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

## Authors

• 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

## Abstract

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 setand the Evader prevents bringing of the state to the terminal set where controlresource of the Pursuer is greater than that of Evader. We obtain a formula for the optimal pursuit timeand construct optimal strategies of the players in explicit form.

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