Data-Driven Control of Linear Parabolic Systems using Koopman Eigenstructure Assignment
<|reference_start|>Data-Driven Control of Linear Parabolic Systems using Koopman Eigenstructure Assignment: This paper considers the data-driven stabilization of linear boundary controlled parabolic PDEs by making use of the Koopman operator. For this, a Koopman eigenstructure assignment problem is solved, which amounts to determine a feedback of the Koopman open-loop eigenfunctionals assigning a desired finite set of closed-loop Koopman eigenvalues and eigenfunctionals to the closed-loop system. It is shown that the designed controller only needs a finite number of open-loop Koopman eigenvalues and modes of the state. They are determined by extending the classical Krylov-DMD to parabolic systems. For this, only a finite number of pointlike outputs and their temporal samples as well as temporal samples of the inputs are required resulting in a data-driven solution of the eigenstructure assignment problem. Exponential stability of the closed-loop system in the presence of small Krylov-DMD errors is verified. An unstable diffusion-reaction system demonstrates the new data-driven controller design technique for distributed-parameter systems.<|reference_end|>
@article{deutscher2024data-driven,
    title={Data-Driven Control of Linear Parabolic Systems using Koopman
  Eigenstructure Assignment},
    author={J. Deutscher},
    journal={arXiv preprint arXiv:2407.00432},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.00432},
    primaryClass={eess.SY cs.SY}
}