Multicriterion differential games with applications to combat problems
type: Item
instance of: scholarly article
title: Multicriterion differential games with applications to combat problems
zbMATH Open document ID: 0698.90105
DOI: 10.1016/0898-1221(89)90129-6
author: N. E. Zubov
publication date: 1989-01-01T00:00:00Z
review text: The dynamics of the considered two-person zero-sum differential game is described by the equation \(\dot x=f(x,u,v,t)\), \(u\in U\), \(v\in V\); the components of the vector criterion are of Bolza type. Two types of strategies are dealt with: open-loop programs and feedback strategies. Various solution concepts using Pareto optimality and an equilibrium property are considered. The determination of these solutions is discussed. Bicriterion games, and in particular, two-target or combat games, are investigated in detail. Reviewer's remark. The authors impose no restrictions on the function f and the function-strategies u(t,x) and v(t,x) so that it is not quite clear in what way a trajectory generated by a pair of strategies (and hence a value of vector criterion) is determined.
Mathematics Subject Classification ID: 91A23
Mathematics Subject Classification ID: 91A24
Mathematics Subject Classification ID: 91A12
Mathematics Subject Classification ID: 91A05
zbMATH DE Number: 4145705
zbMATH Keywords: multicriterion differential game
zbMATH Keywords: two-target game
zbMATH Keywords: two-person zero-sum differential game
zbMATH Keywords: open-loop programs
zbMATH Keywords: feedback strategies
zbMATH Keywords: Pareto optimality
zbMATH Keywords: equilibrium property
zbMATH Keywords: combat games
MaRDI profile type: Publication
full work available at URL: 0898-1221(89)90129-6
OpenAlex ID: W1971049047
cites work: An analog of the minimax theorem for vector payoffs
cites work: Some minimax theorems in vector-valued functions
cites work: Technical note: Games with vector payoffs
cites work: Solution concepts in two-person multicriteria games
cites work: Optimal control of systems with multiple criteria when disturbances are present
cites work: Q4140033
cites work: Qualitative differential games with two targets
cites work: Combat games
cites work: Analysis of a combat problem: the turret game
cites work: Q5532185
cites work: Formulation and analysis of combat problems as zero-sum bicriterion differential games
cites work: Reprisal Strategies in Pursuit Games
cites work: Pursuit-evasion in medium-range air-combat scenarios
cites work: Vector-valued optimization problems in control theory. Transl. from the Russian by John L. Casti
cites work: A two-target game analysis in line-of-sight coordinates
published in: Computers & Mathematics with Applications
Recommended article: Multicriterion differential games
Recommended article: Q4731034
Recommended article: On one feature of multicriteria differential games
Recommended article: Q4897268
Recommended article: Approximations and well-posedness in multicriteria games
Recommended article: Equilibria in Dynamic Multicriteria Games
Recommended article: Multitime hybrid differential games with multiple integral functional
Recommended article: Decomposition of differential games with multiple targets
Recommended article: Q3476642
description: scientific article; zbMATH DE number 4145705