Theory of optimum discrete processes

Certain results obtained earlier for continuous problems with infinite derivatives are extended to discrete control problems. It is found which properties of the set of feasible states of a subsequent step permit transition to an equivalent “lower order” problem and a flow-chart of the transition is given. Sufficient conditions for optimality of discrete – continuous processes are formulated on the bases of V. F. Krotov's sufficient conditions obtained for continuous and discrete processes separately.