# Model-free tracking control of complex dynamical trajectories with machine learning

arXiv: https://arxiv.org/abs/2309.11470 · HTML: https://mlsanity.com/paper/2309.11470/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 77 references that are in the map.
- First posted on arXiv 20 Sep 2023.

## Builds on (most cited first, 11 of 11)

- [Next Generation Reservoir Computing](https://mlsanity.com/paper/2106.07688/) (2021)
- [A Tour of Reinforcement Learning: The View from Continuous Control](https://mlsanity.com/paper/1806.09460/) (2018)
- [Machine learning prediction of critical transition and system collapse](https://mlsanity.com/paper/2012.01545/) (2020)
- [Machine Learning from a Continuous Viewpoint](https://mlsanity.com/paper/1912.12777/) (2019)
- [Model-free prediction of spatiotemporal dynamical systems with recurrent neural networks: Role of network spectral radius](https://mlsanity.com/paper/1910.04426/) (2019)
- [Anticipating synchronization with machine learning](https://mlsanity.com/paper/2103.13358/) (2021)
- [Model-Free Control of Dynamical Systems with Deep Reservoir Computing](https://mlsanity.com/paper/2010.02285/) (2020)
- [Structure-based control of complex networks with nonlinear dynamics](https://mlsanity.com/paper/1605.08415/) (2016)
- [Irrelevance of linear controllability to nonlinear dynamical networks](https://mlsanity.com/paper/1909.01288/) (2019)
- [Machine Learning and Control Theory](https://mlsanity.com/paper/2006.05604/) (2020)
- [Locally Optimal Control of Complex Networks](https://mlsanity.com/paper/1710.07657/) (2017)

## Built on by (most cited first, 13 of 13)

- [Controlling Chaos Using Edge Computing Hardware](https://mlsanity.com/paper/2406.12876/) (2024)
- [Data-driven model discovery with Kolmogorov-Arnold networks](https://mlsanity.com/paper/2409.15167/) (2024)
- [Kolmogorov-Arnold Network Autoencoders](https://mlsanity.com/paper/2410.02077/) (2024)
- [Machine-learning parameter tracking with partial state observation](https://mlsanity.com/paper/2311.09142/) (2023)
- [Conservation-informed Graph Learning for Spatiotemporal Dynamics Prediction](https://mlsanity.com/paper/2412.20962/) (2024)
- [Unsupervised learning for anticipating critical transitions](https://mlsanity.com/paper/2501.01579/) (2025)
- [Confabulation dynamics in a reservoir computer: Filling in the gaps with untrained attractors](https://mlsanity.com/paper/2505.04792/) (2025)
- [Learning to learn ecosystems from limited data -- a meta-learning approach](https://mlsanity.com/paper/2410.07368/) (2024)
- [Reconstructing dynamics from sparse observations with no training on target system](https://mlsanity.com/paper/2410.21222/) (2024)
- [Temporal Convolution Derived Multi-Layered Reservoir Computing](https://mlsanity.com/paper/2407.06771/) (2024)
- [Machine learning approach to detect dynamical states from recurrence measures](https://mlsanity.com/paper/2401.10298/) (2024)
- [Tree-based Learning for High-Fidelity Prediction of Chaos](https://mlsanity.com/paper/2403.13836/) (2024)
- [Deficiency of equation-finding approach to data-driven modeling of dynamical systems](https://mlsanity.com/paper/2509.03769/) (2025)

## Abstract (arXiv)

Nonlinear tracking control enabling a dynamical system to track a desired trajectory is fundamental to robotics, serving a wide range of civil and defense applications. In control engineering, designing tracking control requires complete knowledge of the system model and equations. We develop a model-free, machine-learning framework to control a two-arm robotic manipulator using only partially observed states, where the controller is realized by reservoir computing. Stochastic input is exploited for training, which consists of the observed partial state vector as the first and its immediate future as the second component so that the neural machine regards the latter as the future state of the former. In the testing (deployment) phase, the immediate-future component is replaced by the desired observational vector from the reference trajectory. We demonstrate the effectiveness of the control framework using a variety of periodic and chaotic signals, and establish its robustness against measurement noise, disturbances, and uncertainties.