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Scientific Bulletin of Namangan State University

Abstract

In this work, we will consider a simple pursuit differential game of the fitst order when Gronwall-Bellman type constraints imposed on control functions of the players. The proposed method substantiates the parallel approach strategy in this line differential game of the fitst order. The new sufficient solvability conditions are obtained for problem of the pursuit.

First Page

15

Last Page

20

References

1. Gronwall T.H. Note on the derivatives with respect to a parameter of the solutions of a system of differential equations. Ann. Math., 1919, 20(2): 293-296. 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.

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