---
_id: '16290'
abstract:
- lang: eng
text: The control of complex systems is of critical importance in many branches
of science, engineering, and industry, many of which are governed by nonlinear
partial differential equations. Controlling an unsteady fluid flow is particularly
important, as flow control is a key enabler for technologies in energy (e.g.,
wind, tidal, and combustion), transportation (e.g., planes, trains, and automobiles),
security (e.g., tracking airborne contamination), and health (e.g., artificial
hearts and artificial respiration). However, the high-dimensional, nonlinear,
and multi-scale dynamics make real-time feedback control infeasible. Fortunately,
these high- dimensional systems exhibit dominant, low-dimensional patterns of
activity that can be exploited for effective control in the sense that knowledge
of the entire state of a system is not required. Advances in machine learning
have the potential to revolutionize flow control given its ability to extract
principled, low-rank feature spaces characterizing such complex systems.We present
a novel deep learning modelpredictive control framework that exploits low-rank
features of the flow in order to achieve considerable improvements to control
performance. Instead of predicting the entire fluid state, we use a recurrent
neural network (RNN) to accurately predict the control relevant quantities of
the system, which are then embedded into an MPC framework to construct a feedback
loop. In order to lower the data requirements and to improve the prediction accuracy
and thus the control performance, incoming sensor data are used to update the
RNN online. The results are validated using varying fluid flow examples of increasing
complexity.
article_type: original
author:
- first_name: Katharina
full_name: Bieker, Katharina
id: '32829'
last_name: Bieker
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Steven L.
full_name: Brunton, Steven L.
last_name: Brunton
- first_name: J. Nathan
full_name: Kutz, J. Nathan
last_name: Kutz
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: Bieker K, Peitz S, Brunton SL, Kutz JN, Dellnitz M. Deep model predictive flow
control with limited sensor data and online learning. Theoretical and Computational
Fluid Dynamics. 2020;34:577–591. doi:10.1007/s00162-020-00520-4
apa: Bieker, K., Peitz, S., Brunton, S. L., Kutz, J. N., & Dellnitz, M. (2020).
Deep model predictive flow control with limited sensor data and online learning.
Theoretical and Computational Fluid Dynamics, 34, 577–591. https://doi.org/10.1007/s00162-020-00520-4
bibtex: '@article{Bieker_Peitz_Brunton_Kutz_Dellnitz_2020, title={Deep model predictive
flow control with limited sensor data and online learning}, volume={34}, DOI={10.1007/s00162-020-00520-4},
journal={Theoretical and Computational Fluid Dynamics}, author={Bieker, Katharina
and Peitz, Sebastian and Brunton, Steven L. and Kutz, J. Nathan and Dellnitz,
Michael}, year={2020}, pages={577–591} }'
chicago: 'Bieker, Katharina, Sebastian Peitz, Steven L. Brunton, J. Nathan Kutz,
and Michael Dellnitz. “Deep Model Predictive Flow Control with Limited Sensor
Data and Online Learning.” Theoretical and Computational Fluid Dynamics
34 (2020): 577–591. https://doi.org/10.1007/s00162-020-00520-4.'
ieee: K. Bieker, S. Peitz, S. L. Brunton, J. N. Kutz, and M. Dellnitz, “Deep model
predictive flow control with limited sensor data and online learning,” Theoretical
and Computational Fluid Dynamics, vol. 34, pp. 577–591, 2020.
mla: Bieker, Katharina, et al. “Deep Model Predictive Flow Control with Limited
Sensor Data and Online Learning.” Theoretical and Computational Fluid Dynamics,
vol. 34, 2020, pp. 577–591, doi:10.1007/s00162-020-00520-4.
short: K. Bieker, S. Peitz, S.L. Brunton, J.N. Kutz, M. Dellnitz, Theoretical and
Computational Fluid Dynamics 34 (2020) 577–591.
date_created: 2020-03-13T12:40:09Z
date_updated: 2022-01-06T06:52:48Z
department:
- _id: '101'
doi: 10.1007/s00162-020-00520-4
intvolume: ' 34'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://link.springer.com/content/pdf/10.1007/s00162-020-00520-4.pdf
oa: '1'
page: 577–591
project:
- _id: '52'
name: Computing Resources Provided by the Paderborn Center for Parallel Computing
publication: Theoretical and Computational Fluid Dynamics
publication_identifier:
issn:
- 0935-4964
- 1432-2250
publication_status: published
status: public
title: Deep model predictive flow control with limited sensor data and online learning
type: journal_article
user_id: '47427'
volume: 34
year: '2020'
...
---
_id: '16309'
abstract:
- lang: eng
text: "In recent years, the success of the Koopman operator in dynamical systems\r\nanalysis
has also fueled the development of Koopman operator-based control\r\nframeworks.
