A Pursuit–Evasion Differential Game with Slow Pursuers on the Edge Graph of a Simplex. I

Аннотация

We consider a differential game with several pursuing points and one evading point moving along the 1-skeleton (i.e., the edge graph) of an arbitrary simplex in three-dimensional space or a complete fourth-order graph with rectifiable edges with given maximal velocities of points. The exact statement of the problem is given. Using the strategy of parallel pursuit for the slow pursuer and one numerical characteristic of the simplex expressing its proximity to a regular tetrahedron, we give a complete solution of the performance problem for a three-dimensional simplex. The second part will be devoted to higher-dimensional cases.

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DOI

10.1134/s000511792111014x

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