Table of Contents Author Guidelines Submit a Manuscript
Discrete Dynamics in Nature and Society
Volume 2016 (2016), Article ID 1289456, 6 pages
http://dx.doi.org/10.1155/2016/1289456
Research Article

Linear Pursuit Differential Game under Phase Constraint on the State of Evader

1Department of Informatics, Tashkent University of Information Technologies, TUIT, Amir Temur Str. 108, 100202 Tashkent, Uzbekistan
2Department of Mathematics & Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, Malaysia
3Department of Law and Economics, University Mediterranea of Reggio Calabria, Reggio Calabria, Italy
4ICRIOS, Bocconi University, Milan, Italy

Received 22 June 2016; Accepted 14 September 2016

Academic Editor: Rigoberto Medina

Copyright © 2016 Askar Rakhmanov et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. A. Azamov, A. Sh. Kuchkarov, and B. B. Samatov, “The relation between problems of pursuit, controllability and stability in the large in linear systems with different types of constraints,” Prikladnaya Matematika i Mekhanika, vol. 71, no. 2, pp. 259–263, 2007. View at Google Scholar
  2. A. A. Azamov, “On the problem of kind for the simple motion game with restriction,” Serdika: Bulgarsko Matematichesko Spisanie, vol. 12, pp. 38–43, 1986. View at Google Scholar
  3. A. A. Azamov, “On the evasion problem for a given curve,” Applied Mathematics and Mechanics, no. 4, pp. 694–697, 1982. View at Google Scholar
  4. A. Raxmanov and G. Ibragimov, “Linear discrete pursuit game with phase constraints,” Scientific World Journal, vol. 2014, Article ID 435103, 5 pages, 2014. View at Publisher · View at Google Scholar · View at Scopus
  5. A. Raxmonov and G. I. Ibragimov, “An approach for solving discrete game problems with total constraints on controls,” Abstract and Applied Analysis, vol. 2014, Article ID 674651, 6 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. A. F. Filippov, “On some problems of theory of optimal regulation,” Vestnik Moskovskogo Universiteta, Seriya Matematiki, Mekhaniki, no. 2, pp. 25–32, 1959. View at Google Scholar
  7. G. I. Ibragimov, “A game problem on a closed convex set,” Siberian Advances in Mathematics, vol. 12, no. 3, pp. 16–31, 2002. View at Google Scholar
  8. G. I. Ibragimov, “On the optimal pursuit game of several pursuers and one evader,” Prikladnaya Matematika i Mekhanika, vol. 62, no. 2, pp. 199–205, 1998. View at Google Scholar
  9. G. I. Ibragimov, A. A. Azamov, and M. Khakestari, “Solution of a linear pursuit-evasion game with integral constraints,” ANZIAM Journal, vol. 52, pp. E59–E75, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  10. R. P. Ivanov, “Simple pursuit-evasion on a compact convex set,” Doklady Akademii Nauk SSSR, vol. 254, no. 6, pp. 1318–1321, 1980. View at Google Scholar
  11. N. N. Krasovskii, Control of Dynamic Systems, Nauka, Moscow, Russia, 1985.
  12. A. S. Kuchkarov, G. I. Ibragimov, and M. Khakestari, “On a linear differential game of optimal approach of many pursuers with one evader,” Journal of Dynamical and Control Systems, vol. 19, no. 1, pp. 1–15, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. A. S. Kuchkarov, “On a differential game with integral and phase constraints,” Automation and Remote Control, vol. 74, no. 1, pp. 12–25, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. M. S. Nikol'skii, “A direct method of solution of linear differential pursuit-evasion games,” Mathematical Notes of the Academy of Sciences of the USSR, vol. 33, no. 6, pp. 455–458, 1983. View at Publisher · View at Google Scholar · View at Scopus
  15. A. H. Nishanov and A. T. Rakhmanov, “On a method of prosecution under state constraints on the state of the evader,” European Applied Sciences, no. 6, pp. 48–51, 2013. View at Google Scholar
  16. L. S. Pontryagin, Selected Works, Nauka, Moscow, Russia, 1988.
  17. B. N. Pshenichnii, A. A. Chikrii, and J. S. Rappoport, “Pursuit by several controlled objects in the presence of phase constraints,” Doklady Akademii Nauk SSSR, vol. 259, no. 4, pp. 138–141, 1981. View at Google Scholar
  18. L. A. Petrosyan, “On a family of differential games of survival in space,” Doklady Sciences of the USSR, vol. 161, no. 1, pp. 52–54, 1965. View at Google Scholar
  19. А. Т. Rakhmanov, “Linear pursuit differential game under phase constraint on the state of evader,” in Proceedings of the 7th International Conference on Priority Directions in Science and Technology in the ХХI-th Century, vol. 2, pp. 123–127, Tashkent, Uzbekistan, 2014.
  20. А. Т. Rahmanov, “On a pursuit method in linear differential games with integral constraints on controls,” Differential Equations, vol. 25, no. 5, pp. 785–790, 1989. View at Google Scholar
  21. N. Yu. Satimov, Methods of Solution of Pursuit Problems in the Theory of Differential Games, NUUz Press, Tashkent, Uzbekistan, 2003.
  22. B. T. Samatov, “The differential game with ‘a survival zone’ with different classes of admissible control functions,” in Game Theory and Applications, vol. 13, pp. 143–150, Nova Science, Hauppauge, NY, USA, 2008. View at Google Scholar
  23. B. T. Samatov, “The pursuit-evasion problem under integral-geometric constraints on pursuer controls,” Automation and Remote Control, vol. 74, no. 7, pp. 1072–1081, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. L. P. Yugay, “On differential games with constraints on phase state and controls of players,” Doklady Academy of Sciences of USSSR, no. 4, pp. 5–6, 1977. View at Google Scholar