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On a Fixed Duration Pursuit Differential Game with Geometric and Integral Constraints

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Abstract

In this paper we investigate a differential game in which countably many dynamical objects pursue a single one. All the players perform simple motions. The duration of the game is fixed. The controls of a group of pursuers are subject to integral constraints, and the controls of the other pursuers and the evader are subject to geometric constraints. The payoff of the game is the distance between the evader and the closest pursuer when the game is terminated. We construct optimal strategies for players and find the value of the game.

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Acknowledgments

The authors thank reviewers for their valuable comments and suggestions to improve the readability of the paper.

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Authors and Affiliations

  1. Center for Dynamics and Institute for Analysis, Department of Mathematics, Technische Universität Dresden, 01062, Dresden, Germany

    Mehdi Salimi & Stefan Siegmund

  2. Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia (UPM), 43400, Serdang, Selangor, Malaysia

    Gafurjan I. Ibragimov

  3. Young Researchers and Elite Club, Hamedan Branch, Islamic Azad University, Hamedan, Iran

    Somayeh Sharifi

Authors
  1. Mehdi Salimi
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  2. Gafurjan I. Ibragimov
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  3. Stefan Siegmund
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  4. Somayeh Sharifi
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Correspondence to Mehdi Salimi.

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Salimi, M., Ibragimov, G.I., Siegmund, S. et al. On a Fixed Duration Pursuit Differential Game with Geometric and Integral Constraints. Dyn Games Appl 6, 409–425 (2016). https://doi.org/10.1007/s13235-015-0161-3

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  • DOI: https://doi.org/10.1007/s13235-015-0161-3

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