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Controlling nonlinear dynamical systems into arbitrary states using machine learning

Haluszczynski, Alexander and Räth, Christoph (2021) Controlling nonlinear dynamical systems into arbitrary states using machine learning. Scientific Reports, 11, p. 12991. Nature Publishing Group. doi: 10.1038/s41598-021-92244-6. ISSN 2045-2322.

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Official URL: https://www.nature.com/articles/s41598-021-92244-6


Controlling nonlinear dynamical systems is a central task in many different areas of science and engineering. Chaotic systems can be stabilized (or chaotified) with small perturbations, yet existing approaches either require knowledge about the underlying system equations or large data sets as they rely on phase space methods. In this work we propose a novel and fully data driven scheme relying on machine learning (ML), which generalizes control techniques of chaotic systems without requiring a mathematical model for its dynamics. Exploiting recently developed ML-based prediction capabilities, we demonstrate that nonlinear systems can be forced to stay in arbitrary dynamical target states coming from any initial state. We outline and validate our approach using the examples of the Lorenz and the Rössler system and show how these systems can very accurately be brought not only to periodic, but even to intermittent and different chaotic behavior. Having this highly flexible control scheme with little demands on the amount of required data on hand, we briefly discuss possible applications ranging from engineering to medicine.

Item URL in elib:https://elib.dlr.de/142865/
Document Type:Article
Title:Controlling nonlinear dynamical systems into arbitrary states using machine learning
AuthorsInstitution or Email of AuthorsAuthor's ORCID iDORCID Put Code
Haluszczynski, AlexanderLMU MünchenUNSPECIFIEDUNSPECIFIED
Journal or Publication Title:Scientific Reports
Refereed publication:Yes
Open Access:Yes
Gold Open Access:Yes
In ISI Web of Science:Yes
Page Range:p. 12991
Publisher:Nature Publishing Group
Keywords:Complex Systems, Chaos, Controlling, Prediction, Machine Learning
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Research under Space Conditions
DLR - Research area:Raumfahrt
DLR - Program:R FR - Research under Space Conditions
DLR - Research theme (Project):R - PK-4
Location: Oberpfaffenhofen
Institutes and Institutions:Institute of Materials Physics in Space > Research Group Complex Plasma
Deposited By: Räth, Christoph
Deposited On:14 Jul 2021 15:44
Last Modified:14 Jul 2021 15:44

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