Controlling nonlinear dynamical systems into arbitrary states using machine learning

Abstract 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...

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Autores principales:	Alexander Haluszczynski, Christoph Räth
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/79566013c83c4808a31f467f4f6ba7ab
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spelling	oai:doaj.org-article:79566013c83c4808a31f467f4f6ba7ab2021-12-02T18:02:55ZControlling nonlinear dynamical systems into arbitrary states using machine learning10.1038/s41598-021-92244-62045-2322https://doaj.org/article/79566013c83c4808a31f467f4f6ba7ab2021-06-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-92244-6https://doaj.org/toc/2045-2322Abstract 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.Alexander HaluszczynskiChristoph RäthNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-8 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Alexander Haluszczynski Christoph Räth Controlling nonlinear dynamical systems into arbitrary states using machine learning
description	Abstract 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.
format	article
author	Alexander Haluszczynski Christoph Räth
author_facet	Alexander Haluszczynski Christoph Räth
author_sort	Alexander Haluszczynski
title	Controlling nonlinear dynamical systems into arbitrary states using machine learning
title_short	Controlling nonlinear dynamical systems into arbitrary states using machine learning
title_full	Controlling nonlinear dynamical systems into arbitrary states using machine learning
title_fullStr	Controlling nonlinear dynamical systems into arbitrary states using machine learning
title_full_unstemmed	Controlling nonlinear dynamical systems into arbitrary states using machine learning
title_sort	controlling nonlinear dynamical systems into arbitrary states using machine learning
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/79566013c83c4808a31f467f4f6ba7ab
work_keys_str_mv	AT alexanderhaluszczynski controllingnonlineardynamicalsystemsintoarbitrarystatesusingmachinelearning AT christophrath controllingnonlineardynamicalsystemsintoarbitrarystatesusingmachinelearning
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Controlling nonlinear dynamical systems into arbitrary states using machine learning

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