On the algorithms of dynamic programming for optimal processes

The problem of discrete optimal control which has m consistently applied objective functions is formulated. In this problem the optimal process, also called m-optimal, is sought as a pair of functions defined on a finite set of steps at the links by which one function is uniquely defines the other, with the constraints of these functions with inclusion “∈” of their values in the final multiple values of the functions of the known pair. A uniform representation of sets, forming the k-optimal processes for k not greater than m, is given with construction of nondecreasing sequence, upper limited by this pair by the “⊂” inclusions, on the basis of characterization of solvability of the problem.