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.

MSC

49K20

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

2. Lusternik L.A., Sobolev V.I. Elements of functional analiza (in Russian). Moscow, Russia, Nauka, 1965. 520 р.

3. Kerimbekov A. 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, Krakуw 2013, A series of trends in mathematics.) Switzerland, Springer International Publishing, 2015, vol. XVI, pp. 803-811.