Forward-Backward Extended DMD with an Asymptotic Stability Constraint
<|reference_start|>Forward-Backward Extended DMD with an Asymptotic Stability Constraint: 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.<|reference_end|>
@article{lortie2024forward-backward,
    title={Forward-Backward Extended DMD with an Asymptotic Stability Constraint},
    author={Louis Lortie, Steven Dahdah and James Richard Forbes},
    journal={arXiv preprint arXiv:2403.10623},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.10623},
    primaryClass={eess.SY cs.SY}
}