IJPAM: Volume 70, No. 4 (2011)

AN EVASION DIFFERENTIAL GAME DESCRIBED BY
AN INFINITE SYSTEM OF 2-SYSTEMS OF SECOND ORDER

Fateh Allahabi$^1$, G.I. Ibragimov$^2$
$^1$Department of Mathematics
Faculty of Science
University Putra Malaysia
43400, Serdang, Selangor, MALAYSIA
$^2$Institute for Mathematical Research
and Department of Mathematics
University Putra Malaysia


Abstract. We study a differential game of many pursuers described by infinite systems of second order ordinary differential equations. Controls of players are subjected to geometric constraints. Differential game is considered in Hilbert spaces. We say that evasion is possible if $\vert\vert z_i(t)\vert\vert _{r+1} + \vert\vert\dot z_i(t)\vert\vert _r \neq 0$ for all $i=1,...,m,$ and $t > 0;$ $m$ is the number of pursuers. We proved one theorem on evasion. Moreover, we constructed explicitly a control of the evader.

Received: February 2, 2011

AMS Subject Classification: 49N70, 49N75, 49N90

Key Words and Phrases: differential game, pursuer, evader, control, evasion

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 70
Issue: 4