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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.

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Project information

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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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