The lion and man problem - revisited
type: Item
instance of: scholarly article
title: The lion and man problem - revisited
zbMATH Open document ID: 0569.90108
DOI: 10.1007/BF00941070
author: B. George
published in: Journal of Optimization Theory and Applications
publication date: 1986-01-01T00:00:00Z
review text: A pursuer P, whose speed is bounded by 1, wants to get closer to an evader E, whose speed is bounded by \(\omega >1\). P wants to reduce his distance PE from E below the capture radius \(\rho\). Both players are confined to a circular arena. This problem is equivalent to a problem discussed by \textit{J. Flynn} [SIAM J. Control 12, 581-597 (1974; Zbl 0289.90047)], who characterized and gave numerical bounds to the least upper bound \(d^*\) on the values of PE that E can maintain. He used direct methods and did not use Isaacs' theory. We solve our problem relying on the theory of singular surfaces in differential games. We construct and investigate barriers of the game of kind, and we replace Flynn's bounds on \(d^*\) by analytical (exact) values for various speeds \(\omega\).
Mathematics Subject Classification ID: 91A24
Mathematics Subject Classification ID: 91A23
Mathematics Subject Classification ID: 91A99
zbMATH DE Number: 3910182
zbMATH Keywords: singular surfaces
zbMATH Keywords: barriers of the game of kind
zbMATH Keywords: capture radius
MaRDI profile type: Publication
cites work: Q4088641
cites work: Lion and Man: The Boundary Constraint
cites work: Q4168427
cites work: Q4159206
cites work: Conic surveillance evasion
cites work: Dynamic noncooperative game theory
description: scientific article; zbMATH DE number 3910182