The geometric approach to the construction of the barrier surface in differential games
type: Item
instance of: scholarly article
title: The geometric approach to the construction of the barrier surface in differential games
zbMATH Open document ID: 0632.90102
DOI: 10.1016/0898-1221(87)90093-9
publication date: 1987-01-01T00:00:00Z
review text: The paper deals with qualitative pursuit-evasion differential games. The known Issac's geometric method for the construction of the barrier surface is examined and developed. The authors present a new geometric second-order necessary condition that a valid barrier surface must satisfy. The named geometric approach allows the authors to investigate the parameter dependence in the special cases of the Homicidal Chauffeur differential game and the Game of two cars and in particular, to explain the ``non-classical'' situations in these games. Some other new results concerning the barrier surfaces for the above two games are also presented in the paper.
Mathematics Subject Classification ID: 91A24
Mathematics Subject Classification ID: 91A23
Mathematics Subject Classification ID: 91A99
zbMATH DE Number: 4029315
zbMATH Keywords: qualitative pursuit-evasion differential games
zbMATH Keywords: Issac's geometric method
zbMATH Keywords: barrier surface
zbMATH Keywords: geometric second-order necessary condition
zbMATH Keywords: Homicidal Chauffeur differential game
zbMATH Keywords: Game of two cars
Wikidata QID: Q115362922
author: Meir Pachter
author: Touvia Miloh
reviewed by: O. I. Nikonov
MaRDI profile type: Publication
full work available at URL: 0898-1221(87)90093-9
OpenAlex ID: W2050971977
cites work: Q4140030
cites work: Two-target pursuit-evasion differential games in the plane
cites work: The geometry of the barrier in the ‘game of two cars’
cites work: Dynamic noncooperative game theory
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 4029315