Yu. V. Averboukh
16, S.Kovalevskaja street, 620219, Ekaterinburg GSP-384, RUSSIA,
Institute of Mathematics and Mechanics,
Ural Branch of the Russian Academy of Sciences,
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
The versions of the programmed iteration method are considered. We restrict ourselves to the conflict control problem. The procedure of the value function and the programmed absorption set in sense of N. N. Krasovskii construction is studied. The condition under which the programmed absorption set realizes in the family of the compacts is obtained for the general nonlinear case. The convergence of the iteration procedure to the programmed absorption set in Hausdorf metric is established under the same condition. The family of the continuous functions of the positions with the convex sections is the invariant subspace of the programmed absorption operator for the quasi linear systems. If in addition the Lebesgue sets of the value function are compact then the sections of the iterations of the programmed maximin function is also compact.