IJPAM: Volume 70, No. 7 (2011)

DIFFERENTIAL GAMES DESCRIBED BY INFINITE SYSTEM
OF DIFFERENTIAL EQUATIONS OF SECOND ORDER.
THE CASE OF NEGATIVE COEFFICIENTS

Abbas Badakaya Ja'afaru$^1$, Gafurjan I. Ibragimov$^2$
$^{1,2}$Department of Mathematics
Faculty of Science
Institute for Mathematical Research
Universiti Putra
Malaysia, 43400 UPM Serdang, Selangor, MALAYSIA


Abstract. We study pursuit and evasion differential game problems for an infinite system of differential equations of second order. Control functions are subject to integral constraints.The pursuit is completed if $z(\t) = \dot{z}(\t) = 0$ at some $\t > 0,$ where $z(t)$ is the state of the system. The pursuer tries to complete the pursuit and the evader exactly tries to avoid this. A sufficient condition is obtained for completing the pursuit in the differential game when control recourse of the pursuer greater than that of the evader. In the case where the control recourse of the evader not less than that of the pursuer we study an evasion problem.

Received: March 9, 2011

AMS Subject Classification: 49N70, 49N75, 91A23

Key Words and Phrases: pursuit, evasion, strategy, integral constraint

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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: 7