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  4. Pursuit differential game of many pursuers and one evader in a convex hyperspace

Pursuit differential game of many pursuers and one evader in a convex hyperspace

MMC.
2022;
Volume 9, Number 1
: pp. 9–17
https://doi.org/10.23939/mmc2022.01.009
Received: July 07, 2021
Accepted: November 16, 2021

Mathematical Modeling and Computing, Vol. 9, No. 1, pp. 9–17 (2022)

Authors:
  1. I. A. Alias
  2. K. Jaman
  3. G. Ibragimov
1
Department of Mathematics and Statistics and Institute for Mathematical Research, Universiti Putra Malaysia
2
Department of Mathematics and Statistics and Institute for Mathematical Research, Universiti Putra Malaysia
3
Department of Mathematics and Statistics and Institute for Mathematical Research, Universiti Putra Malaysia

A pursuit differential game of many pursuers and one evader in a nonempty closed convex compact hyperspace is studied.  Pursuit is completed when at least one pursuer coincides with the evader.  Control functions of players are constrained by geometric constraints.  A pursuit game in a set containing a closed convex compact set is solved, and pursuit is shown to be completed in a pursuit game within a finite-dimensional cube.  Parallel strategy and fictitious pursuers are used to solve the game, and a guaranteed pursuit time is obtained.

differential game
parallel strategy
pursuit
cube
convex set
  1. Isaacs R.  Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization.  John Wiley and Sons, New York (1965).
  2. Petrosjan L. A.  Pursuit games with a Survival Zone.  Vestnic Leningard State Univ. 13, 75–85 (1967), (in Russian).
  3. Friedman A.  Differential Games.  John Wiley & Sons, New York (1971).
  4. Ivanov R.  Simple Pursuit–Evasion on Compact.  Doklady Akademii Nauk SSSR. 254 (6), 1318–1321 (1980).
  5. Berkovitz L. D.  Differential Game of Generalized Pursuit and Evasion.  SIAM Journal on Control and Optimization. 24 (3), 361–373 (1986).
  6. Chikrii A. A.  Simple Pursuit of One Evader by a Group.  Cybernetics and Systems Analysis. 28 (3), 438–444 (1992).
  7. Petrosyan L. A.  Differential Games of Pursuit.  World Scientific, Singapore, London (1993).
  8. Ibragimov G., Khakestari M., Kuchkarov A. S.  Solution of a Linear Pursuit–Evasion Differential Game with Closed and Convex Terminal Set.  Journal of Mathematical and Fundamental Sciences. 44 (1), 1–12 (2012).
  9. Ibragimov G., Satimov N.  A Multiplayer Pursuit Differential Game on a Closed Convex Set with Integral Constraints.  Abstract and Applied Analysis. 2012, Article ID 460171, 12 pages (2012).
  10. Alias I. A., Ramli R., Ibragimov G., Narzullaev A.  Simple Motion Pursuit Differential Game of Many Pursuers and One Evader on Convex Compact Set.  International Journal of Pure and Applied Mathematics. 102 (4), 733–745 (2015).
  11. Ferrara M., Ibragimov G., Salimi M.  Pursuit–Evasion Game of Many Players with Coordinate-wise Integral Constraints on a Convex Set in the Plane.  Atti della Accademia Peloritana dei Pericolanti. Classe di Scienze Fisiche, Matematiche e Naturali.  95 (2), A6-1–A6-6 (2017).
  12. Chernous'ko F. L., Zak V. L.  On Differential games of Evasion from Many Pursuers.  Journal of Optimization Theory and Applications. 46 (4), 461–470 (1985).
  13. Borowko P., Rzymowski W., Stachura A.  Evasion from Many Pursuers in the Simple Motion Case.  Journal of Mathematical Analysis and Applications. 135 (1), 75–80 (1988).
  14. Chodun W.  Differential Games of Evasion with Many Pursuers.  Journal of Mathematical Analysis and Applications. 142 (2), 370–389 (1989).
  15. Ibragimov G., Salleh Y.  Simple Motion Evasion Differential Game of Many Pursuers and One Evader with Integral Constraints on Control Functions of Players.  Journal of Applied Mathematics. 2012, Article ID 748096, 10 pages (2012).
  16. Alias I. A., Ibragimov G., Rakhmanov A.  Evasion Differential Game of Infinitely Many Evaders from Infinitely Many Pursuers in Hilbert Space.  Dynamic Games and Applications. 6 (2), 1–13  (2016).
  17. Ibragimov G., Ferrara M., Kuchkarov A., Pansera B. A.  Simple Motion Evasion Differential Game of Many Pursuers and Evaders with Integral Constraints.  Dynamic Games and Applications. 8, 352–378 (2018).
  18. Ibragimov G., Ferrara M., Ruziboev M., Pansera B. A.  Linear Evasion Differential Game of One Evader and Several Pursuers with Integral Constraints.  International Journal of Game Theory. 50, 729–750 (2021).
  19. Krasovskii N. N., Subbotin A. I.  Game-Theoretical Control Problems.  Springer, New York (1988).
  20. Pontryagin L. S.  Selected works.  Nauka, Moscow (1988), (in Russian).