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 Mat. Zametki, 2015, Volume 97, Issue 5, Pages 749–760 (Mi mz8822)

Evasion in a Certain Class of Distributed Control Systems

N. Yu. Satimov, M. Tukhtasinov

National University of Uzbekistan named after M. Ulugbek

Abstract: 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.

Keywords: evasion problem, distributed control system, distributed differential game, evasion differential game, pursuit differential game.

DOI: https://doi.org/10.4213/mzm8822

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English version:
Mathematical Notes, 2015, 97:5, 764–773

Bibliographic databases:

Document Type: Article
Revised: 25.03.2012

Citation: N. Yu. Satimov, M. Tukhtasinov, “Evasion in a Certain Class of Distributed Control Systems”, Mat. Zametki, 97:5 (2015), 749–760; Math. Notes, 97:5 (2015), 764–773

Citation in format AMSBIB
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