# Learning Stabilizable Dynamical Systems via Control Contraction Metrics

arXiv: https://arxiv.org/abs/1808.00113 · HTML: https://mlsanity.com/paper/1808.00113/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jul 2018.

## Built on by (most cited first, 5 of 5)

- [Learning-based Robust Motion Planning with Guaranteed Stability: A Contraction Theory Approach](https://mlsanity.com/paper/2102.12668/) (2021)
- [Learning Contraction Policies from Offline Data](https://mlsanity.com/paper/2112.05911/) (2021)
- [Stable Modular Control via Contraction Theory for Reinforcement Learning](https://mlsanity.com/paper/2311.03669/) (2023)
- [ICODE: Modeling Dynamical Systems with Extrinsic Input Information](https://mlsanity.com/paper/2411.13914/) (2024)
- [Contraction-Aware Reinforcement Learning for Nonlinear Control with Statistical Robustness](https://mlsanity.com/paper/2506.15700/) (2025)

## Abstract (arXiv)

We propose a novel framework for learning stabilizable nonlinear dynamical systems for continuous control tasks in robotics. The key idea is to develop a new control-theoretic regularizer for dynamics fitting rooted in the notion of stabilizability, which guarantees that the learned system can be accompanied by a robust controller capable of stabilizing any open-loop trajectory that the system may generate. By leveraging tools from contraction theory, statistical learning, and convex optimization, we provide a general and tractable semi-supervised algorithm to learn stabilizable dynamics, which can be applied to complex underactuated systems. We validated the proposed algorithm on a simulated planar quadrotor system and observed notably improved trajectory generation and tracking performance with the control-theoretic regularized model over models learned using traditional regression techniques, especially when using a small number of demonstration examples. The results presented illustrate the need to infuse standard model-based reinforcement learning algorithms with concepts drawn from nonlinear control theory for improved reliability.