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

Lars Grüne

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arXiv · 2001.08423

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

Lars Grüne

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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.

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BibTeX RIS

Lars Grüne. 2020-01-23. Overcoming the curse of dimensionality for approximating Lyapunov functions with deep neural networks under a small-gain condition. https://arxiv.org/abs/2001.08423

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