This article is cited in 9 papers

On a pursuit-evasion problem under a linear change of the pursuer resource

B. T. Samatov

Namangam State University, Namangam, Uzbekistan

Abstract: We study a pursuit-evasion problem in the case when an integral constraint is imposed on the pursuer control class which is a generalization of integral as well as geometric constraints and only a geometric constraint is imposed on the evader control class. We prove the theorem of alternative. The optimal pursuit problem is solved by a generalized parallel pursuit strategy, and lower bounds for the distance between the pursuer and the evader are established in the pursuit problem.

Key words: differential game, pursuit problem, evasion problem, $\Pi$-strategy, capture, deviations.

UDC: 518.9

Received: 14.07.2012

 English version: Siberian Advances in Mathematics, 2013, 23:4, 294–302

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