Abstract
An example is considered of the application of a new modification of the well-known programmed iteration method (PIM) for solving a simple problem of control under conditions of noise. It is shown that the construction of a control procedure - a multivalued quasi-strategy-which solves the initial problem by the “direct” version of the PIM, working in the space of multivalued mappings, requires the performance of an infinite number of iterations. The structure of thee iterations is established on the basis of the duality of “direct” and “indirect” versions of the PIM (the latter having been used previously to construct value functions and stable bridges in Krasovskii's sense).
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