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

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 p.
DOI: https://doi.org/10.15495/EPub_UBT_00008094

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 another language

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
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
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 07 Jan 2025 14:17
Last Modified: 07 Jan 2025 14:17
URI: https://eref.uni-bayreuth.de/id/eprint/91515