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URN to cite this document: urn:nbn:de:bvb:703-epub-8856-5
Title data
Sperl, Mario ; Mysliwitz, Jonas ; Grüne, Lars:
On the existence and neural network representation of separable control Lyapunov functions.
In: Automatica.
Vol. 182
(2025)
.
- 112517.
ISSN 0005-1098
DOI der Verlagsversion: https://doi.org/10.1016/j.automatica.2025.112517
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Project information
| Project title: |
Project's official title Project's id Nichtlineare optimale Feedback-Regelung mit tiefen neuronalen Netzen ohne den Fluch der Dimension: Räumlich abnehmende Sensitivität und nichtglatte Probleme 463912816 Open Access Publizieren No information |
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| Project financing: |
Deutsche Forschungsgemeinschaft |
Abstract
In this paper, we investigate the ability of neural networks to mitigate the curse of dimensionality in representing control Lyapunov functions. To achieve this, we first prove an error bound for the approximation of separable functions with neural networks. Subsequently, we discuss conditions on the existence of separable control Lyapunov functions, drawing upon tools from nonlinear control theory. This enables us to bridge the gap between neural networks and the approximation of control Lyapunov functions. Moreover, we present a network architecture and a training algorithm to illustrate the theoretical findings on a 10-dimensional control system.
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