# Learning Stable Models for Prediction and Control

arXiv: https://arxiv.org/abs/2005.04291 · HTML: https://mlsanity.com/paper/2005.04291/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 May 2020.

## Built on by (most cited first, 12 of 12)

- [DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecasting](https://mlsanity.com/paper/2306.01984/) (2023)
- [Dynamical Diffusion: Learning Temporal Dynamics with Diffusion Models](https://mlsanity.com/paper/2503.00951/) (2025)
- [Koopman Spectrum Nonlinear Regulators and Efficient Online Learning](https://mlsanity.com/paper/2106.15775/) (2021)
- [Generalizing Dynamic Mode Decomposition: Balancing Accuracy and Expressiveness in Koopman Approximations](https://mlsanity.com/paper/2108.03712/) (2021)
- [Leveraging Neural Koopman Operators to Learn Continuous Representations of Dynamical Systems from Scarce Data](https://mlsanity.com/paper/2303.06972/) (2023)
- [Stable Linear Subspace Identification: A Machine Learning Approach](https://mlsanity.com/paper/2311.03197/) (2023)
- [Data-Driven Encoding: A New Numerical Method for Computation of the Koopman Operator](https://mlsanity.com/paper/2301.06542/) (2023)
- [Invertible Koopman neural operator for data-driven modeling of partial differential equations](https://mlsanity.com/paper/2503.19717/) (2025)
- [Koopman operator theory: fundamentals, control, and applications](https://mlsanity.com/paper/2607.01819/) (2026)
- [Learned Lifted Linearization Applied to Unstable Dynamic Systems Enabled by Koopman Direct Encoding](https://mlsanity.com/paper/2210.13602/) (2022)
- [MSACL: Multi-Step Actor-Critic Learning with Lyapunov Certificates for Exponentially Stabilizing Control](https://mlsanity.com/paper/2512.24955/) (2025)
- [Reinforcement learning in linear embedding space unlocks generalizable control across soft robot configurations](https://mlsanity.com/paper/2606.08104/) (2026)

## Abstract (arXiv)

This paper demonstrates the benefits of imposing stability on data-driven Koopman operators. The data-driven identification of stable Koopman operators (DISKO) is implemented using an algorithm citemamakoukasstableLDS2020 that computes the nearest textitstable matrix solution to a least-squares reconstruction error. As a first result, we derive a formula that describes the prediction error of Koopman representations for an arbitrary number of time steps, and which shows that stability constraints can improve the predictive accuracy over long horizons. As a second result, we determine formal conditions on basis functions of Koopman operators needed to satisfy the stability properties of an underlying nonlinear system. As a third result, we derive formal conditions for constructing Lyapunov functions for nonlinear systems out of stable data-driven Koopman operators, which we use to verify stabilizing control from data. Lastly, we demonstrate the benefits of DISKO in prediction and control with simulations using a pendulum and a quadrotor and experiments with a pusher-slider system. The paper is complemented with a video: urlhttps://sites.google.com/view/learning-stable-koopman.