Evasion from pursuers in the problem of group pursuit with fractional derivatives and phase constraints

In this paper we consider the evasion problem from the group of pursuers in the finite-dimensional Euclidean space. The motion is describe by the linear system of fractional order (
^C
D
₀
^α
₊
z
_i
) =
Az
_i
+
u
_i
-
v
, where
^C
D
₀
^α
+
f
is the Caputo derivative of order α ϵ (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.