A linear differential game on a plane with a minimum-type functional
Journal
Journal of Applied Mathematics and Mechanics
Journal Volume
71
Journal Issue
2
Pages
234-246
Date Issued
2007
Author(s)
Melikyan A.A.
Abstract
A differential game on a plane with a functional in the form of the minimum, with respect to time, of a certain prescribed phase vector function (quality function) is considered. It is proved that the game value is constant outside a certain bounded region, consisting of two parts. In the first subregion, the value is equal to the quality function, and in the second it satisfies Bellman's equation. For the constant-value region, where the players' optimum strategies are not unique, single-valued guaranteeing players' strategies are proposed. The results of a numerical investigation of the problem are presented. © 2007 Elsevier Ltd. All rights reserved.
Type
journal article