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Section
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Mathematics
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Title
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One problem of group pursuit with fractional derivatives and phase constraints
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Author(-s)
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Petrov N.N.a
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Affiliations
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Udmurt State Universitya
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Abstract
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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.
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Keywords
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differential game, group pursuit, phase restrictions, pursuer, evader
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UDC
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517.977
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MSC
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49N75, 91A23
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DOI
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10.20537/vm170105
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Received
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1 February 2017
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Language
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Russian
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Citation
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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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References
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