preprint
Controlling nonlinear PDEs using low-dimensional bilinear approximations obtained from data
Sebastian
Peitz
author 47427https://orcid.org/0000-0002-3389-793X
101
department
In a recent article, we presented a framework to control nonlinear partial
differential equations (PDEs) by means of Koopman operator based reduced models
and concepts from switched systems. The main idea was to transform a control
system into a set of autonomous systems for which the optimal switching
sequence has to be computed. These individual systems can be approximated very
efficiently by reduced order models obtained from data, and one can guarantee
equality of the full and the reduced objective function under certain
assumptions. In this article, we extend these results to continuous control
inputs using convex combinations of multiple Koopman operators corresponding to
constant controls, which results in a bilinear control system. Although
equality of the objectives can be carried over when the PDE depends linearly on
the control, we show that this approach is also valid in other scenarios using
several flow control examples of varying complexity.
2018
eng
arXiv:1801.06419
@article{Peitz_2018, title={Controlling nonlinear PDEs using low-dimensional bilinear approximations obtained from data}, journal={arXiv:1801.06419}, author={Peitz, Sebastian}, year={2018} }
Peitz, S. (2018). Controlling nonlinear PDEs using low-dimensional bilinear approximations obtained from data. <i>ArXiv:1801.06419</i>.
S. Peitz, “Controlling nonlinear PDEs using low-dimensional bilinear approximations obtained from data,” <i>arXiv:1801.06419</i>. 2018.
Peitz, Sebastian. “Controlling Nonlinear PDEs Using Low-Dimensional Bilinear Approximations Obtained from Data.” <i>ArXiv:1801.06419</i>, 2018.
Peitz S. Controlling nonlinear PDEs using low-dimensional bilinear approximations obtained from data. <i>arXiv:180106419</i>. 2018.
S. Peitz, ArXiv:1801.06419 (2018).
Peitz, Sebastian. “Controlling Nonlinear PDEs Using Low-Dimensional Bilinear Approximations Obtained from Data.” <i>ArXiv:1801.06419</i>, 2018.
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