Differential game of optimal approach of two inertial pursuers to a noninertial evader

Levchenkov, Anatoly; Paahkov, A. G.

doi:10.1007/bf00939563

Cited by 51 publications

(17 citation statements)

References 7 publications

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“…It is shown there that the value function is the program maximin function where the maximum is taken over open-loop controls of the evader and the minimum is taken over open-loop controls of the pursuers. In work [35], two inertial objects chase an inertialless one in the plane. The payoff at some fixed termination instant is the distance between the evader and closest pursuer.…”

Section: Other Pursuit Problems With Many Objectsmentioning

confidence: 99%

Zero-Sum Pursuit-Evasion Differential Games with Many Objects: Survey of Publications

2016

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If a pursuit game with many persons can be formalized in the framework of zerosum differential games, then general methods can be applied to solve it. But difficulties arise connected with very high dimension of the phase vector when there are too many objects. Just due to this problem, special formulations and methods have been elaborated for conflict interaction of groups of objects. This paper is a survey of publications and results on group pursuit games.

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Section: Other Pursuit Problems With Many Objectsmentioning

confidence: 99%

Zero-Sum Pursuit-Evasion Differential Games with Many Objects: Survey of Publications

2016

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“…In the past, differential game theory has been used as a framework to analyze problems in multi-player pursuit-evasion games. Solutions for particular multi-player games were presented by Pashkov and Terekhov (1987), Levchenkov and Pashkov (1990), Hagedorn and Breakwell (1976), Breakwell and Hagedorn (1979) and Shankaran et al (2008). More general treatments of multi-player differential games were presented by Vaisbord and Zhukovskiy (1988), and Zhukovskiy and Salukvadze (1994), and Stipanović et al (2004Stipanović et al ( , 2009).…”

Section: Introductionmentioning

confidence: 97%

Spatial approaches to broadband jamming in heterogeneous mobile networks: a game-theoretic approach

Bhattacharya

Başar

2011

Auton Robot

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In this paper, we address the problem of a mobile intruder jamming the communication network in a vehicular formation. In order to understand the spatial aspect of the jamming problem, we consider a jamming model that takes into account the relative distance of the jammer from the vehicles. We formulate the problem as a zero-sum pursuitevasion game between a jammer and a team of players with players possessing heterogeneous dynamics. We use Isaacs' approach to arrive at the equations governing the optimal strategies of the team of players. Finally, we obtain the optimal trajectories in the neighborhood of termination by numerically simulating the strategies for some variants of the problem.

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“…Analytic solutions using differential games exist for some particular problems with small numbers of pursuers [9], [10], but more general solutions are limited by the curse of dimensionality. Some approaches simplify † These authors contributed equally to this work.…”

Section: Introductionmentioning

confidence: 99%

Guaranteed decentralized pursuit-evasion in the plane with multiple pursuers

Huang

Zhang

Ding

et al. 2011

IEEE Conference on Decision and Control and European Control Conference

133

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Pursuit-evasion games are an important problem in robotics and control, but games with many players are difficult to analyze and solve. This paper studies a game of multiple pursuers cooperating to capture a single evader in a bounded, convex, polytope in the plane. We present a decentralized control scheme based on the Voronoi partion of the game domain, where the pursuers jointly minimize the area of the evader's Voronoi cell. We prove that capturing the evader is guaranteed under this scheme regardless of the evader's actions, and show simulation results demonstrating the pursuit strategy.

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Differential game of optimal approach of two inertial pursuers to a noninertial evader

Cited by 51 publications

References 7 publications

Zero-Sum Pursuit-Evasion Differential Games with Many Objects: Survey of Publications

Zero-Sum Pursuit-Evasion Differential Games with Many Objects: Survey of Publications

Spatial approaches to broadband jamming in heterogeneous mobile networks: a game-theoretic approach

Guaranteed decentralized pursuit-evasion in the plane with multiple pursuers

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