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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 University^{a} 
Abstract  The paper deals with the problem of avoiding a group of pursuers in the finitedimensional Euclidean space. The motion is described by the linear system of fractional order $$\left({}^C D^{\alpha}_{0+}z_i\right)=A z_i+u_iv,$$ 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. 309314. 
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