In this paper, the game of the optimal approach of two identical inertial pursuers to a noninertial evader is investigated. The duration of the game is fixed. The payoff functional is the distance between the evader and the closest pursuer when the game terminates. The value function is constructed for all possible positions of the game. The regions where the pursuit is one-to-one and the regions where it is essentially collective are described algorithmically. Some analogies between this game and the linear differential game with elliptical vectograms are indicated. It is noted that the focal surface and the dispersal surface are in proximity of one another.
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Communicated by N. V. Banichuk
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Levchenkov, A.Y., Pashkov, A.G. Differential game of optimal approach of two inertial pursuers to a noninertial evader. J Optim Theory Appl 65, 501–518 (1990). https://doi.org/10.1007/BF00939563
- Differential games
- value function
- programmed maximin function
- dispersal surface
- focal surface