Overcoming the curse of dimensionality for approximating Lyapunov functions with deep neural networks under a small-gain condition

Titelangaben

Grüne, Lars:
Overcoming the curse of dimensionality for approximating Lyapunov functions with deep neural networks under a small-gain condition.
In: IFAC-PapersOnLine. Bd. 54 (2021) Heft 9 . - S. 317-322.
ISSN 2405-8963
DOI: https://doi.org/10.1016/j.ifacol.2021.06.152

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Abstract

We propose a deep neural network architecture for storing approximate Lyapunov functions of systems of ordinary differential equations. Under a small-gain condition on the system, the number of neurons needed for an approximation of a Lyapunov function with fixed accuracy grows only polynomially in the state dimension, i.e., the proposed approach is able to overcome the curse of dimensionality.