Proportional navigation and the game of two cars
type: Item
instance of: scholarly article
title: Proportional navigation and the game of two cars
zbMATH Open document ID: 0654.90110
DOI: 10.1007/BF00939811
author: R. de Villiers
author: Y. Yavin
published in: Journal of Optimization Theory and Applications
publication date: 1989-01-01T00:00:00Z
review text: A stochastic version of Isaacs's game of two cars is considered. The motion of the players is confined to the pursuer's effective operation zone \(D_ P\), and the cost function of the game is the probability of the event: \(\{\) Before the evader enters his safe zone, the evader enters the pursuer's killing zone \(K_ P\), at some t, \(0\leq t\leq T\), or the evader stays in the domain \(D_ P-K_ P\), for all \(t\in [0,t_ 0]\), \(t_ 0>T\}\). By numerically solving a nonlinear parabolic boundary-value problem on a generalized torus in \({\mathbb{R}}^ 3\), it is shown that, for a range of values of some parameter, a proportional navigation guidance law is an optimal feedback pursuit strategy.
Mathematics Subject Classification ID: 91A24
Mathematics Subject Classification ID: 91A60
Mathematics Subject Classification ID: 91A99
Mathematics Subject Classification ID: 91A23
Mathematics Subject Classification ID: 91A15
zbMATH DE Number: 4068664
zbMATH Keywords: stochastic differential games
zbMATH Keywords: stochastic version
zbMATH Keywords: Isaacs's game of two cars
zbMATH Keywords: nonlinear parabolic boundary-value problem
zbMATH Keywords: generalized torus
zbMATH Keywords: proportional navigation guidance law
zbMATH Keywords: optimal feedback pursuit strategy
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4068664