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

A. S. Bannikov

Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 27 (2017) no. 3, pp. 309-314

Résumé

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.

Détail

Keywords: differential games, Caputo derivative, escape
Mots-clés : simple matrix.