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Monotone Numerical Schemes and Feedback Construction for Hybrid Control Systems

  • Roberto Ferretti
  • Hasnaa Zidani
Article

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.

Keywords

Hybrid systems Approximation of the value function   Optimal feedback law 

Mathematics Subject Classification

34K34 34K35 49L20 65N12 

Notes

Acknowledgments

This work has been partially supported by the EU under the 7th Framework Program Marie Curie Initial Training Network “FP7-PEOPLE-2010-ITN”, GA number 264735-SADCO.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Dipartmento di Matematica e FisicaUniversità Roma TreRomeItaly
  2. 2.Unité de Mathématiques Appliquées (UMA)ENSTA ParisTechPalaiseauFrance

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