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Controlling chaotic maps using next-generation reservoir computing.

Robert M Kent1, Wendson A S Barbosa1, Daniel J Gauthier1,2

  • 1Department of Physics, The Ohio State University, 191 W. Woodruff Ave., Columbus, Ohio 43210, USA.

Chaos (Woodbury, N.Y.)
|February 2, 2024
PubMed
Summary
This summary is machine-generated.

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This study introduces a novel controller merging nonlinear system control with reservoir computing for predicting dynamical systems. The method effectively controls chaotic systems with minimal data, showing robustness to noise and errors.

Area of Science:

  • Dynamical Systems and Control Theory
  • Machine Learning and Artificial Intelligence
  • Nonlinear Dynamics

Background:

  • Dynamical systems present complex behaviors that are challenging to predict and control.
  • Traditional control methods often struggle with chaotic or high-dimensional systems.
  • Reservoir computing offers a powerful framework for modeling and predicting time-series data from dynamical systems.

Purpose of the Study:

  • To develop and evaluate a novel controller integrating nonlinear system control with reservoir computing.
  • To demonstrate the controller's efficacy in managing complex dynamical systems, specifically the chaotic Hénon map.
  • To assess the controller's performance in terms of data requirements, speed, and robustness.

Main Methods:

  • Combined nonlinear system control techniques with next-generation reservoir computing.

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  • Employed a chaotic Hénon map as a benchmark for control tasks.
  • Trained the controller using a minimal dataset (ten data points).

    • Main Results:

    • Successfully controlled the Hénon map between unstable fixed points and to higher-order periodic orbits.
    • Achieved stabilization to arbitrary desired states.
    • Demonstrated control to a desired trajectory in a single iteration.
    • Showcased controller robustness against noise and modeling errors.

    Conclusions:

    • The proposed controller, merging nonlinear control and reservoir computing, is highly effective for dynamical systems.
    • The approach requires minimal training data and exhibits rapid, robust performance.
    • This method advances the application of machine learning in controlling complex nonlinear systems.