---
_id: '35579'
author:
- first_name: Moritz
  full_name: Schulze Darup, Moritz
  last_name: Schulze Darup
- first_name: Gerrit
  full_name: Book, Gerrit
  last_name: Book
citation:
  ama: 'Schulze Darup M, Book G. On Closed-Loop Dynamics of ADMM-Based MPC. In: <i>Recent
    Advances in Model Predictive Control</i>. Springer International Publishing; 2021.
    doi:<a href="https://doi.org/10.1007/978-3-030-63281-6_5">10.1007/978-3-030-63281-6_5</a>'
  apa: Schulze Darup, M., &#38; Book, G. (2021). On Closed-Loop Dynamics of ADMM-Based
    MPC. In <i>Recent Advances in Model Predictive Control</i>. Springer International
    Publishing. <a href="https://doi.org/10.1007/978-3-030-63281-6_5">https://doi.org/10.1007/978-3-030-63281-6_5</a>
  bibtex: '@inbook{Schulze Darup_Book_2021, place={Cham}, title={On Closed-Loop Dynamics
    of ADMM-Based MPC}, DOI={<a href="https://doi.org/10.1007/978-3-030-63281-6_5">10.1007/978-3-030-63281-6_5</a>},
    booktitle={Recent Advances in Model Predictive Control}, publisher={Springer International
    Publishing}, author={Schulze Darup, Moritz and Book, Gerrit}, year={2021} }'
  chicago: 'Schulze Darup, Moritz, and Gerrit Book. “On Closed-Loop Dynamics of ADMM-Based
    MPC.” In <i>Recent Advances in Model Predictive Control</i>. Cham: Springer International
    Publishing, 2021. <a href="https://doi.org/10.1007/978-3-030-63281-6_5">https://doi.org/10.1007/978-3-030-63281-6_5</a>.'
  ieee: 'M. Schulze Darup and G. Book, “On Closed-Loop Dynamics of ADMM-Based MPC,”
    in <i>Recent Advances in Model Predictive Control</i>, Cham: Springer International
    Publishing, 2021.'
  mla: Schulze Darup, Moritz, and Gerrit Book. “On Closed-Loop Dynamics of ADMM-Based
    MPC.” <i>Recent Advances in Model Predictive Control</i>, Springer International
    Publishing, 2021, doi:<a href="https://doi.org/10.1007/978-3-030-63281-6_5">10.1007/978-3-030-63281-6_5</a>.
  short: 'M. Schulze Darup, G. Book, in: Recent Advances in Model Predictive Control,
    Springer International Publishing, Cham, 2021.'
date_created: 2023-01-09T16:36:18Z
date_updated: 2023-01-09T16:43:02Z
department:
- _id: '622'
doi: 10.1007/978-3-030-63281-6_5
extern: '1'
language:
- iso: eng
place: Cham
publication: Recent Advances in Model Predictive Control
publication_identifier:
  isbn:
  - '9783030632809'
  - '9783030632816'
  issn:
  - 0170-8643
  - 1610-7411
publication_status: published
publisher: Springer International Publishing
status: public
title: On Closed-Loop Dynamics of ADMM-Based MPC
type: book_chapter
user_id: '158'
year: '2021'
...
---
_id: '16289'
abstract:
- lang: eng
  text: In the development of model predictive controllers for PDE-constrained problems,
    the use of reduced order models is essential to enable real-time applicability.
    Besides local linearization approaches, proper orthogonal decomposition (POD)
    has been most widely used in the past in order to derive such models. Due to the
    huge advances concerning both theory as well as the numerical approximation, a
    very promising alternative based on the Koopman operator has recently emerged.
    In this chapter, we present two control strategies for model predictive control
    of nonlinear PDEs using data-efficient approximations of the Koopman operator.
    In the first one, the dynamic control system is replaced by a small number of
    autonomous systems with different yet constant inputs. The control problem is
    consequently transformed into a switching problem. In the second approach, a bilinear
    surrogate model is obtained via a convex combination of these autonomous systems.
