# Forward-Backward Extended DMD with an Asymptotic Stability Constraint

arXiv: https://arxiv.org/abs/2403.10623 · HTML: https://mlsanity.com/paper/2403.10623/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Mar 2024.

## Built on by (most cited first, 3 of 3)

- [On Dominant Manifolds in Reservoir Computing Networks](https://mlsanity.com/paper/2604.05967/) (2026)
- [Deep Koopman-layered Model with Universal Property Based on Toeplitz Matrices](https://mlsanity.com/paper/2410.02199/) (2024)
- [Reduced-Order Surrogates for Forced Flexible Mesh Coastal-Ocean Models](https://mlsanity.com/paper/2602.05416/) (2026)

## Abstract (arXiv)

This paper presents a data-driven method to identify an asymptotically stable Koopman system from noisy data. In particular, the proposed approach combines approximations of the system's forward- and backward-in-time dynamics to reduce bias caused by noisy data while enforcing asymptotic stability. A Koopman model of an inherently asymptotically stable system can be unstable due to noisy data and a poor choice of lifting functions. To prevent identifying an unstable model, the proposed approach imposes an asymptotic stability constraint on the Koopman model. The proposed method is formulated as a semidefinite program and its performance is compared to state-of-the-art methods with a simulated Duffing oscillator dataset and experimental soft robot dataset.