In order to preserve the relatively low data requirements for an\r\napproximation
via Dynamic Mode Decomposition, a quantization approach was\r\nrecently proposed
in [Peitz & Klus, Automatica 106, 2019]. This way, control\r\nof nonlinear dynamical
systems can be realized by means of switched systems\r\ntechniques, using only
a finite set of autonomous Koopman operator-based\r\nreduced models. These individual
systems can be approximated very efficiently\r\nfrom data. The main idea is to
transform a control system into a set of\r\nautonomous systems for which the optimal
switching sequence has to be computed.\r\nIn this article, we extend these results
to continuous control inputs using\r\nrelaxation. This way, we combine the advantages
of the data efficiency of\r\napproximating a finite set of autonomous systems
with continuous controls. We\r\nshow that when using the Koopman generator, this
relaxation --- realized by\r\nlinear interpolation between two operators --- does
not introduce any error for\r\ncontrol affine systems. This allows us to control
high-dimensional nonlinear\r\nsystems using bilinear, low-dimensional surrogate
models. The efficiency of the\r\nproposed approach is demonstrated using several
examples with increasing\r\ncomplexity, from the Duffing oscillator to the chaotic
fluidic pinball."
author:
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Samuel E.
full_name: Otto, Samuel E.
last_name: Otto
- first_name: Clarence W.
full_name: Rowley, Clarence W.
last_name: Rowley
citation:
ama: Peitz S, Otto SE, Rowley CW. Data-Driven Model Predictive Control using Interpolated
Koopman Generators. SIAM Journal on Applied Dynamical Systems. 2020;19(3):2162-2193.
doi:10.1137/20M1325678
apa: Peitz, S., Otto, S. E., & Rowley, C. W. (2020). Data-Driven Model Predictive
Control using Interpolated Koopman Generators. SIAM Journal on Applied Dynamical
Systems, 19(3), 2162–2193. https://doi.org/10.1137/20M1325678
bibtex: '@article{Peitz_Otto_Rowley_2020, title={Data-Driven Model Predictive Control
using Interpolated Koopman Generators}, volume={19}, DOI={10.1137/20M1325678},
number={3}, journal={SIAM Journal on Applied Dynamical Systems}, author={Peitz,
Sebastian and Otto, Samuel E. and Rowley, Clarence W.}, year={2020}, pages={2162–2193}
}'
chicago: 'Peitz, Sebastian, Samuel E. Otto, and Clarence W. Rowley. “Data-Driven
Model Predictive Control Using Interpolated Koopman Generators.” SIAM Journal
on Applied Dynamical Systems 19, no. 3 (2020): 2162–93. https://doi.org/10.1137/20M1325678.'
ieee: S. Peitz, S. E. Otto, and C. W. Rowley, “Data-Driven Model Predictive Control
using Interpolated Koopman Generators,” SIAM Journal on Applied Dynamical
Systems, vol. 19, no. 3, pp. 2162–2193, 2020.
mla: Peitz, Sebastian, et al. “Data-Driven Model Predictive Control Using Interpolated
Koopman Generators.” SIAM Journal on Applied Dynamical Systems, vol. 19,
no. 3, 2020, pp. 2162–93, doi:10.1137/20M1325678.
short: S. Peitz, S.E. Otto, C.W. Rowley, SIAM Journal on Applied Dynamical Systems
19 (2020) 2162–2193.
date_created: 2020-03-17T09:53:01Z
date_updated: 2022-01-06T06:52:48Z
department:
- _id: '101'
doi: 10.1137/20M1325678
intvolume: ' 19'
issue: '3'
language:
- iso: eng
main_file_link:
- url: https://epubs.siam.org/doi/pdf/10.1137/20M1325678
page: 2162-2193
publication: SIAM Journal on Applied Dynamical Systems
status: public
title: Data-Driven Model Predictive Control using Interpolated Koopman Generators
type: journal_article
user_id: '47427'
volume: 19
year: '2020'
...
---
_id: '13108'
abstract:
- lang: ger
text: Diagrammatisches Schlie{\ss}en wird im Zusammenhang mit dem Lernen von Mathmematik
und ihrer Symbolsprache als wesentliche Theorie der Wissenskonstruktion diskutiert.
Dabei wird h{\"{a}}ufig davon ausgegangen, dass die Wissenskonstruktion im Sinne
diagrammatischen Schlie{\ss}ens erfolgt. Deskriptive Rekonstruktionen diagrammatischen
Schlie{\ss}ens bei Lernenden stellen jedoch ein Desiderat der mathematikdidaktischen
Forschung dar. Der vorliegende Beitrag befasst sich mit der Fragestellung, wie
sich diagrammatisches Schlie{\ss}en bei Lernenden rekonstruieren l{\"{a}}sst.
