# Learning Stabilizable Deep Dynamics Models

arXiv: https://arxiv.org/abs/2203.09710 · HTML: https://mlsanity.com/paper/2203.09710/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 19 references that are in the map.
- First posted on arXiv 18 Mar 2022.

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

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Neural Lyapunov Control](https://mlsanity.com/paper/2005.00611/) (2020)
- [Learning Stable Deep Dynamics Models](https://mlsanity.com/paper/2001.06116/) (2020)
- [ImitationFlow: Learning Deep Stable Stochastic Dynamic Systems by Normalizing Flows](https://mlsanity.com/paper/2010.13129/) (2020)
- [Learning Dynamics Models with Stable Invariant Sets](https://mlsanity.com/paper/2006.08935/) (2020)
- [Learning Stable Deep Dynamics Models for Partially Observed or Delayed Dynamical Systems](https://mlsanity.com/paper/2110.14296/) (2021)
- [Almost Surely Stable Deep Dynamics](https://mlsanity.com/paper/2103.14722/) (2021)
- [Data-Driven Internal Model Control of Second-Order Discrete Volterra Systems](https://mlsanity.com/paper/2003.14158/) (2020)
- [Structured Hammerstein-Wiener Model Learning for Model Predictive Control](https://mlsanity.com/paper/2107.04247/) (2021)
- [Data-Based System Analysis and Control of Flat Nonlinear Systems](https://mlsanity.com/paper/2103.02892/) (2021)

## Built on by (most cited first, 2 of 2)

- [Data-Driven Control with Inherent Lyapunov Stability](https://mlsanity.com/paper/2303.03157/) (2023)
- [A Policy Optimization Method Towards Optimal-time Stability](https://mlsanity.com/paper/2301.00521/) (2023)

## Abstract (arXiv)

When neural networks are used to model dynamics, properties such as stability of the dynamics are generally not guaranteed. In contrast, there is a recent method for learning the dynamics of autonomous systems that guarantees global exponential stability using neural networks. In this paper, we propose a new method for learning the dynamics of input-affine control systems. An important feature is that a stabilizing controller and control Lyapunov function of the learned model are obtained as well. Moreover, the proposed method can also be applied to solving Hamilton-Jacobi inequalities. The usefulness of the proposed method is examined through numerical examples.