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Invariant Solutions of Differential Games with Measures: A Discontinuous Time Reparameterization Approach

Author

Listed:
  • Elena Goncharova

    (Institute for System Dynamics and Control Theory of the Siberian Branch of the Russian Academy of Sciences)

  • Maxim Staritsyn

    (Institute for System Dynamics and Control Theory of the Siberian Branch of the Russian Academy of Sciences)

Abstract

The paper is devoted to bilevel qualitative games with impulsive dynamics described by a measure differential equation. We study games with fixed impulses, and games with impulsive control in the hands of the lower level player, provided that the upper level player aims to ensure the existence of invariant solutions to a measure differential equation under any admissible answer of the opponent. We give sufficient conditions for weak invariance of time-varying domains with respect to the impulsive dynamical games.

Suggested Citation

  • Elena Goncharova & Maxim Staritsyn, 2015. "Invariant Solutions of Differential Games with Measures: A Discontinuous Time Reparameterization Approach," Journal of Optimization Theory and Applications, Springer, vol. 167(1), pages 382-400, October.
    • Handle: RePEc:spr:joptap:v:167:y:2015:i:1:d:10.1007_s10957-014-0691-7
    DOI: 10.1007/s10957-014-0691-7
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    References listed on IDEAS

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    1. repec:dau:papers:123456789/5561 is not listed on IDEAS
    2. G. J. Olsder, 2009. "Phenomena in Inverse Stackelberg Games, Part 2: Dynamic Problems," Journal of Optimization Theory and Applications, Springer, vol. 143(3), pages 601-618, December.
    3. Jean-Pierre Aubin & Nicolas Seube, 2005. "Conditional Viability for Impulse Differential Games," Annals of Operations Research, Springer, vol. 137(1), pages 269-297, July.
    4. Josef Shinar & Valery Y. Glizer & Vladimir Turetsky, 2012. "Complete Solution Of A Pursuit–Evasion Differential Game With Hybrid Evader Dynamics," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 1-31.
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