ON THE SOLVABILITY OF THE OPTIMIZATION PROBLEM WITH MINIMUM ENERGY UNDER BOUNDARY CONTROL OF THE OSCILLATIONAL PROCESS

Abstract

: The paper studies the solvability of the optimization problem for oscillatory processes described by partial integro-differential equations with an integral Fredholm operator while minimizing the energy integral of the control force. The study was carried out using the concept of a generalized solution of the boundary value problem of a controlled oscillatory process. In the optimization problem, it is required to find a control that transfers the oscillatory process from one state to another given state. In the course of the study, it was established that the desired optimal control is defined as a solution to an infinite-dimensional system of Fredholm integral equations of the first kind, and sufficient conditions for the existence of a solution to this ill-posed problem were found.