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Capture of Given Number of Evaders in Pontryagin’s Nonstationary Example

Author

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  • Nikolai N. Petrov

    (Udmurt State University)

  • Nadezhda A. Solov’eva

    (Udmurt State University)

Abstract

The article deals with Pontryagin’s generalized nonstationary example with n pursuers and m evaders with the same dynamic and inertial capabilities of players. The set of values of admissible controls V is a strictly convex compact set with a smooth boundary. The pursuers use quasi-strategies. Sufficient conditions for the pursuers’ group to capture one evader and the given number of evaders are presented in the terms of the initial position and the parameters of the game. In the problem of catching a given number of evaders, it is assumed that at first all evaders choose their open-loop controls and then the pursuers determine their motions on the basis of the information about the choice of the evaders and, moreover, each pursuer catches no more than one evader.

Suggested Citation

  • Nikolai N. Petrov & Nadezhda A. Solov’eva, 2019. "Capture of Given Number of Evaders in Pontryagin’s Nonstationary Example," Dynamic Games and Applications, Springer, vol. 9(3), pages 614-627, September.
    • Handle: RePEc:spr:dyngam:v:9:y:2019:i:3:d:10.1007_s13235-019-00303-5
    DOI: 10.1007/s13235-019-00303-5
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    References listed on IDEAS

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    1. Dušan M. Stipanović & Arik Melikyan & Naira Hovakimyan, 2010. "Guaranteed Strategies For Nonlinear Multi-Player Pursuit-Evasion Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 12(01), pages 1-17.
    2. Sergey Ganebny & Sergey Kumkov & Stéphane Ménec & Valerii Patsko, 2012. "Model Problem in a Line with Two Pursuers and One Evader," Dynamic Games and Applications, Springer, vol. 2(2), pages 228-257, June.
    Full references (including those not matched with items on IDEAS)

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