About Optimal Control Discrete Problem of the Volterra Type of Two-Dimensional Difference Equa-tions System

An optimal control problem is considered for a discrete process described by a system of two-dimensional Volterra-type difference equations and a Bolza-type cost functional, assuming that the initial function is a solution to a one-dimensional nonlinear Volterra-type difference equation. The control domains are bounded and closed sets. Using a discrete analogue of the needle-type variation, a special increment of the cost functional is calculated. Based on this expression, a discrete version of Pontryagin's maximum principle is established.