Asymptotic Solution of Singularly Perturbed Nonlinear Discrete Periodic Optimal Control Problem

The asymptotic expansion of the solution of a singularly perturbed nonlinear discrete periodic optimal control problem is constructed as series of non-negative integer powers of a small parameter. The estimates are obtained for closeness of the approximate solutions to the exact one and it is proved that the values of the minimized functional do not increase when higher-order approximations to the optimal control are used.