Login
Publications by the same author
plus in the repository
plus in Google Scholar
Bibliografische Daten exportieren		  

On the Existence and Neural Network Representation of Separable Control Lyapunov Functions

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00008101
URN to cite this document: urn:nbn:de:bvb:703-epub-8101-5

Title data

Sperl, Mario ; Mysliwitz, Jonas ; Grüne, Lars:
On the Existence and Neural Network Representation of Separable Control Lyapunov Functions.
Bayreuth , 2025 . - 11 S.

This is the latest version of this item.

[thumbnail of SeparableCLF_NN.pdf]
Format: PDF
Name: SeparableCLF_NN.pdf
Version: Updated Version
Available under License Creative Commons BY 4.0: Attribution
Download (1MB)

Project information

Project title:
Project's official title
Project's id
Curse-of-dimensionality-free nonlinear optimal feedback control with deep neural networks. A compositionality-based approach via Hamilton-Jacobi-Bellman PDEs
463912816
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.

Further data

Item Type: Preprint, postprint
Additional notes (visible to public): Preprint submitted to Automatica
Keywords: control Lyapunov functions; neural networks; curse of dimensionality
DDC Subjects: 500 Science > 510 Mathematics
Institutions of the University: 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 > Advanced Fields > Nonlinear Dynamics
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)
Profile Fields
Profile Fields > Advanced Fields
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-8101-5
Date Deposited: 09 Jan 2025 08:05
Last Modified: 09 Jan 2025 08:05
URI: https://epub.uni-bayreuth.de/id/eprint/8101

Available Versions of this Item

Download Statistics

Downloads

Downloads per month over past year