Application of the Schur Complement in Sum of Squares Optimisation

Elias August, Sigurdur Hafstein, Jacopo Piccini, Stefania Andersen, Anna Bavarsad

2024

Abstract

In this paper, we use the Schur Complement in combination with the sum of squares decomposition, first, to determine whether a nonlinear stochastic dynamical systems has a stable equilibrium and, second, to find a stabilising gain matrix for nonlinear dynamical systems. In both cases, we consider systems whose dynamics can be described using polynomial vector fields. Using many different examples, we highlight the effectivity of using our approaches. In some cases, we manage to obtain results that surpass previous ones. We believe that the presented approaches have many potential applications, for example, in the fields of aerospace and quantum control.

Paper Citation

in Harvard Style

August E., Hafstein S., Piccini J., Andersen S. and Bavarsad A. (2024). Application of the Schur Complement in Sum of Squares Optimisation. In Proceedings of the 21st International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO; ISBN 978-989-758-717-7, SciTePress, pages 424-431. DOI: 10.5220/0013016200003822

in Bibtex Style

@conference{icinco24,
author={Elias August and Sigurdur Hafstein and Jacopo Piccini and Stefania Andersen and Anna Bavarsad},
title={Application of the Schur Complement in Sum of Squares Optimisation},
booktitle={Proceedings of the 21st International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO},
year={2024},
pages={424-431},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0013016200003822},
isbn={978-989-758-717-7},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 21st International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO
TI - Application of the Schur Complement in Sum of Squares Optimisation
SN - 978-989-758-717-7
AU - August E.
AU - Hafstein S.
AU - Piccini J.
AU - Andersen S.
AU - Bavarsad A.
PY - 2024
SP - 424
EP - 431
DO - 10.5220/0013016200003822
PB - SciTePress