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- W2000454767 abstract "SUFFICIENT conditions are obtained for evading any point of space not belonging to a terminal set; the terminal set is convex or has a smooth boundary. Two basic problems are considered in the theory of differential games, according to the player's aims: the problem of making contact, and the problem of evasion. The entire space of initial positions is here divided into two sets, corresponding to the success of the first or second player. In the general statement of a differential game, the problems of contact and of evasion are not distinguished, since one cannot be solved without solving the other. There is a considerable literature on differential games in the general statement, of which [1–4] may be mentioned. In the present paper the problem of evading contact is considered in a narrower formulation: we consider the conditions under which the second player can evade contact from any initial position not belonging to a terminal set, for an infinite time. The problem was considered in this formulation in [5, 6]. For solving the differential game, we shall make use of ε-strategies [3, 7]. Since, when such strategies are used, the evader is discriminated against, i.e., he chooses his own control with a knowledge of no more than the phase coordinates of the object at the current instant, and communicates his control some time in advance to his opponent, it follows that the results obtained below will also hold when other types of strategy are used." @default.
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- W2000454767 date "1974-01-01" @default.
- W2000454767 modified "2023-09-25" @default.
- W2000454767 title "The problem of evading contact in differential games" @default.
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- W2000454767 doi "https://doi.org/10.1016/0041-5553(74)90168-2" @default.
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