On the theory of necessary optimality conditions in discrete systems with a delay in control

In the present paper, a discrete optimization problem with a delay in control is considered. Taking into account the specific character of the discrete system, a necessary optimality condition which is not formulated in terms of the Hamilton-Pontryagin function is obtained with rather general input data (without assumptions of convexity and smoothness). It is shown by special example that the discrete maximum principle, generally speaking, does not hold even for the linear (with respect to a phase variable) discrete problem with delay in a control.