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Representation of practical nonsmooth control Lyapunov functions by piecewise affine functions and neural networks

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00008837
URN to cite this document: urn:nbn:de:bvb:703-epub-8837-0

Title data

Grüne, Lars ; Sperl, Mario ; Chatterjee, Debasish:
Representation of practical nonsmooth control Lyapunov functions by piecewise affine functions and neural networks.
In: Systems & Control Letters. Vol. 202 (2025) . - 106103.
ISSN 1872-7956
DOI der Verlagsversion: https://doi.org/10.1016/j.sysconle.2025.106103

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Nichtlineare optimale Feedback-Regelung mit tiefen neuronalen Netzen ohne den Fluch der Dimension: Räumlich abnehmende Sensitivität und nichtglatte Probleme
463912816
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Project financing: Deutsche Forschungsgemeinschaft

Abstract

In this paper we give conditions under which control Lyapunov functions exist that can be represented by either piecewise affine functions or by neural networks with a suitable number of ReLU layers. The results provide a theoretical foundation for recent computational approaches for computing control Lyapunov functions with optimization-based and machine-learning techniques.

Further data

Item Type: Article in a journal
Additional notes (visible to public): 8 pages
Keywords: control Lyapunov function; semiconcave function; piecewise affine function; ReLU neural network
DDC Subjects: 500 Science > 510 Mathematics
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
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-8837-0
Date Deposited: 30 Jan 2026 08:54
Last Modified: 31 Jan 2026 05:53
URI: https://epub.uni-bayreuth.de/id/eprint/8837
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