IJPAM: Volume 102, No. 4 (2015)

SIMPLE MOTION PURSUIT DIFFERENTIAL GAME
OF MANY PURSUERS AND ONE EVADER
ON CONVEX COMPACT SET

Idham Arif Alias$^1$, Raja Noorsuria Raja Ramli$^2$,
Gafurjan Ibragimov$^3$, Anvar Narzullaev$^4$
$^{1,2,3}$Institute for Mathematical Research and Department of Mathematics
Faculty of Science
Universiti Putra Malaysia
43400 UPM Serdang, Selangor, MALAYSIA
$^4$Faculty of Computer Science and Information Technology
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 $\mathbb{R}^n$. 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 $n$-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 $O(n^3)$ to $O(n^2)$.

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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