文章基本信息

标题：Overcoming the curse of dimensionality for approximating Lyapunov functions with deep neural networks under a small-gain condition
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作者：Lars Grüne
期刊名称：IFAC PapersOnLine
印刷版ISSN：2405-8963
出版年度：2021
卷号：54
期号：9
页码：317-322
DOI：10.1016/j.ifacol.2021.06.152
语种：English
出版社：Elsevier
摘要：AbstractWe 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.
关键词：Keywordsdeep neural networkLyapunov functionstabilitysmall-gain conditioncurse of dimensionality