ЗАДАЧА УБЕГАНИЯ ДЛЯ ДИФФЕРЕНЦИАЛЬНЫХ ИГР ПЕРВОГО ПОРЯДКА С ОГРАНИЧЕНИЕМ ГРОНУОЛЛА - БЕЛЛМАНА
Keywords:
дифференциальная игра, скорость, ограничение Гронуолла, Беллмана, преследователь, убегающий, стратегия
Abstract
В этом работе изучается задача убегания для дифференциальных игр первого порядка, когда управления игроков зависимы при ограничениях Гронуолла - Беллмана. Получены новые достаточные условия разрешимости для задачи убегания.
References
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[6] Azamov A.A., Kuchkarov A.Sh., Samatov B.T. The Relation between Problems of Pursuit, Controllability and Stability in the Large in Linear Systems with Different Types of Constraints, J.Appl.Maths and Mechs. - Elsevier. - Netherlands, 2007. - Vol. 71. - N 2. - P. 229-233.
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[15] Ibragimov G.I., Azamov A.A., Khakestari M. Solution of a linear pursuit-evasion game with integral constraints, ANZIAM Journal. Electronic Supplement. - 2010. - Vol.52. - P. E59-E75.
[16] Krasovskii A.N., Choi Y.S. Stochastic Control with the Leaders-Stabilizers. - Ekaterinburg: IMM Ural Branch of RAS, 2001. - 51 p.
[17] Krasovskii A.N., Krasovskii N.N. Control under Lack of Information. - Berlin etc.: Birkhauser, 1995. – 322, p.
[18] Samatov B.T., Axmedov O.U., Doliyev O.B. The strategy of parallel pursuit for differential game of the first order with Gronwall-Bellman constraints. – Namdu Ilmiy axborotnomasi 4-son, 2020 y. 15-20 b.
[2] Azamov A.A. About the quality problem for the games of simple pursuit with the restriction, Serdika. Bulgarian math. spisanie, 12, 1986, - P.38-43.
[3] Azamov A.A., Samatov B.T. П-Strategy. An Elementary introduction to the Theory of Differential Games. - T.: National Univ. of Uzb., 2000. - 32 p.
[4] Azamov A.A., Samatov B.T. The П-Strategy: Analogies and Appli-cations, The Fourth International Conference Game Theory and Management, June 28-30, 2010, St. Petersburg, Russia, Collected papers. - P.33-47.
[5] Azamov A., Kuchkarov A.Sh. Generalized 'Lion Man' Game of R. Rado, Contributions to game theori and management. Second International Conference "Game Theory and Management" - St.Petersburg, Graduate School of Manage-ment SPbU. - St.Petersburg, 2009. - Vol.11. - P. 8-20.
[6] Azamov A.A., Kuchkarov A.Sh., Samatov B.T. The Relation between Problems of Pursuit, Controllability and Stability in the Large in Linear Systems with Different Types of Constraints, J.Appl.Maths and Mechs. - Elsevier. - Netherlands, 2007. - Vol. 71. - N 2. - P. 229-233.
[7] Barton J.C, Elieser C.J. On pursuit curves, J. Austral. Mat. Soc. B. - London, 2000. - Vol. 41.- N 3. - P. 358-371.
[8] Borovko P., Rzymowsk W., Stachura A. Evasion from many pursuers in the simple case, J. Math. Anal. And Appl. - 1988. - Vol.135. - N 1. - P. 75-80.
[9] Chikrii A.A. Conflict-controlled processes, Boston-London-Dordrecht: Kluwer Academ. Publ., 1997, 424 p.
[10] Fleming W. H. The convergence problem for differential games, J. Math. Anal. Appl. - 1961. - N 3. - P. 102-116.
[11] A. Friedman. Differential Games, New York: Wiley, 1971, - 350 p.
[12] Hajek O. Pursuit Games: An Introduction to the Theory and Appli-cations of Differential Games of Pursuit and Evasion. - NY.:Dove. Pub. 2008. - 288 p.
[13] Isaacs R. Differential Games, J. Wiley, New York-London-Sydney, 1965, 384 p.
[14] Ibragimov G.I. Collective pursuit with integral constrains on the controls of players, Siberian Advances in Mathematics, 2004, v.14, No.2, - P.13-26.
[15] Ibragimov G.I., Azamov A.A., Khakestari M. Solution of a linear pursuit-evasion game with integral constraints, ANZIAM Journal. Electronic Supplement. - 2010. - Vol.52. - P. E59-E75.
[16] Krasovskii A.N., Choi Y.S. Stochastic Control with the Leaders-Stabilizers. - Ekaterinburg: IMM Ural Branch of RAS, 2001. - 51 p.
[17] Krasovskii A.N., Krasovskii N.N. Control under Lack of Information. - Berlin etc.: Birkhauser, 1995. – 322, p.
[18] Samatov B.T., Axmedov O.U., Doliyev O.B. The strategy of parallel pursuit for differential game of the first order with Gronwall-Bellman constraints. – Namdu Ilmiy axborotnomasi 4-son, 2020 y. 15-20 b.
Published
2021-06-18
How to Cite
Cаматов Бахром Тажиахматович, Ахмедов Олимхон Улугбек угли, & Абдуманнопов Мухаммадсодик Мухаммадюсуф угли. (2021). ЗАДАЧА УБЕГАНИЯ ДЛЯ ДИФФЕРЕНЦИАЛЬНЫХ ИГР ПЕРВОГО ПОРЯДКА С ОГРАНИЧЕНИЕМ ГРОНУОЛЛА - БЕЛЛМАНА. CENTRAL ASIAN JOURNAL OF MATHEMATICAL THEORY AND COMPUTER SCIENCES, 2(6), 1-5. Retrieved from https://cajmtcs.centralasianstudies.org/index.php/CAJMTCS/article/view/89
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