Optimization of the Right-hand Sides of Multi-point and Integral Conditions of the Controlled Dynamic System

This paper studies the problem of optimizing the right-hand sides of nonlocal conditions with respect to a system of linear differential equations. Nonseparated nonlocal conditions linearly depend on the point and integral values of the unknown function. In the problem, it is required to determine the optimal values of the right-hand sides of nonlocal conditions. The issues of existence and uniqueness of a solution to a system of differential equations with nonlocal conditions under consideration are investigated, the convexity of the objective functional is proved. The obtained necessary optimality conditions for the values of the right-hand side terms of the nonlocal conditions allow using first-order optimization methods for the numerical solution of the problem. Computational experiments on solving a test problem are given and the results obtained are analyzed.