Contraction Metrics by Numerical Integration and Quadrature: Uniform Error Estimate

Peter Giesl, Sigurdur Hafstein, Iman Mehrabinezhad

2023

Abstract

We show that contraction metrics for continuous time dynamical systems can be computed numerically using numerical integration of certain initial value problems with a subsequent numerical quadrature. Further, we show that for any compact subset of an equilibrium’s basin of attraction and any ε > 0, the parameters for the numerical methods, i.e. the integration interval and the step-size, can be chosen such that the error in the contraction metric is less than ε at any point in the compact subset. These results will be used as a part of a numerical method to rigorously compute contraction metrics.

Paper Citation

in Harvard Style

Giesl P., Hafstein S. and Mehrabinezhad I. (2023). Contraction Metrics by Numerical Integration and Quadrature: Uniform Error Estimate. In Proceedings of the 20th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO; ISBN 978-989-758-670-5, SciTePress, pages 196-205. DOI: 10.5220/0012183300003543

in Bibtex Style

@conference{icinco23,
author={Peter Giesl and Sigurdur Hafstein and Iman Mehrabinezhad},
title={Contraction Metrics by Numerical Integration and Quadrature: Uniform Error Estimate},
booktitle={Proceedings of the 20th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO},
year={2023},
pages={196-205},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0012183300003543},
isbn={978-989-758-670-5},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 20th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO
TI - Contraction Metrics by Numerical Integration and Quadrature: Uniform Error Estimate
SN - 978-989-758-670-5
AU - Giesl P.
AU - Hafstein S.
AU - Mehrabinezhad I.
PY - 2023
SP - 196
EP - 205
DO - 10.5220/0012183300003543
PB - SciTePress