Optimal Number of Pursuers in Differential Games on the 1-Skeleton of an Orthoplex
Абдулла АзамовGafurjan IbragimovDepartment of Mathematics, Institute for Mathematical Research, Universiti Putra Malaysia, Serdang 43400, Selangor, MalaysiaTolanbay IbaydullaevDepartment of Mathematics, Andijan State University, Andijan 170100, UzbekistanIdham Arif AliasDepartment of Mathematics, Institute for Mathematical Research, Universiti Putra Malaysia, Serdang 43400, Selangor, Malaysia
ABI
Аннотация
We study a differential game of many pursuers and one evader. All the players move only along the one-skeleton graph of an orthoplex of dimension d+1. It is assumed that the maximal speeds of the pursuers are less than the speed of the evader. By definition, the pursuit is completed if the position of a pursuer coincides with the position of the evader. Evasion is said to be possible in the game if the movements of players are started from some initial positions and the position of the evader never coincides with the position of any pursuer. We found the optimal number of pursuers in the game. The symmetry of the orthoplex plays an important role in the construction of the players’ strategies.
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