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Chatterjee, Debasish ; Grüne, Lars ; Sperl, Mario:
Representation of practical nonsmooth control Lyapunov functions by piecewise affine functions and neural networks.
Bayreuth
,
2024
. - 8 S.
DOI: https://doi.org/10.15495/EPub_UBT_00008094
Angaben zu Projekten
| Projekttitel: |
Offizieller Projekttitel Projekt-ID Curse-of-dimensionality-free nonlinear optimal feedback control with deep neural networks. A compositionality-based approach via Hamilton-Jacobi-Bellman PDEs 463912816 |
|---|---|
| Projektfinanzierung: |
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.