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

Title data

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

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Project financing:	Deutsche Forschungsgemeinschaft

Abstract in another language

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.

Further data

Item Type:	Article in a journal
Refereed:	Yes
Additional notes:	to appear
Keywords:	deep neural network; Lyapunov function; stability; small-gain condition; curse of dimensionality
Institutions of the University:	Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics Profile Fields Profile Fields > Advanced Fields Profile Fields > Advanced Fields > Nonlinear Dynamics Research Institutions > Research Centres > Forschungszentrum für Modellbildung und Simulation (MODUS) Research Institutions Research Institutions > Research Centres
Result of work at the UBT:	Yes
DDC Subjects:	500 Science > 510 Mathematics
Date Deposited:	20 May 2020 07:19
Last Modified:	27 Sep 2021 04:53
URI:	https://eref.uni-bayreuth.de/id/eprint/55190

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Overcoming the curse of dimensionality for approximating Lyapunov functions with deep neural networks under a small-gain condition. (deposited 27 Jan 2020 14:16)
- Overcoming the curse of dimensionality for approximating Lyapunov functions with deep neural networks under a small-gain condition. (deposited 20 May 2020 07:19) [Currently Displayed]