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Evasion from Several Pursuers in the Game with Coordinate-wise Integral Constraints

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Abstract

We consider a simple motion evasion differential game of one evader from many pursuers in \({\mathbb {R}}^n\). The control functions of players are subjected to coordinate-wise integral constraints. If the position of the evader never coincides with the position of any pursuer, then we say that evasion is possible. In the present paper we obtain sufficient conditions of evasion. For any positive number \(\varepsilon \), a strategy for the evader is constructed, which guarantees the evasion in \(\varepsilon \)-neighborhood of a coordinate axis.

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Acknowledgements

The present research was supported by the National Fundamental Research Grant Scheme FRGS of Malaysia, FRGS/1/2020/STG06/UPM/02/2. The authors express their sincere thanks to the reviewers for their careful reading of the article and several helpful suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Universiti Putra Malaysia, Serdang, Malaysia

    Gafurjan Ibragimov

  2. Department of Law, Economics and Human Sciences, University Mediterranea of Reggio Calabria, Reggio Calabria, Italy

    Gafurjan Ibragimov

  3. Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, Malaysia

    Yusra Salleh

  4. Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, Malaysia

    Idham Arif Alias

  5. Department of Law, Economics and Human Sciences and Decisions Lab, University Mediterranea of Reggio Calabria, Reggio Calabria, Italy

    Bruno Antonio Pansera & Massimiliano Ferrara

  6. ICRIOS - The Invernizzi Centre for Research in Innovation, Organization, Strategy and Entrepreneurship Bocconi University - Department of Management and Technology, Milan, Italy

    Massimiliano Ferrara

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  1. Gafurjan Ibragimov
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  2. Yusra Salleh
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  3. Idham Arif Alias
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  4. Bruno Antonio Pansera
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  5. Massimiliano Ferrara
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Correspondence to Gafurjan Ibragimov.

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Ibragimov, G., Salleh, Y., Alias, I.A. et al. Evasion from Several Pursuers in the Game with Coordinate-wise Integral Constraints. Dyn Games Appl 13, 819–842 (2023). https://doi.org/10.1007/s13235-022-00475-7

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