This article is cited in 5 papers

Persecution of rigidly coordinated evaders in a linear problem with fractional derivatives and a simple matrix

A. I. Machtakova

Udmurt State University, ul. Universitetskaya, 1, Izhevsk, 426034, Russia

Abstract: In the finite-dimensional Euclidean space, the problem of pursuit of a group of evaders by a group of pursuers is considered, which is described by a system of the form
$$D^{(\alpha)} z_{ij} = a z_{ij} + u_i - v,$$
where $D^{(\alpha)} f$ is the Caputo derivative of the order $\alpha \in (0,1)$ of the function $f$. It is assumed that all evaders use the same control. The goal of the pursuers is to catch at least one of the evaders. The evaders use piecewise-program strategies, and the pursuers use piecewise-program counterstrategies. Every pursuer catches not more than one evader. The set of admissible controls is a ball of unit radius with the center at the origin, the target sets are the origin. In terms of initial positions and game parameters, a sufficient conditions for the capture are obtained.

Keywords: differential game, group persecution, pursuer, evader, fractional derivatives.

UDC: 517.977

MSC: 91A23, 49N70

Received: 15.08.2019

DOI: 10.20537/2226-3594-2019-54-04

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