Game problems on a fixed interval in controlled first-order evolution equations

Satimov, N. Yu.; Тухтасинов, М.

doi:10.1007/s11006-006-0177-5

Cited by 27 publications

(14 citation statements)

References 1 publication

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“…(1) Guaranteed pursuit time T defined by (4) improves that of the work of Satimov, Tukhtasinov [28]. (2) The numbers λ 1 , λ 2 , .…”

Section: Discussionmentioning

confidence: 99%

“…Evasion of evader from many pursuers in simple motion differential games was developed by Ibragimov et al in [13] as well. This class of differential games occurs naturally as a reformulation for solving controlled distributed systems described by a parabolic equation as in [28] (see also [4,10] for more details). In [29] Satimov and Tukhtasinov study pursuit and evasion problems for controlled equations of the parabolic type.…”

Section: Introductionmentioning

confidence: 99%

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Pursuit Game for an Infinite System of First-Order Differential Equations with Negative Coefficients

Ibragimov¹,

Феррара²,

Alias³

et al. 2020

Preprint

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In this paper we study a linear pursuit differential game described by an infinite system of first-order differential equations in Hilbert space. The control functions of players are subject to geometric constraints. The pursuer attempts to bring the system from a given initial state to the origin for a finite time and the evader's purpose is opposite. We obtain a guaranteed pursuit time and construct a strategy for pursuer.

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“…(1) Guaranteed pursuit time T defined by (4) improves that of the work of Satimov, Tukhtasinov [28]. (2) The numbers λ 1 , λ 2 , .…”

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Pursuit Game for an Infinite System of First-Order Differential Equations with Negative Coefficients

Ibragimov¹,

Феррара²,

Alias³

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…The concept has been applied in studying differential game problems for systems described by parabolic equations but reduced to the system (2) in Ibragimov [18,19], Ichikawa [26], Osipov [36], Satimov and Tukhtasinov [45].…”

Section: Generalized Eigenvalues Of the Elliptic Operatormentioning

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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“…In these works, players' equations of motion are given as ordinary or partial differential equations of certain order. The works in [20][21][22][23][24] and some references therein are concerned with game problems involving partial differential equations. In the other hand, problem [1][2][3][4][5][6][7][8] and [10][11][12][13][14][15][16][17][18] involve ordinary differential equations of various orders.…”

Section: Introductionmentioning

confidence: 99%

A differential game of pursuit-evasion with constrained players’ energy

Badakaya

Halliru

Jamilu³

et al. 2022

DAAM

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In the Hilbert space l2, we investigate a pursuit-evasion differential game involving countable number of pursuers and one evader. Players move in agreement with certain nth order ordinary differential equations with control functions of players satisfying integral constraints. The period of the game, which is denoted as θ, is fixed. During the game, pursuers want to minimize the distance to the evader and the evader want to maximize it. The game's payoff is the distance between evader and closest pursuer at time θ. Independent of relationship between energy resources of the players, we provide formula that defines value of the game and constructed players' optimal strategies.

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Game problems on a fixed interval in controlled first-order evolution equations

Cited by 27 publications

References 1 publication

Pursuit Game for an Infinite System of First-Order Differential Equations with Negative Coefficients

Pursuit Game for an Infinite System of First-Order Differential Equations with Negative Coefficients

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

A differential game of pursuit-evasion with constrained players’ energy

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