+7 (3412) 91 60 92

## Archive of Issues

Russia Izhevsk
Year
2017
Volume
27
Issue
3
Pages
309-314
 Section Mathematics Title Evasion from pursuers in a problem of group pursuit with fractional derivatives and phase constraints Author(-s) Bannikov A.S.a Affiliations Udmurt State Universitya Abstract 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 $$\left({}^C D^{\alpha}_{0+}z_i\right)=A z_i+u_i-v,$$ 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, simple matrix UDC 517.977.8, 519.837.4 MSC 49N70, 91A23 DOI 10.20537/vm170302 Received 14 August 2017 Language Russian Citation Bannikov A.S. Evasion from pursuers in a problem of group pursuit with fractional derivatives and phase constraints, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2017, vol. 27, issue 3, pp. 309-314. References Blagodatskikh A.I., Petrov N.N. Konfliktnoe vzaimodeistvie grupp upravlyaemykh ob''ektov (Conflict interaction of groups of controlled objects), Izhevsk: Udmurt State University, 2009, 266 p. Krasovskii N.N., Subbotin A.I. Pozitsionnye differentsial'nye igry (Positional differential games), Moscow: Nauka, 1974, 456 p. Chikrii A.A. Conflict-controlled processes, Springer Netherlands, 1997, 404 p. DOI: 10.1007/978-94-017-1135-7 Mamatov M.Sh. The pursuit problem described by differential equations of fractional order, Aktual'nye problemy gumanitarnykh i estestvennykh nauk, 2016, no. 4-1, pp. 28-32 (in Russian). Chikrii A.A., Matichin I.I. Game problems for fractional-order linear systems, Proceedings of the Steklov Institute of Mathematics, 2010, vol. 268, suppl. 1, pp. 54-70. DOI: 10.1134/S0081543810050056 Chikrii A.A., Matichin I.I. On linear conflict-controlled processes with fractional derivatives, Tr. Inst. Mat. Mekh. Ural. Otd. Ross. Akad. Nauk, 2011, vol. 17, no. 2, pp. 256-270 (in Russian). Eidel'man S.D., Chikrii A.A. Dynamic game problems of approach for fractional-order equations, Ukrainian Mathematical Journal, 2000, vol. 52, issue 11, pp. 1787-1806. DOI: 10.1023/A:1010439422856 Petrov N.N. One problem of group pursuit with fractional derivatives and phase constraints, Vestn. Udmurt. Univ. Mat. Mekh. Komp'yut. Nauki, 2017, vol. 27, issue 1, pp. 54-59 (in Russian). DOI: 10.20537/vm170105 Kilbas A.A., Srivastava H.M., Trujillo J.J. Theory and applications of fractional differential equations, Amsterdam: Elsevier, 2006, 540 p. Popov A.Yu., Sedletskii A.M. Distribution of roots of Mittag-Leffler functions, Journal of Mathematical Sciences, 2013, vol. 190, issue 2, pp. 209-409. DOI: 10.1007/s10958-013-1255-3 Full text