APPROXIMATE SOLUTION OF THE PROBLEM OF NONLINEAR OPTIMIZATION OF THE THERMAL PROCESSES DESCRIBED BY A FREDHOLM INTEGRAL-DIFFERENTIAL EQUATIONS

Authors

  • Kerimbekov Akylbek Kyrgyz Russian Slavic University named after the First President of Russia B.N. Yeltsin
  • Ermekbaeva Ayzhan Turdubekovna Osh State University

DOI:

https://doi.org/10.52754/16948645_2023_1_110

Keywords:

boundary value problem, generalized solution, energy integral, functional, boundary control, optimal control.

Abstract

The article investigates some features of the construction of the approximate solution of the problem of nonlinear optimization for the mobile point control of the thermal process in the case, when the boundary value problem of a controlled process in the equation contains the integral Fredholm operator. The convergence of the approximate solution is studied and sufficient conditions for their convergence are found. The methods of the optimal control theory of distributed parameters systems, methods of classical variational calculus, methods of solving of equations of mathematical physics, methods functional analysis and the theory of nonlinear integral equations.

References

Kerimbekov, А. On the solvability of the problem of the boundary control of thermal processes, described by the Fredholm integro-differential equation / А. Kerimbekov // Abstracts of International Congress of Mathematicians. South Korea, Seoul, 2014. – P.570. DOI: https://doi.org/10.1007/978-3-319-12577-0_88

Эрмекбаева, А.Т. Условия оптимальности в задаче подвижного точечного управления тепловыми процессами, описываемыми фредгольмовыми интегро-дифференциальными уравнениями/ А. Керимбеков, А.Т. Эрмекбаева // Журнал «Вестник КРСУ». ̶ Том 16, № 5. – Бишкек, 2016. ̶ C. 45−50.

Эрмекбаева А.Т. Подвижное оптимальное точечное управление тепловыми процессами, описываемыми фредгольмовыми интегро-дифференциальными уравнениями / А.Т. Эрмекбаева // Журнал «Вестник КРСУ». ̶ Том 17, № 1. – Бишкек, 2017. ̶ C. 71-75.

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Published

2023-06-30

How to Cite

Kerimbekov , A., & Ermekbaeva , A. (2023). APPROXIMATE SOLUTION OF THE PROBLEM OF NONLINEAR OPTIMIZATION OF THE THERMAL PROCESSES DESCRIBED BY A FREDHOLM INTEGRAL-DIFFERENTIAL EQUATIONS. Journal of Osh State University. Mathematics. Physics. Technical Sciences, (1(2), 110–115. https://doi.org/10.52754/16948645_2023_1_110

Issue

No. 1(2) (2023): Journal of Osh State University. Mathematics. Physics. Technical Sciences

Section

MATHEMATICS

License

Copyright (c) 2023 Journal of Osh State University. Mathematics. Physics. Technical Sciences

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