Averaging method in optimal control problems for integro-differential equations

Abstract The averaging method is applied to the study of optimal control problems for systems of integro-differential equations with rapidly oscillating coefficients and a small parameter. The original problem is associated with an averaged optimal control problem, formulated for a system of ordinary differential equations, which significantly simplifies the analysis. It is proven that as the small parameter tends to zero, the quality criterion, optimal control, and optimal trajectory of the original problem converge to those of the averaged problem.