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In this article is considered the problem of R. Isaac’s "Life-line", when liner constraint is imposed on the pursuer control class which is a generalization of integral as well as geometric constraints and only a geometric constraint is imposed on the evader control class and here it is studied for win of the pursuer

  • Ссылка в интернете
  • DOI
  • Дата создание в систему UzSCI24-11-2022
  • Количество прочтений155
  • Дата публикации12-11-2020
  • Язык статьиIngliz
  • Страницы22-27
English

In this article is considered the problem of R. Isaac’s "Life-line", when liner constraint is imposed on the pursuer control class which is a generalization of integral as well as geometric constraints and only a geometric constraint is imposed on the evader control class and here it is studied for win of the pursuer

Ўзбек

Ushbu maqolada R.Ayzeksning «Qutulish chizig’i o’yini» masalasi, quvlovchining boshqaruvi chiziqli chegaralanishga, ya’ni integral va geometrik chegaralanishlarning umumlashgan holida, qochuvchinig boshqaruvi esa faqat geometrik chegaralanishga ega holda masala ko’riladi va bunda o’yin quvlovchining foydasiga hal bo’lish holi uchun o’rganilgan

Русский

В этой статье рассматривается задаша Р. Айзекса игра с «линией жизни», когда на класс управлений преследователя налагается линейное огранишение, которое является обобщением как интегральных, так и геометришеских огранишений; а на класс управлений убегающего - только геометришеское и здесь изушена слушай выигрыша преследователя.

№ Имя автора Должность Наименование организации
1 Samatov B.T. DSc of physics-mathematics, professor Namangan state university
2 Xorilov .A. Basic doctoral student Namangan state university
3 Sobitov R.A. teacher at the chair of Mathematics Namangan state university
№ Название ссылки
1 Azamov A.(1986) On the quality problem for simple pursuit games with constraint. Serdica Bulgariacaemath. Publ.Sofia: 12(1): 38–43
2 Azamov A.A., Samatov B.T.(2010) The -Strategy: Analogies and Applications. The Fourth International Conference Game Theory and Management, St.Petersburg: 33–47.
3 Berkovitz L.D. (1967) A Survey of Differential Games, Mathematical Theory of Control. New York, Academic Press 373–385
4 Blagodatskikh A.I., Petrov N.N. (2009). Conflict interaction of groups of controlled objects. Izhevsk: Udmurt State University
5 Chikrii A.A. (1997) Conflict-Controlled Processes. Kluwer, Dordrecht
6 Fleming W.H. (1957) A note on differential games of prescribed duration. Contributions to the Theory of Games. 3: 407–416.
7 Hajek O. (2008) Pursuit Games: An Introduction to the Theory and Applications of Differential Games of Pursuit and Evasion, Dove. Pub. New York
8 Ibragimov G.I. (2005). Optimal pursuit with countable many pursuers and one evader, Differential Equations, 41(5): 627–635
9 Isaacs R. (1965) Differential games. John Wiley and Sons, New York
10 Ibragimov G.I., Abd Rasid N., Kuchkarov A.Sh. and Ismail F. (2015) Multi pursuer differential game of optimal approach with integral constraints on controls of players. Taiwanese Journal of Mathematics, 19(3):963–976, Doi: 10.11650/tjm.19.2015.2288
11 Petrosjan L.A. (1993). Differential games of pursuit. Series on optimization, Vol.2. World Scientific Poblishing, Singapore
12 Samatov B.T. (2013) On a Pursuit-Evasion Problem under a Linear Change of the Pursuer Resource. Siberian Advances in Mathematics, Allerton Press, Inc.Springer. New York: 23(4): 294–302.
13 Samatov B.T. (2013) The Pursuit- Evasion Problem under Integral-Geometric constraints on Pursuer controls. Automation and Remote Control, Pleiades Publishing, Ltd. New York. 74(7): 1072–1081.
14 Samatov B.T. (2014) The Π-strategy in a differential game with linear control constraints. J. Appl. Maths and Mechs, Elsevier. Netherlands. 78(3): 258–263.
15 Pontryagin L.S. (2004) Selected Works. MAKS Press, Moscow
16 Pshenichnii B.N. (1976). Simple pursuit by several objects. Cybernetics and System Analysis. 12(3): 484-485. DOI 10.1007/BF01070036
17 Samatov B.T.(2013) Problems of group pursuit with integral constraints on controls of the players I. Cybernetics and Systems Analysis, 49(5): 756–767.
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