One problem of group pursuit with fractional derivatives and phase constraints
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 27 (2017) no. 1, pp. 54-59
Voir la notice de l'article provenant de la source Math-Net.Ru
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.
@article{VUU_2017_27_1_a4,
author = {N. N. Petrov},
title = {One problem of group pursuit with fractional derivatives and phase constraints},
journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
pages = {54--59},
publisher = {mathdoc},
volume = {27},
number = {1},
year = {2017},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VUU_2017_27_1_a4/}
}
TY - JOUR AU - N. N. Petrov TI - One problem of group pursuit with fractional derivatives and phase constraints JO - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki PY - 2017 SP - 54 EP - 59 VL - 27 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VUU_2017_27_1_a4/ LA - ru ID - VUU_2017_27_1_a4 ER -
%0 Journal Article %A N. N. Petrov %T One problem of group pursuit with fractional derivatives and phase constraints %J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki %D 2017 %P 54-59 %V 27 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/VUU_2017_27_1_a4/ %G ru %F VUU_2017_27_1_a4
N. N. Petrov. One problem of group pursuit with fractional derivatives and phase constraints. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 27 (2017) no. 1, pp. 54-59. http://geodesic.mathdoc.fr/item/VUU_2017_27_1_a4/