On the Solvability of a Boundary Value Problem for Nonlinear Optimization of Oscillatory Processes

The paper investigates the solvability of a boundary value problem in the control of an oscillatory process described by control in partial derivatives of the first order. It has been established that there are an infinite set of controls, as solutions to the system of nonlinear Fredholm integral equations of the first kind, each of which transfers the controlled process from the initial state to the final specified state in a specified time. Sufficient conditions for the existence of a nonlinear optimization solution are found.