Controlling Chaotic Maps using Next-Generation Reservoir Computing

In this work, we combine nonlinear system control techniques with next-generation reservoir computing, a best-in-class machine learning approach for predicting the behavior of dynamical systems. We demonstrate the performance of the controller in a series of control tasks for the chaotic Hénon map,...

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Bibliographic Details
Published inarXiv.org
Main Authors Kent, Robert M, Barbosa, Wendson A S, Gauthier, Daniel J
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 02.02.2024
Subjects
Computation
Computer Science - Learning
Computer Science - Neural and Evolutionary Computing
Computer Science - Systems and Control
Control systems
Control tasks
Controllers
Data points
Dynamical systems
Iterative methods
Machine learning
Nonlinear control
Nonlinear systems
Orbits
Physics - Chaotic Dynamics
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Summary:In this work, we combine nonlinear system control techniques with next-generation reservoir computing, a best-in-class machine learning approach for predicting the behavior of dynamical systems. We demonstrate the performance of the controller in a series of control tasks for the chaotic Hénon map, including controlling the system between unstable fixed-points, stabilizing the system to higher order periodic orbits, and to an arbitrary desired state. We show that our controller succeeds in these tasks, requires only 10 data points for training, can control the system to a desired trajectory in a single iteration, and is robust to noise and modeling error.
ISSN:2331-8422
DOI:10.48550/arxiv.2307.03813