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Error Estimates for Numerical Approximation of Hamilton–Jacobi Equations Related to Hybrid Control Systems

  • R. Ferretti
  • A. Sassi
  • H. Zidani
Article
  • 23 Downloads

Abstract

Hybrid control systems are dynamical systems that can be controlled by a combination of both continuous and discrete actions. In this paper we study the approximation of optimal control problems associated to this kind of systems, and in particular of the quasi-variational inequality which characterizes the value function. Our main result features the error estimates between the value function of the problem and its approximation. We also focus on the hypotheses describing the mathematical model and the properties defining the class of numerical scheme for which the result holds true.

Keywords

Hybrid control Dynamic Programming Semi-Lagrangian schemes Error estimates 

Mathematics Subject Classification

34A38 49L20 49M25 49N25 65K15 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Dipartimento di Matematica e FisicaUniversità Roma TreRomaItaly
  2. 2.Unité de Maths Appl. (UMA)ENSTA ParisTechPalaiseauFrance

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