581-6
3. Naidu D. S. Optimal control systems. (Electrical engineering textbook series). Boca Raton: CRC Press, 2003.
4. Sirazetdinov T. K. Optimization of systems with distributed parameters. Moscow: Nauka, 1977 (in Russian).
5. Roitenberg Ya. N. Automatic control. Moscow: Nauka, 1978 (in Russian).