Abstract:
The conflictive control system
\begin {equation}
\frac{dx}{dt}=f(t,x,u,v),\qquad u\in P,\quad v\in Q,
\end{equation}
is considered, where $P$ and $Q$ are compact. The positional game problem of attaining a guaranteed result by means of the trajectories of (1) is studied for the functional $\inf_t\psi(t,x(t))$ with values in a linearly ordered set $X$. An iterative method, based on an auxiliary programmed construction using generalized programmed control measures, is proposed.
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