Uncertainty Modelling and Robust Observer Synthesis using the Koopman Operator
<|reference_start|>Uncertainty Modelling and Robust Observer Synthesis using the Koopman Operator: This paper proposes a robust nonlinear observer synthesis method for a population of systems modelled using the Koopman operator. The Koopman operator allows nonlinear systems to be rewritten as infinite-dimensional linear systems. A finite-dimensional approximation of the Koopman operator can be identified directly from data, yielding an approximately linear model of a nonlinear system. The proposed observer synthesis method is made possible by this linearity that in turn allows uncertainty within a population of Koopman models to be quantified in the frequency domain. Using this uncertainty model, linear robust control techniques are used to synthesize robust nonlinear Koopman observers. A population of several dozen motor drives is used to experimentally demonstrate the proposed method. Manufacturing variation is characterized in the frequency domain, and a robust Koopman observer is synthesized using mixed $\mathcal{H}_2$-$\mathcal{H}_\infty$ optimal control.<|reference_end|>
@article{dahdah2024uncertainty,
    title={Uncertainty Modelling and Robust Observer Synthesis using the Koopman
  Operator},
    author={Steven Dahdah, James Richard Forbes},
    journal={arXiv preprint arXiv:2410.01057},
    year={2024},
    archivePrefix={arXiv},
    eprint={2410.01057},
    primaryClass={eess.SY cs.LG cs.SY math.DS}
}