Solution of a Linear Pursuit-Evasion Differential Game with Closed and Convex Terminal Set

Gafurjan I. Ibragimov (1INSPEM and Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, Serdang, Malaysia)
Marzieh Khakestari (2Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, Malaysia)
Atamurat Sh. Kuchkarov (2Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, Malaysia 3Institute of Mathematics and Information Technology of Academy of Sciences of Uzbekistan, 100125, Durman yuli, 29, Tashkent, Uzbekistan)

Journal of Mathematical and Fundamental Sciences
Vol. 44 No. 1 (2012)

A linear two-person zero-sum pursuit-evasion differential game is considered. Control functions of players are subject to integral constraints. Terminal set is a closed convex subset of  The Pursuer tries to bring the state of the system to the terminal set and the Evader  prevents bringing of the state to the terminal set where control resource of the Pursuer is greater than that of Evader.   We obtain a formula for the optimal pursuit time and construct optimal strategies of the players in explicit form.