On the stability property in positional differential games
type: Item
instance of: scholarly article
title: On the stability property in positional differential games
zbMATH Open document ID: 1261.49010
DOI: 10.1134/S1064562412020329
author: Xianqiang Yang
published in: Doklady Mathematics
publication date: 2012-11-15T00:00:00Z
review text: In the space \(\mathbb R^m\), a pursuit game problem for a conflict control system, the behavior of which is described by the differential equation \[ \dot{x}=f(t,x,u,v),\;t\in [t_0,\vartheta],\;u\in P,\;v\in Q, \] \[ x(t_0)=x_0, \] is considered. Here, \(u\) and \(v\) are the controls of the first and second players, \(P\subset \mathbb R^p\) and \(Q\subset \mathbb R^q\) are compact sets. The goal of the first player is to ensure that the state vector \(x[\vartheta]\) of the system reaches a given compact set \(M\subset \mathbb R^m\). In this paper, some basic constructions and properties are presented concerning the stability. The sets (stable bridges) from which the game can be successfully completed for the first (pursuing) player are distinguished. Moreover, ``it is shown how the stability defect can be used to estimate the neighborhood of the target set that the first player guarantees the conflict control system reaches''.
reviewed by: T. Tadumadze
Mathematics Subject Classification ID: 49N75
Mathematics Subject Classification ID: 91A24
zbMATH DE Number: 6106439
zbMATH Keywords: pursuit differential games
zbMATH Keywords: positional differential games
zbMATH Keywords: stable bridges
MaRDI profile type: Publication
cites work: Q5331036
cites work: On a supplement to the stability property in differential games
full work available at URL: s1064562412020329
OpenAlex ID: W2091782970
description: scientific article; zbMATH DE number 6106439