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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2017, Volume 27, Issue 3, Pages 309–314 (Mi vuu590)  

MATHEMATICS

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

A. S. Bannikov

Udmurt State University, ul. Universitetskaya, 1, Izhevsk, 426034, Russia

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
\begin{gather*} ( ^C D^{\alpha}_{0+}z_i)=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.

Keywords: differential games, Caputo derivative, escape, simple matrix.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-000346_а


DOI: https://doi.org/10.20537/vm170302

Full text: PDF file (205 kB)
References: PDF file   HTML file

Document Type: Article
UDC: 517.977.8, 519.837.4
MSC: 49N70, 91A23
Received: 14.08.2017

Citation: A. S. Bannikov, “Evasion from pursuers in a problem of group pursuit with fractional derivatives and phase constraints”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 27:3 (2017), 309–314

Citation in format AMSBIB
\Bibitem{Ban17}
\by A.~S.~Bannikov
\paper Evasion from pursuers in a problem of group pursuit with fractional derivatives and phase constraints
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2017
\vol 27
\issue 3
\pages 309--314
\mathnet{http://mi.mathnet.ru/vuu590}
\crossref{https://doi.org/10.20537/vm170302}
\elib{http://elibrary.ru/item.asp?id=30267242}


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  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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