Data-driven control of input-affine systems: the role of the signature transform
<|reference_start|>Data-driven control of input-affine systems: the role of the signature transform: One of the most challenging tasks in control theory is arguably the design of a regulator for nonlinear systems when the dynamics are unknown. To tackle it, a popular strategy relies on finding a direct map between system responses and the controller, and the key ingredient is a predictor for system outputs trained on past trajectories. Focusing on continuous-time, input-affine systems, we show that the so-called signature transform provides rigorous and practically effective features to represent and predict system trajectories. Building upon such a tool, we propose a novel signature-based control strategy that is promising in view of data-driven predictive control.<|reference_end|>
@article{scampicchio2024data-driven,
    title={Data-driven control of input-affine systems: the role of the signature
  transform},
    author={Anna Scampicchio and Melanie N. Zeilinger},
    journal={arXiv preprint arXiv:2409.05685},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.05685},
    primaryClass={eess.SY cs.SY}
}