Controlling Chaotic Maps using Next-Generation Reservoir Computing

TL;DR

This paper introduces a novel reservoir computing-based controller capable of stabilizing and controlling chaotic systems efficiently, requiring minimal data and demonstrating robustness to noise and errors.

Contribution

It presents a new control method combining reservoir computing with nonlinear control techniques for chaotic maps, achieving rapid and robust control with minimal training data.

Findings

Successfully controlled the Hénon map to various states

Achieved control with only 10 training data points

Controlled system in a single iteration

Abstract

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 H\'enon 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.