Positively Invariant Sets for ODEs and Numerical Integration

Peter Giesl; Sigurdur Hafstein; Iman Mehrabinezhad

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Paper

Positively Invariant Sets for ODEs and Numerical Integration

Topics: Nonlinear Signals and Systems; Optimization Algorithms

In Proceedings of the 20th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO, 44-53, 2023 , Rome, Italy

Authors: Peter Giesl ¹ ; Sigurdur Hafstein ² and Iman Mehrabinezhad ²

Affiliations: ¹ Department of Mathematics, University of Sussex, Falmer, BN1 9QH, U.K. ; ² Science Institute, University of Iceland, Dunhagi 3, 107 Reykjavík, Iceland

Keyword(s): Positively Invariant Sets, Ordinary Differential Equations, Numerical Integration.

Abstract: We show that for an ordinary differential equation (ODE) with an exponentially stable equilibrium and any compact subset of its basin of attraction, we can find a larger compact set that is positively invariant for both the dynamics of the system and a numerical method to approximate its solution trajectories. We establish this for both one-step numerical integrators and multi-step integrators using sufficiently small time-steps. Further, we show how to localize such sets using continuously differentiable Lyapunov-like functions and numerically computed continuous, piecewise affine (CPA) Lyapunov-like functions.

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Paper citation in several formats:

Giesl, P., Hafstein, S. and Mehrabinezhad, I. (2023). Positively Invariant Sets for ODEs and Numerical Integration. In Proceedings of the 20th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO; ISBN 978-989-758-670-5; ISSN 2184-2809, SciTePress, pages 44-53. DOI: 10.5220/0012189700003543

@conference{icinco23,
author={Peter Giesl and Sigurdur Hafstein and Iman Mehrabinezhad},
title={Positively Invariant Sets for ODEs and Numerical Integration},
booktitle={Proceedings of the 20th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO},
year={2023},
pages={44-53},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0012189700003543},
isbn={978-989-758-670-5},
issn={2184-2809},
}

TY - CONF

JO - Proceedings of the 20th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO
TI - Positively Invariant Sets for ODEs and Numerical Integration
SN - 978-989-758-670-5
IS - 2184-2809
AU - Giesl, P.
AU - Hafstein, S.
AU - Mehrabinezhad, I.
PY - 2023
SP - 44
EP - 53
DO - 10.5220/0012189700003543
PB - SciTePress