Abstract:
A simple pursuit-evasion differential game of one pursuer and one evader is studied. The players' controls are subject to differential constraints in the form of the integral Grönwall inequality. The pursuit is considered completed if the state of the pursuer coincides with the state of the evader. The main goal of this work is to construct optimal strategies for the players and find the optimal pursuit time. A parallel approach strategy for Grönwall-type constraints is constructed and it is proved that it is the optimal strategy of the pursuer. In addition, the optimal strategy of the evader is constructed and the optimal pursuit time is obtained. The concept of a parallel pursuit strategy (Π-strategy for short) was introduced and used to solve the quality problem for “life-line” games by L.A. Petrosjan. This work develops and expands the works of Isaacs, Petrosjan, Pshenichnyi, and other researchers, including the authors.
The present research was partially supported by the National Fundamental Research Grant Scheme FRGS of Malaysia (Project No. 01-01-17-1921FR) and by the National Fundamental Research Grant Scheme of the National University Uzbekistan (Project No. FR-GS-33).
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Document Type:
Article
Language: English
Citation:
Bahrom T. Samatov, Gafurjan Ibragimov, Iroda V. Khodjibayeva, “Pursuit-evasion differential games with Grönwall-type constraints on controls”, Ural Math. J., 6:2 (2020), 95–107
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\paper Pursuit-evasion differential games with Gr\"{o}nwall-type constraints on controls
\jour Ural Math. J.
\yr 2020
\vol 6
\issue 2
\pages 95--107
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https://www.mathnet.ru/eng/umj/v6/i2/p95
This publication is cited in the following 14 articles:
Bahrom Samatov, Ulmasjon Soyibboev, IUTAM Bookseries, 40, Proceedings of the IUTAM Symposium on Optimal Guidance and Control for Autonomous Systems 2023, 2024, 165
B. T. Samatov, A. Kh. Akbarov, “Differential game with a “life line” under the Grönwall constraint on controls”, Vestn. S.-Peterburg. un-ta. Ser. 10. Prikl. matem. Inform. Prots. upr., 20:2 (2024), 265–280
Abdulla Azamov, Bahrom Samatov, Ulmasjon Soyibboev, “The Game with a “Life-Line” for Simple Harmonic Motions of Objects”, Int. Game Theory Rev., 26:04 (2024)
B. T. Samatov, U. B. Soyibboev, “Differential game with “lifeline” for Pontryagin's control example”, Izv. IMI UdGU, 61 (2023), 94–113
Gafurjan Ibragimov, Ikrombek Yusupov, Massimiliano Ferrara, “Optimal Pursuit Game of Two Pursuers and One Evader with the Grönwall-Type Constraints on Controls”, Mathematics, 11:2 (2023), 374
Jewaidu Rilwan, Massimiliano Ferrara, Abbas Ja'afaru Badakaya, Bruno Antonio Pansera, “On pursuit and evasion game problems with Gr¨onwall-type constraints”, Qual Quant, 57:6 (2023), 5551
Gafurjan Ibragimov, Omongul Egamberganova, Idham Arif Alias, Shravan Luckraz, “On some new results in a pursuit differential game with many pursuers and one evader”, MATH, 8:3 (2023), 6581
B. T. Samatov, S. I. Uralova, “Differential Games with Inertial Players Under the Langenhop Type Constraints on Controls”, Lobachevskii J Math, 44:10 (2023), 4370
Jewaidu Rilwan, Pasquale Fotia, Massimiliano Ferrara, “On game value of a differential game problem with Grönwall-type constraints on players control functions”, Decisions Econ Finan, 46:1 (2023), 319
B. T. Samatov, A. Kh. Akbarov, B. I. Zhuraev, “Pursuit–evasion differential games with Gr-constraints on controls”, Izv. IMI UdGU, 59 (2022), 67–84
B. T. Samatov, M. A. Horilov, A. Ah. Akbarov, “Differential Game: "Life Line" for Non-Stationary Geometric Constraints On Controls”, Lobachevskii J Math, 43:1 (2022), 237
Abbas Ja'afaru Badakaya, Hassan Abdullahi, Mehdi Salimi, “A Pursuit Game in a Closed Convex Set on a Euclidean Space”, Differ Equ Dyn Syst, 2022
Bahrom T. Samatov, Ulmasjon B. Soyibboev, “Differential game with a lifeline for the inertial movements of players”, Ural Math. J., 7:2 (2021), 94–109
B. T. Samatov, N. T. Umaraliyeva, S. I. Uralova, “Differential Games with the Langenhop Type Constrains on Controls”, Lobachevskii J Math, 42:12 (2021), 2942
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