Stability-Certified Learning of Control Systems with Quadratic Nonlinearities
<|reference_start|>Stability-Certified Learning of Control Systems with Quadratic Nonlinearities: This work primarily focuses on an operator inference methodology aimed at constructing low-dimensional dynamical models based on a priori hypotheses about their structure, often informed by established physics or expert insights. Stability is a fundamental attribute of dynamical systems, yet it is not always assured in models derived through inference. Our main objective is to develop a method that facilitates the inference of quadratic control dynamical systems with inherent stability guarantees. To this aim, we investigate the stability characteristics of control systems with energy-preserving nonlinearities, thereby identifying conditions under which such systems are bounded-input bounded-state stable. These insights are subsequently applied to the learning process, yielding inferred models that are inherently stable by design. The efficacy of our proposed framework is demonstrated through a couple of numerical examples.<|reference_end|>
@article{duff2024stability-certified,
    title={Stability-Certified Learning of Control Systems with Quadratic
  Nonlinearities},
    author={Igor Pontes Duff and Pawan Goyal and Peter Benner},
    journal={arXiv preprint arXiv:2403.00646},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.00646},
    primaryClass={cs.LG math.DS math.OC}
}