# Model-Free Control of Dynamical Systems with Deep Reservoir Computing

arXiv: https://arxiv.org/abs/2010.02285 · HTML: https://mlsanity.com/paper/2010.02285/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Oct 2020.

## Built on by (most cited first, 12 of 12)

- [Next Generation Reservoir Computing](https://mlsanity.com/paper/2106.07688/) (2021)
- [Model-free tracking control of complex dynamical trajectories with machine learning](https://mlsanity.com/paper/2309.11470/) (2023)
- [Controlling Chaos Using Edge Computing Hardware](https://mlsanity.com/paper/2406.12876/) (2024)
- [Attractor reconstruction with reservoir computers: The effect of the reservoir's conditional Lyapunov exponents on faithful attractor reconstruction](https://mlsanity.com/paper/2401.00885/) (2023)
- [Controlling Chaotic Maps using Next-Generation Reservoir Computing](https://mlsanity.com/paper/2307.03813/) (2023)
- [Reservoir Computing Benchmarks: a tutorial review and critique](https://mlsanity.com/paper/2405.06561/) (2024)
- [A Meta-learning Approach to Reservoir Computing: Time Series Prediction with Limited Data](https://mlsanity.com/paper/2110.03722/) (2021)
- [Time-shift selection for reservoir computing using a rank-revealing QR algorithm](https://mlsanity.com/paper/2211.17095/) (2022)
- [Suppressing unknown disturbances to dynamical systems using machine learning](https://mlsanity.com/paper/2307.03690/) (2023)
- [Detecting disturbances in network-coupled dynamical systems with machine learning](https://mlsanity.com/paper/2307.12771/) (2023)
- [Cell reprogramming design by transfer learning of functional transcriptional networks](https://mlsanity.com/paper/2403.04837/) (2024)
- [Deficiency of equation-finding approach to data-driven modeling of dynamical systems](https://mlsanity.com/paper/2509.03769/) (2025)

## Abstract (arXiv)

We propose and demonstrate a nonlinear control method that can be applied to unknown, complex systems where the controller is based on a type of artificial neural network known as a reservoir computer. In contrast to many modern neural-network-based control techniques, which are robust to system uncertainties but require a model nonetheless, our technique requires no prior knowledge of the system and is thus model-free. Further, our approach does not require an initial system identification step, resulting in a relatively simple and efficient learning process. Reservoir computers are well-suited to the control problem because they require small training data sets and remarkably low training times. By iteratively training and adding layers of reservoir computers to the controller, a precise and efficient control law is identified quickly. With examples on both numerical and high-speed experimental systems, we demonstrate that our approach is capable of controlling highly complex dynamical systems that display deterministic chaos to nontrivial target trajectories.