We study the application of the method of averaging to the problems of optimal control over functional-differential
equations. The procedure of averaging allows us to replace the original problem with the problem of optimal control by a
system of ordinary differential equations. It is proved that the optimal control over the averaged problem is almost optimal
for the exact problem. The optimal control problems are investigated on finite and infinite horizons.
Citation Example:Koval’chuk T. V., Kravets V. I., Mohyl'ova V. V., Stanzhitskii A. N. Application of the method
of averaging to the problems of optimal control over functional-differential equations // Ukr. Mat. Zh. - 2018. - 70, № 2. - pp. 206-215.