Affiliation:
1. Udmurt State University
Abstract
In a finite-dimensional Euclidean space $\mathbb R^k$, we consider a linear problem of pursuit of one evader by a group of pursuers, which is described on the given time scale $\mathbb{T}$ by equations of the form
\begin{gather*}
z_i^{\Delta} = a z_i + u_i - v,
\end{gather*}
where $z_i^{\Delta}$ is the $\Delta$-derivative of the functions $z_i$ on the time scale $\mathbb{T}$, $a$ is an arbitrary number not equal to zero. The set of admissible controls for each participant is a unit ball centered at the origin, the terminal sets are given convex compact sets in $\mathbb R^k$. The pursuers act according to the counter-strategies based on the information about the initial positions and the evader control history. In terms of initial positions and game parameters, a sufficient capture condition has been obtained. For the case of setting the time scale in the form $\mathbb T = \{ \tau k \mid k \in \mathbb Z,\ \tau \in \mathbb R,\ \tau >0\}$ sufficient pursuit and evasion problems solvability conditions have been found. In the study, in both cases, the resolving function method is used as basic one.
Subject
Fluid Flow and Transfer Processes,General Mathematics,General Computer Science
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献