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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 Universitya
Abstract In the finite-dimensional 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 piecewise-program strategies, and the pursuers use piecewise-program 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. 54-59.
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