Authors E.Ya. Rubinovich
Month, Year 01, 2018 @en
Index UDC 519.87
Abstract The differential game considered in this paper belongs to the class of differential pursuit-evasion games in which the pursuers are less than the targets. Targets usually form a coalition, so pursuers have to deal with a group target. For the game to make sense, the dynamics of pursuers in such games should allow to realize capture (approaching, etc.) of at least one target. This class is closely adjacent to the games in which, on the contrary, targets are less than pursuers. In such games, as a rule, "clumsy" pursuers catch "brisk" escapers. For a statement to be correct in these games the pursuers, usually, are supplied with "areas of capture", and when being inside them the escapers are considered to be caught. Recently, a special interest is attracted to games with three players of such types as Attacker-Target-Defender or Missile-Target-Defender, respectively, ATD or MTD. In these statements, the attacking player seeks to catch (hit) the fleeing target, while the task of the mobile defender is to catch the attacking player. In this paper, we give a statement and a solution to the problem of another interesting class of differential games, namely a pursuit-evasion games with a false target. Namely, the differential game of one pursuer against a coalition of two coherently dodging targets, one of which is false, is considered on the plane. The probabilities of target classification are given. The targets have simple movements. The pursuer has a restriction on the minimum allowable turning radius. The main criterion is the mathematical expectation of the distance to the true target of the terminal point in time that is not fixed in advance and chosen by the pursuer in the process of a pursuit. The saddle point of the game in program and positional strategies was found. Illustrative examples are given.

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Keywords Game of pursuit-evasion; false targets.
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