Als m{\"{o}}gliche Werkzeuge f{\"{u}}r eine solche Rekonstruktion werden Toulmins
Argumentationsschema und Vergnauds Schema-Begriff exemplarisch angewandt, um das
diagrammatische Schlie{\ss}en eines Sch{\"{u}}lerpaars beim Einstieg in die Subtraktion
negativer Zahlen zu rekonstruieren. Abschlie{\ss}end wird die tats{\"{a}}chliche
Eignung der beiden Ans{\"{a}}tze zur Rekonstruktion diagrammatischen Schlie{\ss}ens
diskutiert.
author:
- first_name: Jan
full_name: Schumacher, Jan
id: '26809'
last_name: Schumacher
orcid: 0000-0002-6676-9774
- first_name: Sebastian
full_name: Rezat, Sebastian
last_name: Rezat
citation:
ama: 'Schumacher J, Rezat S. Rekonstruktion diagrammatischen Schließens beim Erlernen
der Subtraktion negativer Zahlen. Vergleich zweier methodischer Zugänge. In: Kadunz
G, ed. Zeichen und Sprache im Mathematikunterricht. Springer; 2020. doi:10.1007/978-3-662-61194-4_5'
apa: Schumacher, J., & Rezat, S. (2020). Rekonstruktion diagrammatischen Schließens
beim Erlernen der Subtraktion negativer Zahlen. Vergleich zweier methodischer
Zugänge. In G. Kadunz (Ed.), Zeichen und Sprache im Mathematikunterricht.
Springer. https://doi.org/10.1007/978-3-662-61194-4_5
bibtex: '@inbook{Schumacher_Rezat_2020, title={Rekonstruktion diagrammatischen Schließens
beim Erlernen der Subtraktion negativer Zahlen. Vergleich zweier methodischer
Zugänge}, DOI={10.1007/978-3-662-61194-4_5},
booktitle={Zeichen und Sprache im Mathematikunterricht}, publisher={Springer},
author={Schumacher, Jan and Rezat, Sebastian}, editor={Kadunz, GertEditor}, year={2020}
}'
chicago: Schumacher, Jan, and Sebastian Rezat. “Rekonstruktion diagrammatischen
Schließens beim Erlernen der Subtraktion negativer Zahlen. Vergleich zweier methodischer
Zugänge.” In Zeichen und Sprache im Mathematikunterricht, edited by Gert
Kadunz. Springer, 2020. https://doi.org/10.1007/978-3-662-61194-4_5.
ieee: J. Schumacher and S. Rezat, “Rekonstruktion diagrammatischen Schließens beim
Erlernen der Subtraktion negativer Zahlen. Vergleich zweier methodischer Zugänge,”
in Zeichen und Sprache im Mathematikunterricht, G. Kadunz, Ed. Springer,
2020.
mla: Schumacher, Jan, and Sebastian Rezat. “Rekonstruktion diagrammatischen Schließens
beim Erlernen der Subtraktion negativer Zahlen. Vergleich zweier methodischer
Zugänge.” Zeichen und Sprache im Mathematikunterricht, edited by Gert Kadunz,
Springer, 2020, doi:10.1007/978-3-662-61194-4_5.
short: 'J. Schumacher, S. Rezat, in: G. Kadunz (Ed.), Zeichen und Sprache im Mathematikunterricht,
Springer, 2020.'
date_created: 2019-08-30T12:00:51Z
date_updated: 2022-01-06T06:51:28Z
department:
- _id: '360'
- _id: '98'
doi: 10.1007/978-3-662-61194-4_5
editor:
- first_name: Gert
full_name: Kadunz, Gert
last_name: Kadunz
language:
- iso: ger
publication: Zeichen und Sprache im Mathematikunterricht
publication_status: published
publisher: Springer
quality_controlled: '1'
status: public
title: Rekonstruktion diagrammatischen Schließens beim Erlernen der Subtraktion negativer
Zahlen. Vergleich zweier methodischer Zugänge
type: book_chapter
user_id: '26809'
year: '2020'
...
---
_id: '31873'
author:
- first_name: Jan
full_name: Schumacher, Jan
id: '26809'
last_name: Schumacher
orcid: 0000-0002-6676-9774
citation:
ama: 'Schumacher J. Deduktion und Abduktion beim diagrammatischen Schließen – das
didaktische Potential der Peirceschen Semiotik. In: LibreCat University; 2020.
doi:10.17877/DE290R-21555'
apa: Schumacher, J. (2020). Deduktion und Abduktion beim diagrammatischen Schließen
– das didaktische Potential der Peirceschen Semiotik. https://doi.org/10.17877/DE290R-21555
bibtex: '@inproceedings{Schumacher_2020, title={Deduktion und Abduktion beim diagrammatischen
Schließen – das didaktische Potential der Peirceschen Semiotik}, DOI={10.17877/DE290R-21555},
publisher={LibreCat University}, author={Schumacher, Jan}, year={2020} }'
chicago: Schumacher, Jan. “Deduktion Und Abduktion Beim Diagrammatischen Schließen
– Das Didaktische Potential Der Peirceschen Semiotik.” LibreCat University, 2020.
