Differential Games for an Infinite 2-Systems of Differential Equations

Muminjon Tukhtasinov, Gafurjan Ibragimov, Sarvinoz Kuchkarova and Risman Mat Hasim
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Muminjon Tukhtasinov: National University of Uzbekistan, University Street, Al-Mazar District, Tashkent 1000174, Uzbekistan
Gafurjan Ibragimov: Department of Mathematics, Faculty of Science, University Putra Malaysia, Serdang 43400, Malaysia
Sarvinoz Kuchkarova: National University of Uzbekistan, University Street, Al-Mazar District, Tashkent 1000174, Uzbekistan
Risman Mat Hasim: Department of Mathematics, Faculty of Science, University Putra Malaysia, Serdang 43400, Malaysia

Mathematics, 2021, vol. 9, issue 13, 1-9

Abstract: A pursuit differential game described by an infinite system of 2-systems is studied in Hilbert space l 2 . Geometric constraints are imposed on control parameters of pursuer and evader. The purpose of pursuer is to bring the state of the system to the origin of the Hilbert space l 2 and the evader tries to prevent this. Differential game is completed if the state of the system reaches the origin of l 2 . The problem is to find a guaranteed pursuit and evasion times. We give an equation for the guaranteed pursuit time and propose an explicit strategy for the pursuer. Additionally, a guaranteed evasion time is found.

Keywords: pursuer; evader; constraints; strategy (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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