On the Solvability of the Nonlinear Optimization Problem for Point Boundary Control of the Thermal Process

In the article, the solvability of a nonlinear optimization problem for point-boundary control of a thermal process described by a partial integro-differential equation with the Fredholm integral operator was investigated. The investigation was carried out using the concept of generalized solution of the boundary value problem of the controlled process. Sufficient conditions of unique solvability of the problem were established, and an algorithm for constructing of complete solution of the nonlinear optimization problem was developed.