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Scientific Bulletin of Namangan State University

Abstract

The main aim of this work is to present some natural applications of Gronwall type inequalities in the Differential Games. We study the evasion problem for differential game of the first order when geometrical constraint imposed on control function of pursuer and Gronwall type constraint imposed on control function of evader. The Gronwall type constraint generalizes geometrical constraint. To solve the evasion problem, we suggest a particular strategy for evader and study its structure depending on the parameters. Here the new sufficient solvability conditions for solution of evasion problem will be proposed.

First Page

3

Last Page

8

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. P-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 P-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 theory 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. Chikrii A.A. Conflict-controlled processes, Boston-London-Dordrecht: Kluwer Academ. Publ., 1997, 424 p. 7. Fleming W. H. The convergence problem for differential games, J. Math. Anal. Appl. - 1961. - N 3. - P. 102-116. 8. A. Friedman. Differential Games, New York: Wiley, 1971, - 350 p. 9. Samatov B.T. On a Pursuit-Evasion Problem under a Linear Change of the Pursuer Resource, Siberian Advances in Mathematics. – Allerton Press, Inc. Springer. - New York, 2013. V. 23. - No 4. - P. 294-302. 10. Samatov B.T. The P-strategy in a differential game with linear control constraints, J.Appl.Maths and Mechs. - Elsevier. - Netherlands, 2014. - V. 78. - No 3. - P. 258-263. 11. Samatov B.T., Soyibboyev U.B., Akbarov A.Kh. Evasion problem in linear differential game with Gronwall type constraint. Scientific Bulletin of Namangan State University 1(10), 25-33, 2019.

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