Simple Motion Evasion Differential Game of Many Pursuers and One Evader with Integral Constraints on Control Functions of Players

Ibragimov, Gafurjan; Salleh, Yusra

doi:10.1155/2012/748096

Cited by 18 publications

(11 citation statements)

References 6 publications

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“…The considered in Ibragimov and Yusra(2012) is a special case of the problem considered in this paper. That is, the present work is a generalization in the work Ibragimov and Yusra(2012).…”

Section: Introductionmentioning

confidence: 91%

“…We obtain sufficient conditions for which evasion is possible in the game. The problem considered in Ibragimov and Yusra(2012) is a special case of the problem considered in this paper. That is, the present work is a generalization in the work…”

Section: Statement Of the Problemmentioning

confidence: 99%

“…There are many publications from researches involving this type of differential game problem. Some of these publications include Azamov (1964), Chodun (1987), Ibragimov and Yusra (2012), Hasim(2012), Ibragimov et. al.…”

Section: Introductionmentioning

confidence: 99%

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An evasion differential game problem on the plane

Badakaya¹,

Umar²

2019

Bayero J. Pure App. Sci.

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“…The considered in Ibragimov and Yusra(2012) is a special case of the problem considered in this paper. That is, the present work is a generalization in the work Ibragimov and Yusra(2012).…”

Section: Introductionmentioning

confidence: 91%

Section: Statement Of the Problemmentioning

confidence: 99%

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An evasion differential game problem on the plane

Badakaya¹,

Umar²

2019

Bayero J. Pure App. Sci.

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“…In addition, the strategy (24) ensures z j+1 ( j+1 ) = 0 if adopted by the pursuers on the time interval [ j , j+1 ]. That is, pursuit will be completed at time j+1 and so on.…”

Section: Completion Of Pursuitmentioning

confidence: 99%

A Differential Game Problem of Many Pursuers and One Evader in the Hilbert Space $$\ell_2$$

Rilwan

Ibragimov

Badakaya

et al. 2020

Differ Equ Dyn Syst

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In this paper, we investigate a differential game problem of multiple number of pursuers and a single evader with motions governed by a certain system of first-order differential equations. The problem is formulated in the Hilbert space 2 , with control functions of players subject to integral constraints. Avoidance of contact is guaranteed if the geometric position of the evader and that of any of the pursuers fails to coincide for all time t. On the other hand, pursuit is said to be completed if the geometric position of at least one of the pursuers coincides with that of the evader. We obtain sufficient conditions that guarantees avoidance of contact and construct evader's strategy. Moreover, we prove completion of pursuit subject to some sufficient conditions. Finally, we demonstrate our results with some illustrative examples.

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“…An evasion differential game of many pursuers and one evader with integral constraints in the plane is considered in another paper of Ibragimov et al [6]. The game is described by simple differential equations where each component of the control functions of players is subjected to integral constraint.…”

Section: Introductionmentioning

confidence: 99%

Evasion Differential Game of Two Pursuers and One Evader With Coordinate-Wise Integral Constraints

Karapanan¹,

Ibragimov²,

Alias³

2017

Int. J. of Pure and Appl. Math.

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An evasion differential game of two pursuers and one evader in R 2 is studied. Unlike the traditional integral constraints, in the present work, integral constraints are imposed on each component of control functions of the players. By definition, evasion is said to be possible if the state of a pursuer does not coincide with that of the evader for all t ≥ 0. Sufficient conditions of evasion are obtained and then strategies for the evader are constructed.

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Simple Motion Evasion Differential Game of Many Pursuers and One Evader with Integral Constraints on Control Functions of Players

Cited by 18 publications

References 6 publications

An evasion differential game problem on the plane

An evasion differential game problem on the plane

A Differential Game Problem of Many Pursuers and One Evader in the Hilbert Space $$\ell_2$$

Evasion Differential Game of Two Pursuers and One Evader With Coordinate-Wise Integral Constraints

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