Geodesic
An approximate solution of distributed and boundary control problem for the thermal process
The Bulletin of Irkutsk State University. Series Mathematics, Tome 16 (2016), pp. 71-88
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A problem of nonlinear optimal distribution and boundary control of a thermal process, described by a Fredholm integral-differential equations, is considered. The unique solvability of a system of nonlinear integral equations of optimal controls is investigated. It was found the sufficient conditions for the existence of a unique solution of the problem of nonlinear optimization. The algorithm for constructing approximate solutions was developed and their convergence on optimal control, optimal processes and functionality, were proved, that it is necessary to distinguish between three types of approximations of the optimal process.
Keywords: functional, the maximum principle, the optimal control, system of nonlinear integral equations, approximate solution
Mots-clés : convergence. 
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A. Kerimbekov; R. J. Nametkulova; A. K. Kadirimbetova. An approximate solution of distributed and boundary control problem for the thermal process. The Bulletin of Irkutsk State University. Series Mathematics, Tome 16 (2016), pp. 71-88. http://geodesic.mathdoc.fr/item/IIGUM_2016_16_a5/

[1] Kerimbekov A., Nametkulova R. J., Kadirimbetova A. K., “Optimality conditions in the problem of thermal control with integral-differential equations”, The bulletin of Irkutsk State University. Mathematics, 15 (2016), 41–52 (in Russian)

[2] Lusternik L. A., Sobolev V. I., Elements of functional analiza, Nauka, M., 1965, 520 pp. (in Russian) | MR

[3] A. Kerimbekov, “On the Solvability of a Nonlinear Optimal Control Problem for the Thermal Processes Described by Fredholm Integro-Differential Equations”, Current Trends in Analysis and Its Applications, Proceedings of the 9th ISAAC Congress (Krakyw, 2013), Research Perspectives, XVI, Springer International Publishing, Switzerland, 2015, 803–811