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

Titelangaben

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

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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.