# Data-Driven Control with Inherent Lyapunov Stability

arXiv: https://arxiv.org/abs/2303.03157 · HTML: https://mlsanity.com/paper/2303.03157/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 29 references that are in the map.
- First posted on arXiv 6 Mar 2023.

## Builds on (most cited first, 18 of 18)

- [Learning Hand-Eye Coordination for Robotic Grasping with Deep Learning and Large-Scale Data Collection](https://mlsanity.com/paper/1603.02199/) (2016)
- [Safe Control with Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction methods](https://mlsanity.com/paper/2202.11762/) (2022)
- [Neural Lyapunov Control](https://mlsanity.com/paper/2005.00611/) (2020)
- [Learning Stable Deep Dynamics Models](https://mlsanity.com/paper/2001.06116/) (2020)
- [The Lyapunov Neural Network: Adaptive Stability Certification for Safe Learning of Dynamical Systems](https://mlsanity.com/paper/1808.00924/) (2018)
- [From Motor Control to Team Play in Simulated Humanoid Football](https://mlsanity.com/paper/2105.12196/) (2021)
- [Learning Certified Control using Contraction Metric](https://mlsanity.com/paper/2011.12569/) (2020)
- [Learning Stability Certificates from Data](https://mlsanity.com/paper/2008.05952/) (2020)
- [Neural Lyapunov Control of Unknown Nonlinear Systems with Stability Guarantees](https://mlsanity.com/paper/2206.01913/) (2022)
- [Adaptive-Control-Oriented Meta-Learning for Nonlinear Systems](https://mlsanity.com/paper/2103.04490/) (2021)
- [Learning Stabilizable Nonlinear Dynamics with Contraction-Based Regularization](https://mlsanity.com/paper/1907.13122/) (2019)
- [A Comparative Study of Nonlinear MPC and Differential-Flatness-Based Control for Quadrotor Agile Flight](https://mlsanity.com/paper/2109.01365/) (2021)
- [Learning Contracting Vector Fields For Stable Imitation Learning](https://mlsanity.com/paper/1804.04878/) (2018)
- [Structured Mechanical Models for Robot Learning and Control](https://mlsanity.com/paper/2004.10301/) (2020)
- [Control-oriented meta-learning](https://mlsanity.com/paper/2204.06716/) (2022)
- [Teleoperator Imitation with Continuous-time Safety](https://mlsanity.com/paper/1905.09499/) (2019)
- [Nonlinear System Identification with Prior Knowledge of the Region of Attraction](https://mlsanity.com/paper/2003.12330/) (2020)
- [Learning Stabilizable Deep Dynamics Models](https://mlsanity.com/paper/2203.09710/) (2022)

## Built on by (most cited first, 6 of 6)

- [HardNet: Hard-Constrained Neural Networks with Universal Approximation Guarantees](https://mlsanity.com/paper/2410.10807/) (2024)
- [LMI-Net: Linear Matrix Inequality--Constrained Neural Networks via Differentiable Projection Layers](https://mlsanity.com/paper/2604.05374/) (2026)
- [Certified Training with Branch-and-Bound for Lyapunov-stable Neural Control](https://mlsanity.com/paper/2411.18235/) (2024)
- [ECO: Energy-Constrained Operator Learning for Chaotic Dynamics with Boundedness Guarantees](https://mlsanity.com/paper/2512.01984/) (2025)
- [Neural Lyapunov Function Approximation with Self-Supervised Reinforcement Learning](https://mlsanity.com/paper/2503.15629/) (2025)
- [CAffNet: Hard Constraint-Affine Neural Networks](https://mlsanity.com/paper/2605.24437/) (2026)

## Abstract (arXiv)

Recent advances in learning-based control leverage deep function approximators, such as neural networks, to model the evolution of controlled dynamical systems over time. However, the problem of learning a dynamics model and a stabilizing controller persists, since the synthesis of a stabilizing feedback law for known nonlinear systems is a difficult task, let alone for complex parametric representations that must be fit to data. To this end, we propose Control with Inherent Lyapunov Stability (CoILS), a method for jointly learning parametric representations of a nonlinear dynamics model and a stabilizing controller from data. To do this, our approach simultaneously learns a parametric Lyapunov function which intrinsically constrains the dynamics model to be stabilizable by the learned controller. In addition to the stabilizability of the learned dynamics guaranteed by our novel construction, we show that the learned controller stabilizes the true dynamics under certain assumptions on the fidelity of the learned dynamics. Finally, we demonstrate the efficacy of CoILS on a variety of simulated nonlinear dynamical systems.