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Русская версия

**A. G. Chentsov**

16, S.Kovalevskaja street, 620219, Ekaterinburg GSP-384, RUSSIA,

Institute of Mathematics and Mechanics,

Ural Branch of the Russian Academy of Sciences

**D. V. Khlopin**

16, S.Kovalevskaja street, 620219, Ekaterinburg GSP-384, RUSSIA,

Institute of Mathematics and Mechanics,

Ural Branch of the Russian Academy of Sciences,

This article is devoted to a nonlinear problem of control with
incomplete information. The problem formulated for the first player
is to approach the second point by the first within a distance not
exceeding a given number. The input data for the first player is the
position of the second player. The second player distorts the input
by additive noise. In this article the solution for the first player
is a quasistrategy. This solution is constructed by the iteration
programmed method. The optimal quasistrategy is unrealizable,
but it can be approximated by a sequence of admissible trajectories.
Such sequence of trajectories is generated by piecewise-constant
controls and constructed by the method of extremal shift
of N.N. Krasovskii.

This work was partially supported by Russian Science Support Foundation