Controlling Chaotic Maps using Next-Generation Reservoir Computing
This addresses control of chaotic systems for applications in physics or engineering, but it is incremental as it combines existing techniques.
The paper tackled controlling chaotic systems like the Hénon map using next-generation reservoir computing, achieving tasks such as stabilizing periodic orbits with only 10 training data points and single-iteration control.
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.