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Monotone Numerical Schemes and Feedback Construction for Hybrid Control Systems

Author

Listed:
  • Roberto Ferretti

    (Università Roma Tre)

  • Hasnaa Zidani

    (ENSTA ParisTech)

Abstract

Hybrid systems are a general framework which can model a large class of control systems arising whenever a set of continuous and discrete dynamics are mixed in a single system. In this paper, we study the convergence of monotone numerical approximations of value functions associated to control problems governed by hybrid systems. We discuss also the feedback reconstruction and derive a convergence result for the approximate feedback control law. Some numerical examples are given to show the robustness of the monotone approximation schemes.

Suggested Citation

  • Roberto Ferretti & Hasnaa Zidani, 2015. "Monotone Numerical Schemes and Feedback Construction for Hybrid Control Systems," Journal of Optimization Theory and Applications, Springer, vol. 165(2), pages 507-531, May.
    • Handle: RePEc:spr:joptap:v:165:y:2015:i:2:d:10.1007_s10957-014-0637-0
    DOI: 10.1007/s10957-014-0637-0
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    Cited by:

    1. Dharmatti Sheetal, 2016. "Viscosity Solutions of Hybrid Game Problems with Unbounded Cost Functionals," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(01), pages 1-26, March.
    2. 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.

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