ERef Bayreuth

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On the existence and neural network representation of separable control Lyapunov functions

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: 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
Project financing:	Deutsche Forschungsgemeinschaft

Abstract in another language

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.

Further data

Item Type:	Article in a journal
Refereed:	Yes
Keywords:	control Lyapunov functions; neural networks; curse of dimensionality
Institutions of the University:	Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics Profile Fields Profile Fields > Advanced Fields Profile Fields > Advanced Fields > Nonlinear Dynamics Research Institutions > Central research institutes > Research Center for AI in Science and Society Research Institutions Research Institutions > Central research institutes
Result of work at the UBT:	Yes
DDC Subjects:	500 Science > 510 Mathematics
Date Deposited:	02 Sep 2025 05:59
Last Modified:	05 Feb 2026 13:48
URI:	https://eref.uni-bayreuth.de/id/eprint/94574

Available Versions of this Item

Approximation of Separable Control Lyapunov Functions with Neural Networks. (deposited 11 Nov 2023 22:01)
- Approximation of Separable Control Lyapunov Functions with Neural Networks. (deposited 22 Aug 2024 08:05)
  - On the Existence and Neural Network Representation of Separable Control Lyapunov Functions. (deposited 09 Jan 2025 10:06)
    - On the Existence and Neural Network Representation of Separable Control Lyapunov Functions. (deposited 20 May 2025 13:01)
      - On the existence and neural network representation of separable control Lyapunov functions. (deposited 02 Sep 2025 05:59) [Currently Displayed]