Evasion in a linear differential game with many pursuers
Gafurjan IbragimovV.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, 100174, Tashkent, UzbekistanT.G. TursunalievV.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, 100174, Tashkent, UzbekistanShravan LuckrazSchool of Economics and CeDEx China, University of Nottingham Ningbo, China
ABI
Abstract
We study a differential game of one evader and $ n $ pursuers on $ R^d $, where the control sets are given by the unit ball for the pursuers and the ball of radius $ \sigma $, where $ \sigma>1 $, for the evader. Evasion is said to be possible if the state of the evader doesn't coincide with that of any pursuer for all $ t $. We propose a new evasion strategy which guarantees evasion from any initial positions of the players. We use the strategy to show that the number of approach times is bounded above by $ n(n+1)/2 $.
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