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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_00008094
URN to cite this document: urn:nbn:de:bvb:703-epub-8094-9

Title data

Chatterjee, Debasish ; Grüne, Lars ; Sperl, Mario:
Representation of practical nonsmooth control Lyapunov functions by piecewise affine functions and neural networks.
Bayreuth , 2024 . - 8 S.

Format:	PDF
Name:	main.pdf
Version:	Preprint
Available under License	German copyright law. The document may be used free of charge for personal use. In addition, the reproduction, editing, distribution and any kind of exploitation require the written consent of the respective rights holder.

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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 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:	Preprint, postprint
Keywords:	control Lyapunov function; semiconcave function; piecewise affine function; ReLU neural network
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-8094-9
Date Deposited:	13 Dec 2024 08:16
Last Modified:	13 Dec 2024 08:17
URI:	https://epub.uni-bayreuth.de/id/eprint/8094

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