Differential games of survival
type: Item
instance of: scholarly article
title: Differential games of survival
zbMATH Open document ID: 0641.90107
DOI: 10.1016/0022-247X(88)90267-3
author: Leonard David Berkovitz
published in: Journal of Mathematical Analysis and Applications
publication date: 1988-01-01T00:00:00Z
review text: Differential games of survival are studied using the definitions of strategy and payoff introduced recently by the author [SIAM J. Control Optimization 23, 172-196 (1985; Zbl 0572.90108)]. The Isaacs condition is assumed to hold at all points and a capturability condition is assumed to hold at boundary points of the terminal set. The dynamics and the integrand of the payoff are assumed to be Lipschitz continuous in the state, while the terminal payoff function is assumed to be Lipschitz in time and state. Under these hypotheses, the value exists, is continuous on the closure of the set \({\mathcal R}\) of initial positions (t,x) and is Lipschitz continuous on compact subsets of \({\mathcal R}\). The upper and lower directional derivates of the value satisfy a condition which can be viewed as a generalization of the Isaacs equation. These relations imply that the value is a viscosity solution of the Isaacs equation.
Mathematics Subject Classification ID: 91A23
Mathematics Subject Classification ID: 91A24
Mathematics Subject Classification ID: 91A99
zbMATH DE Number: 4045530
zbMATH Keywords: Differential games of survival
zbMATH Keywords: Isaacs condition
zbMATH Keywords: upper and lower directional derivates
zbMATH Keywords: Isaacs equation
zbMATH Keywords: viscosity solution
MaRDI profile type: Publication
cites work: The Existence of Value and Saddle Point in Games of Fixed Duration
cites work: Differential Games of Generalized Pursuit and Evasion
cites work: Characterizations of the values of differential games
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description: scientific article; zbMATH DE number 4045530