An approximate solution of distributed and boundary control problem for the thermal process

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.