    Using a recent convergence result for extended dynamic mode decomposition (EDMD),
    convergence of the reduced objective function can be shown. We study the properties
    of these two strategies with respect to solution quality, data requirements, and
    complexity of the resulting optimization problem using the 1-dimensional Burgers
    equation and the 2-dimensional Navier–Stokes equations as examples. Finally, an
    extension for online adaptivity is presented.
author:
- first_name: Sebastian
  full_name: Peitz, Sebastian
  id: '47427'
  last_name: Peitz
  orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Stefan
  full_name: Klus, Stefan
  last_name: Klus
citation:
  ama: 'Peitz S, Klus S. Feedback Control of Nonlinear PDEs Using Data-Efficient Reduced
    Order Models Based on the Koopman Operator. In: <i>Lecture Notes in Control and
    Information Sciences</i>. Vol 484. Lecture Notes in Control and Information Sciences.
    Cham: Springer; 2020:257-282. doi:<a href="https://doi.org/10.1007/978-3-030-35713-9_10">10.1007/978-3-030-35713-9_10</a>'
  apa: 'Peitz, S., &#38; Klus, S. (2020). Feedback Control of Nonlinear PDEs Using
    Data-Efficient Reduced Order Models Based on the Koopman Operator. In <i>Lecture
    Notes in Control and Information Sciences</i> (Vol. 484, pp. 257–282). Cham: Springer.
    <a href="https://doi.org/10.1007/978-3-030-35713-9_10">https://doi.org/10.1007/978-3-030-35713-9_10</a>'
  bibtex: '@inbook{Peitz_Klus_2020, place={Cham}, series={Lecture Notes in Control
    and Information Sciences}, title={Feedback Control of Nonlinear PDEs Using Data-Efficient
    Reduced Order Models Based on the Koopman Operator}, volume={484}, DOI={<a href="https://doi.org/10.1007/978-3-030-35713-9_10">10.1007/978-3-030-35713-9_10</a>},
    booktitle={Lecture Notes in Control and Information Sciences}, publisher={Springer},
    author={Peitz, Sebastian and Klus, Stefan}, year={2020}, pages={257–282}, collection={Lecture
    Notes in Control and Information Sciences} }'
  chicago: 'Peitz, Sebastian, and Stefan Klus. “Feedback Control of Nonlinear PDEs
    Using Data-Efficient Reduced Order Models Based on the Koopman Operator.” In <i>Lecture
    Notes in Control and Information Sciences</i>, 484:257–82. Lecture Notes in Control
    and Information Sciences. Cham: Springer, 2020. <a href="https://doi.org/10.1007/978-3-030-35713-9_10">https://doi.org/10.1007/978-3-030-35713-9_10</a>.'
  ieee: 'S. Peitz and S. Klus, “Feedback Control of Nonlinear PDEs Using Data-Efficient
    Reduced Order Models Based on the Koopman Operator,” in <i>Lecture Notes in Control
    and Information Sciences</i>, vol. 484, Cham: Springer, 2020, pp. 257–282.'
  mla: Peitz, Sebastian, and Stefan Klus. “Feedback Control of Nonlinear PDEs Using
    Data-Efficient Reduced Order Models Based on the Koopman Operator.” <i>Lecture
    Notes in Control and Information Sciences</i>, vol. 484, Springer, 2020, pp. 257–82,
    doi:<a href="https://doi.org/10.1007/978-3-030-35713-9_10">10.1007/978-3-030-35713-9_10</a>.
  short: 'S. Peitz, S. Klus, in: Lecture Notes in Control and Information Sciences,
    Springer, Cham, 2020, pp. 257–282.'
date_created: 2020-03-13T12:38:52Z
date_updated: 2022-01-06T06:52:48Z
department:
- _id: '101'
doi: 10.1007/978-3-030-35713-9_10
intvolume: '       484'
language:
- iso: eng
page: 257-282
place: Cham
publication: Lecture Notes in Control and Information Sciences
publication_identifier:
  isbn:
  - '9783030357122'
  - '9783030357139'
  issn:
  - 0170-8643
  - 1610-7411
publication_status: published
publisher: Springer
series_title: Lecture Notes in Control and Information Sciences
status: public
title: Feedback Control of Nonlinear PDEs Using Data-Efficient Reduced Order Models
  Based on the Koopman Operator
type: book_chapter
user_id: '47427'
volume: 484
year: '2020'
...