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Stochastic hybrid differential games and match race problems

Author

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  • Cacace, S.
  • Ferretti, R.
  • Festa, A.

Abstract

We discuss the general framework of a stochastic two-player, hybrid differential game, and we apply it to the modelling of a “match race” between two sailing boats, namely a competition in which the goal of both players is to proceed in the windward direction, while trying to slow down the other player. We provide a convergent approximation scheme for the computation of the value function of the game, and we validate the approach on some typical racing scenarios.

Suggested Citation

  • Cacace, S. & Ferretti, R. & Festa, A., 2020. "Stochastic hybrid differential games and match race problems," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    • Handle: RePEc:eee:apmaco:v:372:y:2020:i:c:s0096300319309580
    DOI: 10.1016/j.amc.2019.124966
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    References listed on IDEAS

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    1. Robert C Dalang & Frédéric Dumas & Sylvain Sardy & Stephan Morgenthaler & Juan Vila, 2015. "Stochastic optimization of sailing trajectories in an upwind regatta," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(5), pages 807-821, May.
    2. Hamadène, Said & Zhang, Jianfeng, 2010. "Switching problem and related system of reflected backward SDEs," Stochastic Processes and their Applications, Elsevier, vol. 120(4), pages 403-426, April.
    3. Roberto Ferretti & Adriano Festa, 2019. "Optimal Route Planning for Sailing Boats: A Hybrid Formulation," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 1015-1032, June.
    4. A. B. Philpott & S. G. Henderson & D. Teirney, 2004. "A Simulation Model for Predicting Yacht Match Race Outcomes," Operations Research, INFORMS, vol. 52(1), pages 1-16, February.
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