Some problems in the theory of differential pursuit games in systems with distributed parameters

Тухтасинов, М.

doi:10.1016/0021-8928(95)00126-3

Cited by 25 publications

(19 citation statements)

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“…It was studied in [9], [10] for a certain class of games. The proof of our main result uses some ideas of [12].…”

Section: Resultsmentioning

confidence: 99%

“…(2) For game (6), (9) with any ρ > 0 and σ > 0, there exist two infinite sets of initial positions such that, from the points of the first set, pursuit can be completed in finite time, and from the points of the second set, evasion is possible.…”

Section: Resultsmentioning

confidence: 99%

“…(1) (a) Consider game (6), (7) (games (6), (8); (6), (9); and (6), (10) are considered later on). Suppose that σ ≥ ρ, T is any positive number, u 0 ( · ) is any pursuer control with u 0 (t) ≤ ρ, and z 0 = 0 is any initial position.…”

Section: Proofmentioning

confidence: 99%

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Evasion in a certain class of distributed control systems

Satimov

Тухтасинов

2015

Math Notes

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The differential game of evasion in a system described by a control partial differential equation containing the second time derivative and an elliptic operator is considered. The control parameters of the players are additive terms on the right-hand side of the equation. New spaces depending on a nonnegative parameter are introduced by using generalized eigenvalues and generalized eigenfunctions of the given elliptic operator. Games are introduced and studied on the entire scale of these spaces. Sufficient conditions for the possibility of evasion in games obtained under various constraints on the control parameters are given.

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“…It was studied in [9], [10] for a certain class of games. The proof of our main result uses some ideas of [12].…”

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Evasion in a certain class of distributed control systems

Satimov

Тухтасинов

2015

Math Notes

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“…The pursuit problem has been studied earlier in [5,6] and, in particular, when p > ~, the possibility of completing a pursuit in Game 2 from an arbitrary initial position z (~ has been established [5]. Interesting classes of control problems are considered in [3,[7][8][9][10].…”

Section: Definition 2 In Game 3 (Game 4) Completion Of a Pursuit Fromentioning

confidence: 99%

Some game problems in distributed controlled systems

Satimov¹,

Тухтасинов²

2005

Journal of Applied Mathematics and Mechanics

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“…Control and differential game problems for systems described by partial differential equations are also of increasing interest [4][5][6][7][8][9][10] . In Refs.…”

Section: Introductionmentioning

confidence: 99%

Optimal pursuit time for a differential game in the Hilbert space l2

Ibragimov¹

2013

ScienceAsia

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We consider a two-person zero-sum pursuit-evasion differential game in the Hilbert space l2. The control functions of the players are subject to integral constraints. It is assumed that the control resource of the pursuer is greater than that of the evader. The pursuer tries to force the state of the system towards the origin of the space l2, and the evader tries to avoid this. We give a solution to the optimal pursuit problem for the differential game. More precisely, we obtain an equation for the optimal pursuit time and construct optimal strategies for the players in an explicit form. To prove the main result we solve a time-optimal control problem.

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Some problems in the theory of differential pursuit games in systems with distributed parameters

Cited by 25 publications

References 0 publications

Evasion in a certain class of distributed control systems

Evasion in a certain class of distributed control systems

Some game problems in distributed controlled systems

Optimal pursuit time for a differential game in the Hilbert space l2

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