A DIFFERENTIAL GAME OF ALTERNATE PURSUIT WITH CRITERION «A MISS ON THE TRUE TARGET»
Abstract
On the plane the differential game of one pursuer against two consistently evading targets and , one of which is false, is considered. Players have simple movements. The targets form a coalition. The pursuer, having an advantage in speed, does not know which of the targets is false, i.e. both targets are identical for him. The task of the pursuer is to capture the true target or minimize the miss to it in the worst case for the pursuer, when he initially caught a false target. It turns out that in the game there is always the last moment of the decision of the pursuer about the beginning of the alternate pursuit, i.e. the instant from which the order of the alternate pursuit or does not change until the end of the game. The specificity of the statement is that at this instant the pursuer loses sight of the second in order of the pursuit target and if the first target is false (which is determined at the time of the meeting), the only information about the second target, which has a pursuer, are its coordinates at the instant of the beginning of the alternate pursuit. For this reason, the pursuer is forced to move to the point where he saw the second target last time in such a way as to minimize the terminal miss on the second target at this point. Since the choice of the instant of the beginning of the alternate pursuit is carried out by the pursuer, the instant is in fact his control. This instant can be chosen programmatically, i.e. at the beginning of the game (the sequence of meetings is fixed from the very beginning and does not change until the end of the game) or positionally, i.e. during the pursuit, as a function of the current positions of the players. In the considered statement the instant of transition to alternate pursuit is carried out positionally and it is shown that in this case the stage of alternate pursuit is preceded by the stage of joint pursuit of two targets on the interval during which the pursuer holds the targets in the conditions of uncertainty concerning the forthcoming order of pursuer.
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