Differential-difference games of pursuit

Liubarshchuk Ievgen

Liubarshchuk Ievgen ¹

¹ Department of Aplied Mathematics and Information Technologies, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, 58000, Ukraine

Keywords: differential-difference games of pursuit

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Abstract

We consider the pursuit problem for 2-person conflict-controlled process with single pursuer and single evader. The problem is given by a system of differential-difference equations with time lag. The players pursuing their own goals and choose controls in the form of certain functions. The goal of the pursuer is to catch the evader in the shortest possible time. The goal of the evader is to avoid the meeting of the players’ trajectories on a whole semiinfinite interval of time or if it is impossible to postpone maximally the moment of meeting. For such a conflict-controlled process we present conditions on its parameters and initial state, which are sufficient for the trajectories of the players to meet no later than a certain moment of time for any counteractions of the evader. Results obtained by the Method of Resolving Functions for such conflict-controlled process we also compare to Pontryagin’s First Direct Method.

References

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ACS Style: Liubarshchuk, I. Differential-difference games of pursuit. Bukovinian Mathematical Journal. 2016, 2
AMA Style: Liubarshchuk I. Differential-difference games of pursuit. Bukovinian Mathematical Journal. 2016; 2(2-3).
Chicago/Turabian Style: Ievgen Liubarshchuk. 2016. "Differential-difference games of pursuit". Bukovinian Mathematical Journal. 2 no. 2-3.

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