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Mat. Zametki, 2008, Volume 84, Issue 2, Pages 273–280 (Mi mz5240)  

This article is cited in 6 scientific papers (total in 6 papers)

On Pursuit Problems in Controlled Distributed Systems

M. Tukhtasinov, M. Sh. Mamatov

National University of Uzbekistan named after M. Ulugbek

Abstract: In the present paper, we study the problem of transferring a system from one state into another state in the presence of a player trying to prevent the occurrence of this transfer in the system. The system dynamics is described by partial differential equations whose right-hand sides contain the player controls in additive form. In a similar setting, the problem was solved in several papers, but it has not been considered for the case in which various constraints are imposed on the controls of the players. Here, in contrast to several other papers, we consider games in the entire scale of spaces $H_r$, $r\ge 0$. We propose a new approach for completing the pursuit under various constraints on the player controls.

Keywords: pursuit problem, control, differential game, differential operator, partial differential equation, finite function, self-adjoint operator


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English version:
Mathematical Notes, 2008, 84:2, 256–262

Bibliographic databases:

UDC: 517.977.56
Received: 09.07.2007

Citation: M. Tukhtasinov, M. Sh. Mamatov, “On Pursuit Problems in Controlled Distributed Systems”, Mat. Zametki, 84:2 (2008), 273–280; Math. Notes, 84:2 (2008), 256–262

Citation in format AMSBIB
\by M.~Tukhtasinov, M.~Sh.~Mamatov
\paper On Pursuit Problems in Controlled Distributed Systems
\jour Mat. Zametki
\yr 2008
\vol 84
\issue 2
\pages 273--280
\jour Math. Notes
\yr 2008
\vol 84
\issue 2
\pages 256--262

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    This publication is cited in the following articles:
    1. Badakaya Ja'afaru A. Ibragimov G., “On some pursuit and evasion differential game problems for an infinite number of first-order differential equations”, J. Appl. Math., 2012 (2012), 717124, 13 pp.  crossref  mathscinet  zmath  isi  scopus
    2. M. Sh. Mamatov, Kh. N. Alimov, “Solving a pursuit problem in high-order controlled distributed systems”, Siberian Adv. Math., 24:4 (2014), 229–239  mathnet  crossref  mathscinet
    3. Ibragimov G. Akhmedov A. Izzati P.N. Manaf A.N., “Pursuit Differential Game Described By Infinite First Order 2-Systems of Differential Equations”, Malays. J. Math. Sci., 11:2 (2017), 181–190  mathscinet  isi
    4. Waziri U. Ibragimov G. Alias I.A. Ibrahim Z.B., 3Rd International Conference on Mathematical Sciences and Statistics, Journal of Physics Conference Series, 1132, ed. Chen C. Lee L. Kilicman A. Ismail F. Midi H. Gafurjan I. Husain S. Ibrahim S., IOP Publishing Ltd, 2018  crossref  isi
    5. M. Sh. Mamatov, Kh. Kh. Sobirov, “K teorii differentsialnykh igr presledovaniya po pozitsii”, Materialy nauchnoi konferentsii «Problemy sovremennoi topologii i ee prilozheniya», 11–12 Maya 2017 g., Tashkent, Uzbekistan, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 144, VINITI RAN, M., 2018, 39–46  mathnet  mathscinet
    6. Ibragimov G. Alias I.A. Waziri U. Ja'afaru A.B., “Differential Game of Optimal Pursuit For An Infinite System of Differential Equations”, Bull. Malays. Math. Sci. Soc., 42:1 (2019), 391–403  crossref  mathscinet  zmath  isi  scopus
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