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- W2007392375 abstract "Abstract A differential game of approach of one evader with n dynamic pursuers is investigated. All the players have simple motions. The velocities of the players and the time of the game are limited. The case of a game with both similar arbitrary pursuers and pursuers of different types whose velocities exceed that of the evader are considered. The payoff is taken to be the distance between the evader and the closest pursuer at the instant when the game terminates. The formalization used is the same as that employed in [1, 2]. The method used in [3, 4]of solving problems of the approach of two pursuers with a single evader in a plane is extended to the solution of the problem of the approach of n pursuers with a single evader in space R n . The value function of the game is constructed not only in a regular region [5], but also in a separate singular manifold. A programmed maximin function is introduced, the space of the initial positions is decomposed into regions, and the u -stability of the function over the whole of the space is proved. An example of a game of pursuit of “three after one” in a three-dimensional Euclidean space is given, and the optimal trajectories and the level surfaces of the value of the game are constructed." @default.
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- W2007392375 date "1993-01-01" @default.
- W2007392375 modified "2023-09-25" @default.
- W2007392375 title "Construction of the value function in a game of approach with several pursuers" @default.
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- W2007392375 doi "https://doi.org/10.1016/0021-8928(93)90098-7" @default.
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