# An Energy-based Approach to Ensure the Stability of Learned Dynamical Systems

arXiv: https://arxiv.org/abs/2003.11290 · HTML: https://mlsanity.com/paper/2003.11290/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Mar 2020.

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

- [Continual Learning from Demonstration of Robotics Skills](https://mlsanity.com/paper/2202.06843/) (2022)
- [Scalable and Efficient Continual Learning from Demonstration via a Hypernetwork-generated Stable Dynamics Model](https://mlsanity.com/paper/2311.03600/) (2023)
- [Fusion Dynamical Systems with Machine Learning in Imitation Learning: A Comprehensive Overview](https://mlsanity.com/paper/2403.19916/) (2024)
- [Periodic DMP formulation for Quaternion Trajectories](https://mlsanity.com/paper/2110.10510/) (2021)
- [Imitation Learning-based Visual Servoing for Tracking Moving Objects](https://mlsanity.com/paper/2309.07729/) (2023)
- [Learning Orbitally Stable Systems for Diagrammatically Teaching](https://mlsanity.com/paper/2309.10298/) (2023)
- [A Robust Task-Level Control Architecture for Learned Dynamical Systems](https://mlsanity.com/paper/2511.09790/) (2025)

## Abstract (arXiv)

Non-linear dynamical systems represent a compact, flexible, and robust tool for reactive motion generation. The effectiveness of dynamical systems relies on their ability to accurately represent stable motions. Several approaches have been proposed to learn stable and accurate motions from demonstration. Some approaches work by separating accuracy and stability into two learning problems, which increases the number of open parameters and the overall training time. Alternative solutions exploit single-step learning but restrict the applicability to one regression technique. This paper presents a single-step approach to learn stable and accurate motions that work with any regression technique. The approach makes energy considerations on the learned dynamics to stabilize the system at run-time while introducing small deviations from the demonstrated motion. Since the initial value of the energy injected into the system affects the reproduction accuracy, it is estimated from training data using an efficient procedure. Experiments on a real robot and a comparison on a public benchmark shows the effectiveness of the proposed approach.