Efficient Algorithms for Simplicial Complexes Used in the Computation of Lyapunov Functions for Nonlinear Systems

Sigurdur Freyr Hafstein

2017

Abstract

Several algorithms have been suggested to parameterize continuous and piecewise affine Lyapunov functions for nonlinear systems in various settings. In these algorithms linear constraints are formulated for the values of a Lyapunov function at all vertices of a simplicial complex. They are then either solved using convex optimization or computed by other means and then verified. Originally these algorithms were designed for continuous-time systems and their adaptation to discrete-time systems and control systems poses some challenges in designing and implementing efficient algorithms and data structures for simplicial complexes. In this paper we discuss several of these and give efficient implementations in C++

Paper Citation

in Harvard Style

Freyr Hafstein S. (2017). Efficient Algorithms for Simplicial Complexes Used in the Computation of Lyapunov Functions for Nonlinear Systems . In Proceedings of the 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH, ISBN 978-989-758-265-3, pages 398-409. DOI: 10.5220/0006480003980409

in Bibtex Style

@conference{simultech17,
author={Sigurdur Freyr Hafstein},
title={Efficient Algorithms for Simplicial Complexes Used in the Computation of Lyapunov Functions for Nonlinear Systems},
booktitle={Proceedings of the 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,},
year={2017},
pages={398-409},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0006480003980409},
isbn={978-989-758-265-3},
}

in EndNote Style

TY - CONF
JO - Proceedings of the 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,
TI - Efficient Algorithms for Simplicial Complexes Used in the Computation of Lyapunov Functions for Nonlinear Systems
SN - 978-989-758-265-3
AU - Freyr Hafstein S.
PY - 2017
SP - 398
EP - 409
DO - 10.5220/0006480003980409