On a Game Problem of Converging at a Given Instant of Time

Solution of the positional problem on the minimax functional at a given instant is studied for the nonlinear, competitively controlled system . Iterative processes are proposed, permitting one to find the minimax of the payoff as a function of position, and also the sets of positional absorption. The cases are considered in which the indicated elements are determined after a single application of operators of special form to the program maximin function and the program absorption set. Bibliography: 18 titles.