Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

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

Error Estimates for Numerical Approximation of Hamilton–Jacobi Equations Related to Hybrid... 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 approx- imation. 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 This work is partially supported by the EU under the 7th Framework Programme Marie Curie Initial Training Network “FP7-PEOPLE-2010-ITN”, SADCO project, GA Number 264735-SADCO. For the second and third authors, also by iCODE Institute project funded by the IDEX Paris-Saclay, ANR-11-IDEX-0003-02. The first author has also been funded by Roma Tre University and INdAM–GNCS. B R. Ferretti ferretti@mat.uniroma3.it A. Sassi ach.sassi@gmail.com H. Zidani hasnaa.zidani@ensta-paristech.fr Dipartimento di Matematica e Fisica, Università Roma Tre, L.go S. Leonardo Murialdo, 1, 00146 Roma, Italy Unité de Maths Appl. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

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

Download PDF
37 pages

Loading next page...
 
/lp/springer-journals/error-estimates-for-numerical-approximation-of-hamilton-jacobi-yZRCwe17ky

References (20)

Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
DOI
10.1007/s00245-018-9515-8
Publisher site
See Article on Publisher Site

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 approx- imation. 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 This work is partially supported by the EU under the 7th Framework Programme Marie Curie Initial Training Network “FP7-PEOPLE-2010-ITN”, SADCO project, GA Number 264735-SADCO. For the second and third authors, also by iCODE Institute project funded by the IDEX Paris-Saclay, ANR-11-IDEX-0003-02. The first author has also been funded by Roma Tre University and INdAM–GNCS. B R. Ferretti ferretti@mat.uniroma3.it A. Sassi ach.sassi@gmail.com H. Zidani hasnaa.zidani@ensta-paristech.fr Dipartimento di Matematica e Fisica, Università Roma Tre, L.go S. Leonardo Murialdo, 1, 00146 Roma, Italy Unité de Maths Appl.

Journal

Applied Mathematics and Optimization – Springer Journals

Published: Aug 9, 2018

There are no references for this article.