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Game problem on a convex closed set. (English) Zbl 1138.91349
Summary: The movements of Pursuer $P$ and Evader $E$ in $\Bbb R^n$ are described by the equations $P$: $\dot x = a(t) u$ and $E$: $\dot y = a(t) v$, where $u$ and $v$ are control parameters of $P$ and $E$. A closed convex subset $S$ of $\Bbb R^n$ 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 author’s article [Mat. Tr. 4, No. , 96-112 (2001; Zbl 0998.91006)].

91A23Differential games (game theory)
91A24Positional games