On the Solvability of a Nonlinear Optimization Problem for Thermal Processes Described by Fredholm Integro-Differential Equations with External and Boundary Controls

Authors

Akylbek Kerimbekov, Department of Topology and Functional Analysis, Institute of Theoretical and Applied Mathematics, National Academy of Sciences of the Kyrgyz Republic\\ Department of Applied Mathematics and Informatics, Faculty of Natural and Technical, Kyrgyz-Russian Slavic University, 720000 Bishkek, KyrgyzstanFollow
Elmira Abdyldaeva, Department of Mathematics, Faculty of Sciences, Kyrgyz-Turkish Manas University, 720044 Bishkek, KyrgyzstanFollow
Raihan Nametkulova, Department of Physics and Informatics, Taraz State University, Taraz Kazakhstan; Department of Applied Mathematics and Informatics, Faculty of Natural and Technical, Kyrgyz-Russian Slavic University, 720000 Bishkek, KyrgyzstanFollow
Aisha Kadirimbetova, Department of Physics and Informatics, Taraz State University, Taraz Kazakhstan; Department of Applied Mathematics and Informatics, Faculty of Natural and Technical, Kyrgyz-Russian Slavic University, 720000 Bishkek, KyrgyzstanFollow

Author Country (or Countries)

Kyrgyzstan

Abstract

In the present paper we studied the problem of nonlinear optimal control of the thermal processes described by Fredholm integro-differential equations when the control parameters are nonlinearly included into the equation as well as into the boundary condition. The concept of weak generalized solution of the boundary value problem is introduced and the algorithm for its construction is indicated. It is established that optimal control is defined as the solution of the system of nonlinear integral equations which contain unknown functions under and out of the integral and satisfy the additional condition in the form of the system of inequalities. Sufficient conditions for the existence of a unique solution of the problem of nonlinear optimization are given, and algorithm of its construction has been developed.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/100121

Recommended Citation

Kerimbekov, Akylbek; Abdyldaeva, Elmira; Nametkulova, Raihan; and Kadirimbetova, Aisha (2016) "On the Solvability of a Nonlinear Optimization Problem for Thermal Processes Described by Fredholm Integro-Differential Equations with External and Boundary Controls," Applied Mathematics & Information Sciences: Vol. 10: Iss. 1, Article 21.
DOI: http://dx.doi.org/10.18576/amis/100121
Available at: https://digitalcommons.aaru.edu.jo/amis/vol10/iss1/21