Geodesic
Evasion from pursuers in a problem of group pursuit with fractional derivatives and phase constraints
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 27 (2017) no. 3, pp. 309-314 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper deals with the problem of avoiding a group of pursuers in the finite-dimensional Euclidean space. The motion is described by the linear system of fractional order \begin{gather*} \left({}^C D^{\alpha}_{0+}z_i\right)=A z_i+u_i-v, \end{gather*} where ${}^C D^{\alpha}_{0+}f$ is the Caputo derivative of order $\alpha\in(0,1)$ of the function $f$ and $A$ is a simple matrix. The initial positions are given at the initial time. The set of admissible controls of all players is a convex compact. It is further assumed that the evader does not leave the convex polyhedron with nonempty interior. In terms of the initial positions and the parameters of the game, sufficient conditions for the solvability of the evasion problem are obtained.
Keywords: differential games, Caputo derivative, escape
Mots-clés : simple matrix. 
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     title = {Evasion from pursuers in a problem of group pursuit with fractional derivatives and phase constraints},
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A. S. Bannikov. Evasion from pursuers in a problem of group pursuit with fractional derivatives and phase constraints. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 27 (2017) no. 3, pp. 309-314. http://geodesic.mathdoc.fr/item/VUU_2017_27_3_a1/

[1] Blagodatskikh A. I., Petrov N. N., Conflict interaction of groups of controlled objects, Udmurt State University, Izhevsk, 2009, 266 pp.

[2] Krasovskii N. N., Subbotin A. I., Positional differential games, Nauka, M., 1974, 456 pp.

[3] Chikrii A. A., Conflict-controlled processes, Springer Netherlands, 1997, 404 pp. | DOI | MR

[4] Mamatov M. Sh., “The pursuit problem described by differential equations of fractional order”, Aktual'nye problemy gumanitarnykh i estestvennykh nauk, 2016, no. 4-1, 28–32 (in Russian)

[5] Chikrii A. A., Matichin I. I., “Game problems for fractional-order linear systems”, Proceedings of the Steklov Institute of Mathematics, 268, suppl. 1 (2010), 54–70 | DOI | MR | Zbl

[6] Chikrii A. A., Matichin I. I., “On linear conflict-controlled processes with fractional derivatives”, Tr. Inst. Mat. Mekh. Ural. Otd. Ross. Akad. Nauk, 17, no. 2 (2011), 256–270 (in Russian)

[7] Éidel'man S. D., Chikrii A. A., “Dynamic game problems of approach for fractional-order equations”, Ukrainian Mathematical Journal, 52:11 (2000), 1787–1806 | DOI | MR | Zbl

[8] Petrov N. N., “One problem of group pursuit with fractional derivatives and phase constraints”, Vestn. Udmurt. Univ. Mat. Mekh. Komp'yut. Nauki, 27:1 (2017), 54–59 (in Russian) | DOI | Zbl

[9] Kilbas A. A., Srivastava H. M., Trujillo J. J., Theory and applications of fractional differential equations, Elsevier, Amsterdam, 2006, 540 pp. | MR | Zbl

[10] Popov A. Yu., Sedletskii A. M., “Distribution of roots of Mittag–Leffler functions”, Journal of Mathematical Sciences, 190:2 (2013), 209–409 | DOI | MR