Abstract:
Solution of the positional problem on the minimax functional $f_0(x[\vartheta])$ at a given instant $\vartheta$ is studied for the nonlinear, competitively controlled system $dx/dt=f(t,x,u,v)$. Iterative processes are proposed, permitting one to find the minimax of the payoff $f_0$ 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.
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