Differential LG - Game of Many Participant Players


  • (1)  N.S. Ruzuddinov            Kazakh National University named Al-Farabi.  
            Kazakhstan

  • (2)  S.A. Gafforov            Center for the Development of Professional Qualifications of Medical Workers of the Ministry of Health of the Republic of Uzbekistan.  
            Uzbekistan

  • (3)  S. Ruzuddinov            Kazakh National University named Al-Farabi.  
            Uzbekistan

    (*) Corresponding Author

DOI:

https://doi.org/10.47494/mesb.v16i.724

Keywords:

Differential game, evader, pursuer, strategy, geometric representation, integral constraint, attainability domain

Abstract

In this article, we have considered a simple motion differential game of   pursuers and one evader in. Here controls of the pursuers are subjected to linear constraints which is the generalization of both integral and geometrical constraints, and control of the evader is subjected to a geometrical constraint. To solve a pursuit problem, the attainability domain of each pursuer has been constructed and therefore, necessary and sufficient conditions have been obtained by intersection of them.

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References

Azamov A. (1986) On the quality problem for simple pursuit games with constraint. Serdica Bulgariacaemath. Publ.Sofia: 12(1): 38–43.

Azamov A.A., Samatov B.T. (2010) The -Strategy: Analogies and Applications. The Fourth International Conference Game Theory and Management, St.Petersburg: 33–47.

Bakolas E., Tsiotras P. (2011) On the relay pursuit of a maneuvering target by a group of pursuers. In 50th IEEE Conference on Decision and Control and European Control Conference, Orlando, FL, pp. 4270–4275.

Basar T. Stochastik differential games and intricacy of information structures. Dynamic Games in Economics.- Springer, 2014.- P.23-49.

Basar T., Bernhard P. H-infinity optimal control and related mini-max design problems: a dynamic game approach. - Boston: Birkhauser, 1995.- P. 428.

Berkovitz L.D. (1967) A Survey of Differential Games, Mathematical Theory of Control. New York, Academic Press 373–385.

Berkovitz L.D. (1986) Differential game of generalized pursuit and evasion. SIAM J. Contr.: 24(3): 361–373.

Blagodatskikh V.I. (2001). Introduction to optimal control. Linear theory. Moscow. Graduate School.

Chikrii A.A. (1997) Conflict-Controlled Processes. Kluwer, Dordrecht.

Elliot R.J., Kalton N.J. (1972) The Existence of Value for Differential Games. American Mathematical Soc.

Fleming W.H. (1957) A note on differential games of prescribed duration. Contributions to the Theory of Games. 3: 407–416.

Fleming W. H. (1961) The convergence problem for differential games. J. Math. Anal. Appl. 3: 102–116.

Friedman A. (1971) Differential Games. Wiley Interscience, New York.

Grigorenko N.L. (1990). Mathematical Methods of Control for Several Dynamic Processes. Izdat. Gos. Univ., Moscow.

Hajek O. (1975). Pursuit games. New York, Academic Press.

Hajek O. (2008) Pursuit Games: An Introduction to the Theory and Applications of Differential Games of Pursuit and Evasion, Dove. Pub. New York.

Ho Y., Bryson A., Baron S. (1965) Differential games and optimal pursuit-evasion strategies. IEEE Trans Autom Control 10: 385-389.

Ibragimov G.I. (1998). On the optimal pursuit game of several pursuers and one evader. Prikladnaya Matematika i Mekhanika. 62(2): 199–205.

Ibragimov G.I. (2005). Optimal pursuit with countable many pursuers and one evader, Differential Equations, 41(5): 627–635.

Ibragimov G.I. (2013). The optimal pursuit problem reduced to an infinite system of differential equations. J. Appl. Maths Mekhs. 77(5): 470–476.

Ibragimov G.I. (2013). Optimal pursuit time for a differential game in the Hilbert space l2. ScienceAsia, 39S: 25– 30.

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.

Isaacs R. (1965) Differential games. John Wiley and Sons, New York.

Krasovskii N.N., Subbotin A.I. (1974) Positional Differential Games. Nauka, Moscow. (in Russian)

Pashkov A.G. and Terekhov S.D. (1987) A differential game of approach with two pursuers and one evader. Journal of Optimization Theory and Applications, 55(2): 303–311.

Petrosjan L.A. (1993). Differential games of pursuit. Series on optimization, Vol.2. World Scientific Poblishing, Singapore.

Pontryagin L.S. (2004) Selected Works. MAKS Press, Moscow.

Pshenichnyi B.N. (1976). Simple pursuit by several objects. Cybernetics and System Analysis. 12(3): 484-485. DOI 10.1007/BF01070036.

Pshenichnyi B.N., Chikrii A.A., and Rappoport J.S. (1981) An efficient method of solving differential games with many pursuers, Dokl. Akad. Nauk SSSR 256, 530–535. (in Russian).

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.

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.

Published

2021-09-24

How to Cite

Ruzuddinov, N. ., Gafforov, S. ., & Ruzuddinov, S. . (2021). Differential LG - Game of Many Participant Players. Middle European Scientific Bulletin, 16. https://doi.org/10.47494/mesb.v16i.724

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Technology