IJPAM: Volume 102, No. 4 (2015)
OF MANY PURSUERS AND ONE EVADER
ON CONVEX COMPACT SET


Gafurjan Ibragimov



Faculty of Science
Universiti Putra Malaysia
43400 UPM Serdang, Selangor, MALAYSIA

Universiti Putra Malaysia
43400 UPM Serdang, Selangor, MALAYSIA
Abstract. We study a differential game of many pursuers and single evader in nonempty closed bounded convex subset of . In this game, all players cannot leave the given set. Control parameters of all players are subjected to geometric constraints. Maximum speeds of all players are equal to 1. Pursuit is said to be completed if geometric position of at least one pursuer coincides with that of the evader. Pursuers try to complete the pursuit. Problem is to find estimate for guaranteed pursuit time. To solve the problem, first, we study the same problem in an
-dimensional cube. Then, we reduce the main problem to the game in the cube. To this end, we use method of fictitious pursuers. In this paper, we improve the estimate for guaranteed pursuit time from
to
.
Received: March 29, 2015
AMS Subject Classification: 49N70, 93C95
Key Words and Phrases: differential game, control, strategy, state constraint
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DOI: 10.12732/ijpam.v102i4.11 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 102
Issue: 4
Pages: 733 - 745
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This work is licensed under the Creative Commons Attribution International License (CC BY).