Archive of Issues
Russia Izhevsk
Section  Mathematics 
Title  To a nonlinear pursuit problem with discrete control 
Author(s)  Shchelchkov K.A.^{a} 
Affiliations  Udmurt State University^{a} 
Abstract  A twoperson differential game is considered. The game is described by the following system of differential equations $\dot x = f(x, u) + g(x, v)$, where $x \in \mathbb R^k$, $u \in U$, $v \in V$. The pursuer's admissible control set is a finite subset of phase space. The evader's admissible control set is a compact subset of phase space. The pursuer's purpose is a translation of phase coordinates to zero. The evader's purpose is to prevent implementation of pursuer's purpose. Sufficient conditions on game parameters for the existence of zero neighborhood from which a capture occurs, that is translation of phase coordinates to zero, have been received. Also, it is proved that a period of time necessary for the pursuer to translate phase coordinates to zero tends to zero with the approaching of the initial position to zero. It happens regardless of the evader's control. 
Keywords  differential game, pursuer, evader, nonlinear system 
UDC  517.977 
MSC  49N70, 49N75 
DOI  10.20537/vm170308 
Received  26 June 2017 
Language  Russian 
Citation  Shchelchkov K.A. To a nonlinear pursuit problem with discrete control, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2017, vol. 27, issue 3, pp. 389395. 
References 

Full text 