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A Differential Game Problem of Many Pursuers and One Evader in the Hilbert Space \(\ell_2\)

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Abstract

In this paper, we investigate a differential game problem of multiple number of pursuers and a single evader with motions governed by a certain system of first-order differential equations. The problem is formulated in the Hilbert space \(\ell_2,\) with control functions of players subject to integral constraints. Avoidance of contact is guaranteed if the geometric position of the evader and that of any of the pursuers fails to coincide for all time t. On the other hand, pursuit is said to be completed if the geometric position of at least one of the pursuers coincides with that of the evader. We obtain sufficient conditions that guarantees avoidance of contact and construct evader’s strategy. Moreover, we prove completion of pursuit subject to some sufficient conditions. Finally, we demonstrate our results with some illustrative examples.

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Acknowledgements

The authors acknowledge the financial support provided by King Mongkut’s University of Technology Thonburi through the “KMUTT \(55^{th}\) Anniversary Commemorative Fund”. The first author was supported by the Petchra Pra Jom Klao Doctoral Scholarship Academic for Ph.D. Program at KMUTT. This project is supported by the Theoretical and Computational Science (TaCS) Center under Computational and Applied Science for Smart Innovation (CLASSIC), Faculty of Science, KMUTT. The present research was partially supported by the National Fundamental Research Grant Scheme FRGS of Malaysia, 01-01-17-1921FR. Moreover, Poom Kumam was supported by the Thailand Research Fund and the King Mongkut’s University of Technology Thonburi under the TRF Research Scholar Grant No.RSA6080047.

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Authors and Affiliations

  1. KMUTTFixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok, 10140, Thailand

    Jewaidu Rilwan & Idris Ahmed

  2. Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok, 10140, Thailand

    Poom Kumam

  3. Institute for Mathematical Research and Department of Mathematics, Faculty of Science (FS), Universiti Putra Malaysia, Serdang, Selangor, 43400, Malaysia

    Gafurjan Ibragimov

  4. Department of Mathematical Sciences, Bayero University, Kano, Nigeria

    Jewaidu Rilwan & Abbas Ja’afaru Badakaya

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  1. Jewaidu Rilwan
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  2. Poom Kumam
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  3. Gafurjan Ibragimov
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  4. Abbas Ja’afaru Badakaya
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  5. Idris Ahmed
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Correspondence to Poom Kumam.

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Rilwan, J., Kumam, P., Ibragimov, G. et al. A Differential Game Problem of Many Pursuers and One Evader in the Hilbert Space \(\ell_2\). Differ Equ Dyn Syst 31, 925–943 (2023). https://doi.org/10.1007/s12591-020-00545-5

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