ERef Bayreuth

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

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: https://doi.org/10.1016/j.sysconle.2025.106103

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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 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:	Article in a journal
Refereed:	Yes
Additional notes:	8 pages
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:	28 Apr 2025 07:24
Last Modified:	28 Apr 2025 07:24
URI:	https://eref.uni-bayreuth.de/id/eprint/93357

Available Versions of this Item

Representation of practical nonsmooth control Lyapunov functions by piecewise affine functions and neural networks. (deposited 07 Jan 2025 14:17)
- Representation of practical nonsmooth control Lyapunov functions by piecewise affine functions and neural networks. (deposited 10 Feb 2025 07:40)
  - Representation of practical nonsmooth control Lyapunov functions by piecewise affine functions and neural networks. (deposited 28 Apr 2025 07:24) [Currently Displayed]