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.
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. 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. 10. Isaacs R. (1965) Differential games. John Wiley and Sons, New York. 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.
Samatov, Bahrom Tadjiakhmatovich; Xorilov, Maxmud Abdumalikovich; and Sobitov, Ravshan Abdurayimxonovich
"ABOUT ONE OF THE PROBLEM ISAACS FOR LG GAME,"
Scientific Bulletin of Namangan State University: Vol. 2
, Article 4.
Available at: https://uzjournals.edu.uz/namdu/vol2/iss11/4