# Inference of Continuous Linear Systems from Data with Guaranteed Stability

arXiv: https://arxiv.org/abs/2301.10060 · HTML: https://mlsanity.com/paper/2301.10060/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 28 references that are in the map.
- First posted on arXiv 24 Jan 2023.

## Builds on (most cited first, 10 of 10)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Dynamic mode decomposition with control](https://mlsanity.com/paper/1409.6358/) (2014)
- [Discovery of Nonlinear Dynamical Systems using a Runge-Kutta Inspired Dictionary-based Sparse Regression Approach](https://mlsanity.com/paper/2105.04869/) (2021)
- [Physics-informed regularization and structure preservation for learning stable reduced models from data with operator inference](https://mlsanity.com/paper/2107.02597/) (2021)
- [Operator inference with roll outs for learning reduced models from scarce and low-quality data](https://mlsanity.com/paper/2212.01418/) (2022)
- [On computing the distance to stability for matrices using linear dissipative Hamiltonian systems](https://mlsanity.com/paper/1611.00595/) (2016)
- [Approximating the nearest stable discrete-time system](https://mlsanity.com/paper/1802.08033/) (2018)
- [Vector Fitting for Matrix-valued Rational Approximation](https://mlsanity.com/paper/1503.00411/) (2015)
- [On Reduced Input-Output Dynamic Mode Decomposition](https://mlsanity.com/paper/1712.08447/) (2017)

## Abstract (arXiv)

Machine-learning technologies for learning dynamical systems from data play an important role in engineering design. This research focuses on learning continuous linear models from data. Stability, a key feature of dynamic systems, is especially important in design tasks such as prediction and control. Thus, there is a need to develop methodologies that provide stability guarantees. To that end, we leverage the parameterization of stable matrices proposed in [Gillis/Sharma, Automatica, 2017] to realize the desired models. Furthermore, to avoid the estimation of derivative information to learn continuous systems, we formulate the inference problem in an integral form. We also discuss a few extensions, including those related to control systems. Numerical experiments show that the combination of a stable matrix parameterization and an integral form of differential equations allows us to learn stable systems without requiring derivative information, which can be challenging to obtain in situations with noisy or limited data.