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Decomposition of Differential Games with Multiple Targets

Author

Listed:
  • Adriano Festa

    (RICAM - Austrian Academy of Sciences (ÖAW))

  • Richard B. Vinter

    (Imperial College)

Abstract

This paper provides a decomposition technique for the purpose of simplifying the solution of certain zero-sum differential games. The games considered terminate when the state reaches a target, which can be expressed as the union of a collection of target subsets considered as ‘multiple targets’; the decomposition consists in replacing the original target by each of the target subsets. The value of the original game is then obtained as the lower envelope of the values of the collection of games, resulting from the decomposition, which can be much easier to solve than the original game. Criteria are given for the validity of the decomposition. The paper includes examples, illustrating the application of the technique to pursuit/evasion games and to flow control.

Suggested Citation

  • Adriano Festa & Richard B. Vinter, 2016. "Decomposition of Differential Games with Multiple Targets," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 848-875, June.
    • Handle: RePEc:spr:joptap:v:169:y:2016:i:3:d:10.1007_s10957-016-0908-z
    DOI: 10.1007/s10957-016-0908-z
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    References listed on IDEAS

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    1. M. Falcone, 2006. "Numerical Methods For Differential Games Based On Partial Differential Equations," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 8(02), pages 231-272.
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    Cited by:

    1. Alexander Moll & Meir Pachter & Eloy Garcia & David Casbeer & Dejan Milutinović, 2020. "Robust Policies for a Multiple-Pursuer Single-Evader Differential Game," Dynamic Games and Applications, Springer, vol. 10(1), pages 202-221, March.

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