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Russia Izhevsk
Section  Mathematics 
Title  One problem of group pursuit with fractional derivatives and phase constraints 
Author(s)  Petrov N.N.^{a} 
Affiliations  Udmurt State University^{a} 
Abstract  In the finitedimensional Euclidean space, we consider the problem of persecution of one evader by the group of pursuers, which is described by the system $$D^{(\alpha)}z_i = a z_i + u_i  v,$$ where $D^{(\alpha)}f$ is the Caputo derivative of order $\alpha \in (0, 1)$ of the function $f$. It is further assumed that the evader does not leave the convex polyhedron with nonempty interior. The evader uses piecewiseprogram strategies, and the pursuers use piecewiseprogram counterstrategies. The set of admissible controls is a convex compact, the target sets are the origin of coordinates, and $a$ is a real number. In terms of the initial positions and the parameters of the game, sufficient conditions for the solvability of the pursuit problem are obtained. 
Keywords  differential game, group pursuit, phase restrictions, pursuer, evader 
UDC  517.977 
MSC  49N75, 91A23 
DOI  10.20537/vm170105 
Received  1 February 2017 
Language  Russian 
Citation  Petrov N.N. One problem of group pursuit with fractional derivatives and phase constraints, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2017, vol. 27, issue 1, pp. 5459. 
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