Game problem on a convex closed set.

*(English)*Zbl 1138.91349Summary: The movements of Pursuer $P$ and Evader $E$ in ${\mathbb{R}}^{n}$ are described by the equations $P$: $\dot{x}=a\left(t\right)u$ and $E$: $\dot{y}=a\left(t\right)v$, where $u$ and $v$ are control parameters of $P$ and $E$. A closed convex subset $S$ of ${\mathbb{R}}^{n}$ is given. The players $P$ and $E$ must not leave $S$. Integral restrictions are imposed on the controls of the players. For arbitrary initial locations ${x}_{0},{y}_{0}\in S$ of the players, the optimal time of pursuit is found and optimal strategies for the players are constructed.

This is an English translation of the authorâ€™s article [Mat. Tr. 4, No. , 96-112 (2001; Zbl 0998.91006)].