A stochastic two-target pursuit-evasion differential game with three players moving in a plane
type: Item
instance of: scholarly article
title: A stochastic two-target pursuit-evasion differential game with three players moving in a plane
zbMATH Open document ID: 0626.90109
DOI: 10.1016/0898-1221(87)90099-X
publication date: 1987-01-01T00:00:00Z
review text: The differential game considered in the paper involves three players P, \(Q_ 1\) and \(Q_ 2\), and is based on a noise-corrupted kinematic model. Minimum turning radii of the players are: \(R_ P\), \(R_{Q_ 1}\) and \(R_{Q_ 2}\), respectively. It is assumed, however, that \(R_{Q_ 1}=R_{Q_ 2}=0\). The player P has a weapon system of range \(\rho_ P\) and a half-squint-angle \(\alpha\). The players \(Q_ 1\), \(Q_ 2\) have weapon systems with an all-aspect range \(\rho_ Q\). If the distance between P and \(Q_ i\) is not less than some fixed constant \(R_ 0\) then P and \(Q_ i\) will break off contact. The goal of P is to intercept at least one of \(Q_ 1\) or \(Q_ 2\), or to break off contact with at least one of them before being intercepted by either of them. The goal of \(Q_ 1\) and \(Q_ 2\) is that at least one of them will intercept P before P intercepts or breaks off contact with either of them. A simplified version of this game is considered at the end of the paper. Sufficient conditions on optimal strategies requiring the existence of some smooth solution to a nonlinear partial differential equation on a generalized torus in \({\mathbb{R}}^ 4\) are obtained.
reviewed by: Witold Rzymowski
Mathematics Subject Classification ID: 91A24
Mathematics Subject Classification ID: 91A60
Mathematics Subject Classification ID: 91A99
Mathematics Subject Classification ID: 91A23
zbMATH DE Number: 4018821
zbMATH Keywords: planar game
zbMATH Keywords: two-targed stochastic differential pursuit-evasion games
zbMATH Keywords: three players
zbMATH Keywords: noise-corrupted kinematic model
zbMATH Keywords: optimal strategies
author: Y. Yavin
MaRDI profile type: Publication
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full work available at URL: 0898-1221(87)90099-x
OpenAlex ID: W2019314123
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 4018821