Space-Filling Regularization for Robust and Interpretable Nonlinear State Space Models

Hermann Klein, Max Heinz Herkersdorf, Oliver Nelles

2025

Abstract

The state space dynamics representation is the most general approach for nonlinear systems and often chosen for system identification. During training, the state trajectory can deform significantly leading to poor data coverage of the state space. This can cause significant issues for space-oriented training algorithms which e.g. rely on grid structures, tree partitioning, or similar. Besides hindering training, significant state trajectory deformations also deteriorate interpretability and robustness properties. This paper proposes a new type of space-filling regularization that ensures a favorable data distribution in state space via introducing a data-distribution-based penalty. This method is demonstrated in local model network architectures where good interpretability is a major concern. The proposed approach integrates ideas from modeling and design of experiments for state space structures. This is why we present two regularization techniques for the data point distributions of the state trajectories for local affine state space models. Beyond that, we demonstrate the results on a widely known system identification benchmark.

Paper Citation

in Harvard Style

Klein H., Herkersdorf M. and Nelles O. (2025). Space-Filling Regularization for Robust and Interpretable Nonlinear State Space Models. In Proceedings of the 22nd International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO; ISBN 978-989-758-770-2, SciTePress, pages 409-416. DOI: 10.5220/0013698800003982

in Bibtex Style

@conference{icinco25,
author={Hermann Klein and Max Herkersdorf and Oliver Nelles},
title={Space-Filling Regularization for Robust and Interpretable Nonlinear State Space Models},
booktitle={Proceedings of the 22nd International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO},
year={2025},
pages={409-416},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0013698800003982},
isbn={978-989-758-770-2},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 22nd International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO
TI - Space-Filling Regularization for Robust and Interpretable Nonlinear State Space Models
SN - 978-989-758-770-2
AU - Klein H.
AU - Herkersdorf M.
AU - Nelles O.
PY - 2025
SP - 409
EP - 416
DO - 10.5220/0013698800003982
PB - SciTePress