ASYMPTOTIC SOLUTION OF CONTROL PROBLEMS FOR DISCRETE WEAKLY CONTROLLABLE SYSTEMS

—The asymptotic expansion of the solution of a nonlinear discrete optimal control problem for one class of weakly controllable systems is constructed as series of non-negative integer powers of a small parameter. The estimates are obtained for the 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 for the optimal control are used.