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

Kumkov, Sergey S.; Ménec, Stéphane Le; Patsko, V.S.

doi:10.1007/s13235-016-0209-z

Cited by 56 publications

(15 citation statements)

References 48 publications

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“…Moreover, "nontargeted" evaders are always able to escape. We refer to Kumkov et al (2017) for a survey of results on differential games of many players with geometric constraints. In the case of integral constraints, simple motion evasion games of many players were solved in Alias et al (2016), Ibragimov et al (2012) and Ibragimov et al (2018).…”

Section: Introductionmentioning

confidence: 99%

Linear evasion differential game of one evader and several pursuers with integral constraints

et al. 2021

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An evasion differential game of one evader and many pursuers is studied. The dynamics of state variables $$x_1,\ldots , x_m$$ x 1 , … , x m are described by linear differential equations. The control functions of players are subjected to integral constraints. If $$x_i(t) \ne 0$$ x i ( t ) ≠ 0 for all $$i \in \{1,\ldots ,m\}$$ i ∈ { 1 , … , m } and $$t \ge 0$$ t ≥ 0 , then we say that evasion is possible. It is assumed that the total energy of pursuers doesn’t exceed the energy of evader. We construct an evasion strategy and prove that for any positive integer m evasion is possible.

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Section: Introductionmentioning

confidence: 99%

Linear evasion differential game of one evader and several pursuers with integral constraints

et al. 2021

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“…Moreover one can approximate the solution of smooth Hamilton-Jacobi equations by parabolic equations or by the solution of the system of ordinary differential equations (Krasovskii and Kotelnikova (2010), Averboukh (2016)). This make it possible to use for the Hamiltonian -Jacobi equation with the discontinuous Hamiltonian the numerical methods developed in following works: Subbotin (1993), Kumkov et al (2017), Falcone and Ferretti (1994), Quincampoix et al (1999). We show the convergence to zero in space L 1 the Hausdorff distance between graphs of M -solution and continuous minimax/viscosity solutions.…”

Section: Introductionmentioning

confidence: 99%

Approximation of a Multivalued Solution of the Hamilton–Jacobi Equation

Kolpakova

2020

Math Notes

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The paper deals with the Cauchy problem for Hamilton-Jacobi equation with discontinuous w.r.t. state variable Hamiltonian. In this case we use the notion of M-solution proposed by Subbotin. We consider the sequence of auxiliary Cauchy problems for Hamilton-Jacobi equations with Lipschitz continuous w.r.t. phase variable Hamiltonians. We show that the sequence of distances between of graphs of solutions for auxiliary Cauchy problems and graph of M-solution tends to zero in metrics L 1 .

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“…Following [1], many researchers took an interest in multiplayer PE games, motivated by applications such as collision avoidance [2], cooperative surveillance [3], and defense and security systems [4][5][6]. An extensive amount of literature is now available, and a recent survey on zero-sum PE games with multiple agents is available in [7].…”

Section: Introductionmentioning

confidence: 99%

Optimal Evading Strategies for Two-Pursuer/One-Evader Problems

Makkapati

Sun

Tsiotras

2018

Journal of Guidance, Control, and Dynamics

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Pursuit-evasion problems involving two pursuers and one evader are presented and analyzed. Two distinct scenarios differing in the type of information that the pursuers have about the evader's strategy are analyzed. The first scenario involves pursuers that have access to the evader's position and velocity at each instant of time, and consequently they follow a constant-bearing strategy. In the second scenario, it is assumed that the pursuers have only information about the evader's instantaneous position, and they follow a pure-pursuit strategy. In both these scenarios, the evader has information about the pursuers' location at every instant of time, and in addition, it also knows their pursuit strategy. The evading strategies maximizing capture time in both scenarios are studied under an optimal control framework. The two scenarios are further analyzed assuming that there is only one active pursuer. Such a case arises when the two pursuers follow a relay pursuit strategy.

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

Cited by 56 publications

References 48 publications

Linear evasion differential game of one evader and several pursuers with integral constraints

Linear evasion differential game of one evader and several pursuers with integral constraints

Approximation of a Multivalued Solution of the Hamilton–Jacobi Equation

Optimal Evading Strategies for Two-Pursuer/One-Evader Problems

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