# Controlling Chaotic Maps using Next-Generation Reservoir Computing

arXiv: https://arxiv.org/abs/2307.03813 · HTML: https://mlsanity.com/paper/2307.03813/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 47 references that are in the map.
- First posted on arXiv 7 Jul 2023.

## Builds on (most cited first, 8 of 8)

- [Next Generation Reservoir Computing](https://mlsanity.com/paper/2106.07688/) (2021)
- [Learning Spatiotemporal Chaos Using Next-Generation Reservoir Computing](https://mlsanity.com/paper/2203.13294/) (2022)
- [Model-Free Control of Dynamical Systems with Deep Reservoir Computing](https://mlsanity.com/paper/2010.02285/) (2020)
- [Embedding Theory of Reservoir Computing and Reducing Reservoir Network Using Time Delays](https://mlsanity.com/paper/2303.09042/) (2023)
- [Reservoir kernels and Volterra series](https://mlsanity.com/paper/2212.14641/) (2022)
- [Symmetry-Aware Reservoir Computing](https://mlsanity.com/paper/2102.00310/) (2021)
- [Controlling nonlinear dynamical systems into arbitrary states using machine learning](https://mlsanity.com/paper/2102.12969/) (2021)
- [Incremental Learning and State-Space Evolving Fuzzy Control of Nonlinear Time-Varying Systems with Unknown Model](https://mlsanity.com/paper/2102.09503/) (2021)

## Built on by (most cited first, 7 of 7)

- [Controlling Chaos Using Edge Computing Hardware](https://mlsanity.com/paper/2406.12876/) (2024)
- [Infinite-dimensional next-generation reservoir computing](https://mlsanity.com/paper/2412.09800/) (2024)
- [How more data can hurt: Instability and regularization in next-generation reservoir computing](https://mlsanity.com/paper/2407.08641/) (2024)
- [On the emergence of numerical instabilities in Next Generation Reservoir Computing](https://mlsanity.com/paper/2505.00846/) (2025)
- [Controlling Dynamical Systems into Unseen Target States Using Machine Learning](https://mlsanity.com/paper/2412.10251/) (2024)
- [A tensor network approach for chaotic time series prediction](https://mlsanity.com/paper/2505.17740/) (2025)
- [Taming Epilepsy: Mean Field Control of Whole-Brain Dynamics](https://mlsanity.com/paper/2603.18035/) (2026)

## Abstract (arXiv)

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.