Pursuit‐Evasion Differential Game with Many Inertial Players

Ibragimov, Gafurjan; Salimi, Mehdi

doi:10.1155/2009/653723

Cited by 28 publications

(30 citation statements)

References 5 publications

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“…In this case, by Theorem 10, evasion is possible from any initial points. In addition, in the proof of this statement, we have used only inequality (15), and other properties of multivalued mapping −1 :…”

Section: (41)mentioning

confidence: 99%

“…→ R have not been used. Therefore, if ≤ , then evasion is possible in the game of type (11)-(12) from any initial points that satisfy (15).…”

Section: (41)mentioning

confidence: 99%

“…In differential games of many pursuers studied by Ivanov and Ledyaev [12], Ibragimov [13], Ibragimov and Rikhsiev [14], Ibragimov and Salimi [15], and Ibragimov et al [16], optimal strategies of players were constructed.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Simple Motion Pursuit and Evasion Differential Games with Many Pursuers on Manifolds with Euclidean Metric

Kuchkarov

Ibragimov

Феррара

2016

Discrete Dynamics in Nature and Society

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We consider pursuit and evasion differential games of a group of pursuers and one evader on manifolds with Euclidean metric. The motions of all players are simple, and maximal speeds of all players are equal. If the state of a pursuer coincides with that of the evader at some time, we say that pursuit is completed. We establish that each of the differential games (pursuit or evasion) is equivalent to a differential game of groups of countably many pursuers and one group of countably many evaders in Euclidean space. All the players in any of these groups are controlled by one controlled parameter. We find a condition under which pursuit can be completed, and if this condition is not satisfied, then evasion is possible. We construct strategies for the pursuers in pursuit game which ensure completion the game for a finite time and give a formula for this time. In the case of evasion game, we construct a strategy for the evader. Hindawi Publishing Corporation

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Section: (41)mentioning

confidence: 99%

“…→ R have not been used. Therefore, if ≤ , then evasion is possible in the game of type (11)-(12) from any initial points that satisfy (15).…”

Section: (41)mentioning

confidence: 99%

See 1 more Smart Citation

Simple Motion Pursuit and Evasion Differential Games with Many Pursuers on Manifolds with Euclidean Metric

Kuchkarov

Ibragimov

Феррара

2016

Discrete Dynamics in Nature and Society

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“…Multiagent cooperative pursuit is a known multiagent problem [4,5]. Based on identical conditions between pursuers and evaders, the pursuit-evasion problem can be classified into single object pursuit and multiobject pursuit.…”

Section: Introductionmentioning

confidence: 99%

A New Decentralized Approach of Multiagent Cooperative Pursuit Based on the Iterated Elimination of Dominated Strategies Model

Souidi

Piao

2016

Mathematical Problems in Engineering

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Game Theory is a promising approach to acquire coalition formations in multiagent systems. This paper is focused on the importance of the distributed computation and the dynamic formation and reformation of pursuit groups in pursuit-evasion problems. In order to address this task, we propose a decentralized coalition formation algorithm based on the Iterated Elimination of Dominated Strategies (IEDS). This Game Theory process is common to solve problems requiring the withdrawal of dominated strategies iteratively. Furthermore, we have used the Markov Decision Process (MDP) principles to control the motion strategy of the agents in the environment. The simulation results demonstrate the feasibility and the validity of the given approach in comparison with different decentralized methods.

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“…In [2] Ibragimov studies a differential game of optimal approach of countably many pursuers to one evader in a Hilbert space with geometric constraints on the controls of the players. Ibragimov and Salimi [3] study such a differential game for inertial players with integral constraints under the assumption that the control resource of the evader is less than that of each pursuer. Evasion from many pursuers in simple motion differential games with integral constraints was investigated by Ibragimov et al in [4] as well.…”

Section: Introductionmentioning

confidence: 99%

On a Fixed Duration Pursuit Differential Game with Geometric and Integral Constraints

et al. 2015

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In this paper we investigate a differential game in which countably many dynamical objects pursue a single one. All the players perform simple motions. The duration of the game is fixed. The controls of a group of pursuers are subject to geometric constraints and the controls of the other pursuers and the evader are subject to integral constraints. The payoff of the game is the distance between the evader and the closest pursuer when the game is terminated. We construct optimal strategies for players and find the value of the game.2010 Mathematics Subject Classification. 91A23.

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Pursuit‐Evasion Differential Game with Many Inertial Players

Cited by 28 publications

References 5 publications

Simple Motion Pursuit and Evasion Differential Games with Many Pursuers on Manifolds with Euclidean Metric

Simple Motion Pursuit and Evasion Differential Games with Many Pursuers on Manifolds with Euclidean Metric

A New Decentralized Approach of Multiagent Cooperative Pursuit Based on the Iterated Elimination of Dominated Strategies Model

On a Fixed Duration Pursuit Differential Game with Geometric and Integral Constraints

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