We study a differential game of two pursuers and one evader, whose dynamics are described by linear differential equations, in $\mathbb{R}^n$. The control functions of pursuers and evader are subjected to the Grönwall type constraints. The game is said to be completed when the state of the evader coincides with the state of any pursuer. The pursuers aim to complete game as soon as possible, while the evader tries to either evade capture or prolong the time until capture. We construct optimal strategies of players and find an equation for the optimal pursuit time.
| Mualliflar | Ibragimov G.I., Yusupov I.M. |
|---|---|
| Jurnal | O‘zbekiston matematika jurnali |
| Nashriyot | Ўзбекистон Республикаси ФА Математика институти |
| ISSN | 2010-7269 |
| Nashr sanasi | 2025-09-06 |
| Jild | 69 |
| Son | 3 |
| Betlar | 83-92 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| DOI | 10.29229/uzmj.2025-3-8 |
| Indeksga qo‘shilgan | 2026-08-26 |
DOI: 10.29229/uzmj.2025-3-8 · Maqolaning asl sahifasi
Differential game, Gr\"{o}nwall constraints, pursuer, evader, optimal pursuit time, optimal strategy
| APA | Ibragimov G.I., & Yusupov I.M. (2025). Optimal pursuit game of two pursuers and one evader with the Grönwall type constraints on controls. O‘zbekiston matematika jurnali, 69(3), 83-92. https://doi.org/10.29229/uzmj.2025-3-8 |
|---|---|
| GOST (OAK) | Ibragimov G.I., Yusupov I.M. Optimal pursuit game of two pursuers and one evader with the Grönwall type constraints on controls // O‘zbekiston matematika jurnali. – 2025. – T. 69, № 3. – P. 83-92. – DOI: 10.29229/uzmj.2025-3-8. |
| MLA | Ibragimov G.I., and Yusupov I.M. “Optimal pursuit game of two pursuers and one evader with the Grönwall type constraints on controls.” O‘zbekiston matematika jurnali, 69(3), 83-92, 2025. https://doi.org/10.29229/uzmj.2025-3-8 |
| Chicago | Ibragimov G.I., and Yusupov I.M. “Optimal pursuit game of two pursuers and one evader with the Grönwall type constraints on controls.” O‘zbekiston matematika jurnali, 69(3), 83-92 (2025). https://doi.org/10.29229/uzmj.2025-3-8 |
| Harvard | Ibragimov G.I., and Yusupov I.M (2025) ‘Optimal pursuit game of two pursuers and one evader with the Grönwall type constraints on controls’, O‘zbekiston matematika jurnali, 69(3), 83-92. https://doi.org/10.29229/uzmj.2025-3-8 |
| BibTeX | @article{ibragimovgi2025,
title = {Optimal pursuit game of two pursuers and one evader with the Grönwall type constraints on controls},
author = {Ibragimov G.I. and Yusupov I.M.},
journal = {O‘zbekiston matematika jurnali},
year = {2025},
volume = {69},
number = {3},
pages = {83-92},
doi = {10.29229/uzmj.2025-3-8},
url = {https://doi.org/10.29229/uzmj.2025-3-8}
} |
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