Abstract
AbstractA differential game of evasion with many participants (a game of kind in the terminology of Isaacs1) is considered. One controlled object (the evader) seeks to avoid contact with each of several pursuers. The motion of the evader is subject to a phase constraint. An efficient method (up to the explicit formulae) of constructing the evader's strategy is proposed. This strategy ensures evasion on the infinite time interval and the fulfilment of the phase constraint. The evader's control corresponding to this strategy is always a piecewise‐programme function of time, and the number of programme pieces is finite (there is an upper estimate for this number). There is a lower estimate for the minimal distance between the evader and the pursuers.
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