phone +7 (3412) 91 60 92

Archive of Issues

Russia Izhevsk
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.
  1. 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.
  2. Krasovskii N.N., Subbotin A.I. Pozitsionnye differentsial'nye igry (Positional differential games), Moscow: Nauka, 1974, 456 p.
  3. Chikrii A.A. Conflict-controlled processes, Springer Netherlands, 1997, 404 p. DOI: 10.1007/978-94-017-1135-7
  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, pp. 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, 2010, vol. 268, suppl. 1, pp. 54-70. DOI: 10.1134/S0081543810050056
  6. 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).
  7. 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
  8. 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
  9. Kilbas A.A., Srivastava H.M., Trujillo J.J. Theory and applications of fractional differential equations, Amsterdam: Elsevier, 2006, 540 p.
  10. 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
<< Previous article
Next article >>