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Model Problem in a Line with Two Pursuers and One Evader

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Abstract

An antagonistic differential game is considered where motion occurs in a straight line. Deviations between the first and second pursuers and the evader are computed at the instants T 1 and T 2, respectively. The pursuers act in coordination. Their aim is to minimize the resultant miss, which is equal to the minimum of the deviations happened at the instants T 1 and T 2. Numerical study of value function level sets (Lebesgue sets) for qualitatively different cases is given. A method for constructing optimal feedback controls is suggested on the basis of switching lines. The results of a numerical simulation are shown.

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Acknowledgements

This work was supported by the Russian Foundation for Fundamental Research under grants No. 10-01-96006, 11-01-12088, 12-01-00537.

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, S.Kovalevskaya str., 16, Ekaterinburg, 620990, Russia

    Sergey A. Ganebny, Sergey S. Kumkov & Valerii S. Patsko

  2. EADS/MBDA France, 1 avenue Réaumur, 92358, Le Plessis-Robinson Cedex, France

    Stéphane Le Ménec

Authors
  1. Sergey A. Ganebny
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  2. Sergey S. Kumkov
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  3. Stéphane Le Ménec
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  4. Valerii S. Patsko
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Correspondence to Sergey S. Kumkov.

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Ganebny, S.A., Kumkov, S.S., Le Ménec, S. et al. Model Problem in a Line with Two Pursuers and One Evader. Dyn Games Appl 2, 228–257 (2012). https://doi.org/10.1007/s13235-012-0041-z

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