https://doi.org/10.17877/DE290R-21555.
ieee: 'J. Schumacher, “Deduktion und Abduktion beim diagrammatischen Schließen –
das didaktische Potential der Peirceschen Semiotik,” 2020, doi: 10.17877/DE290R-21555.'
mla: Schumacher, Jan. Deduktion Und Abduktion Beim Diagrammatischen Schließen
– Das Didaktische Potential Der Peirceschen Semiotik. LibreCat University,
2020, doi:10.17877/DE290R-21555.
short: 'J. Schumacher, in: LibreCat University, 2020.'
date_created: 2022-06-14T07:10:29Z
date_updated: 2022-06-14T07:15:34Z
department:
- _id: '360'
- _id: '98'
doi: 10.17877/DE290R-21555
language:
- iso: eng
publication_status: published
publisher: LibreCat University
status: public
title: Deduktion und Abduktion beim diagrammatischen Schließen – das didaktische Potential
der Peirceschen Semiotik
type: conference
user_id: '26809'
year: '2020'
...
---
_id: '34789'
article_type: original
author:
- first_name: Habib
full_name: Amiri, Habib
last_name: Amiri
- first_name: Helge
full_name: Glöckner, Helge
id: '178'
last_name: Glöckner
- first_name: Alexander
full_name: Schmeding, Alexander
last_name: Schmeding
citation:
ama: Amiri H, Glöckner H, Schmeding A. Lie groupoids of mappings taking values in
a Lie groupoid. Archivum Mathematicum. 2020;56(5):307–356. doi:10.5817/AM2020-5-307
apa: Amiri, H., Glöckner, H., & Schmeding, A. (2020). Lie groupoids of mappings
taking values in a Lie groupoid. Archivum Mathematicum, 56(5), 307–356.
https://doi.org/10.5817/AM2020-5-307
bibtex: '@article{Amiri_Glöckner_Schmeding_2020, title={Lie groupoids of mappings
taking values in a Lie groupoid}, volume={56}, DOI={10.5817/AM2020-5-307},
number={5}, journal={Archivum Mathematicum}, author={Amiri, Habib and Glöckner,
Helge and Schmeding, Alexander}, year={2020}, pages={307–356} }'
chicago: 'Amiri, Habib, Helge Glöckner, and Alexander Schmeding. “Lie Groupoids
of Mappings Taking Values in a Lie Groupoid.” Archivum Mathematicum 56,
no. 5 (2020): 307–356. https://doi.org/10.5817/AM2020-5-307.'
ieee: 'H. Amiri, H. Glöckner, and A. Schmeding, “Lie groupoids of mappings taking
values in a Lie groupoid,” Archivum Mathematicum, vol. 56, no. 5, pp. 307–356,
2020, doi: 10.5817/AM2020-5-307.'
mla: Amiri, Habib, et al. “Lie Groupoids of Mappings Taking Values in a Lie Groupoid.”
Archivum Mathematicum, vol. 56, no. 5, 2020, pp. 307–356, doi:10.5817/AM2020-5-307.
short: H. Amiri, H. Glöckner, A. Schmeding, Archivum Mathematicum 56 (2020) 307–356.
date_created: 2022-12-21T19:13:24Z
date_updated: 2022-12-21T19:15:59Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
doi: 10.5817/AM2020-5-307
intvolume: ' 56'
issue: '5'
keyword:
- 22A22
- '22E65'
- '22E67'
- 46T10
- 47H30
- 58D15
- 58H05
language:
- iso: eng
page: 307–356
publication: Archivum Mathematicum
publication_identifier:
issn:
- 0044-8753
quality_controlled: '1'
status: public
title: Lie groupoids of mappings taking values in a Lie groupoid
type: journal_article
user_id: '178'
volume: 56
year: '2020'
...
---
_id: '34787'
article_type: original
author:
- first_name: Helge
full_name: Glöckner, Helge
id: '178'
last_name: Glöckner
- first_name: Niku
full_name: Masbough, Niku
last_name: Masbough
citation:
ama: Glöckner H, Masbough N. Products of regular locally compact spaces are k_R-spaces.
Topology Proceedings. 2020;55:35–38.
apa: Glöckner, H., & Masbough, N. (2020). Products of regular locally compact
spaces are k_R-spaces. Topology Proceedings, 55, 35–38.
bibtex: '@article{Glöckner_Masbough_2020, title={Products of regular locally compact
spaces are k_R-spaces}, volume={55}, journal={Topology Proceedings}, author={Glöckner,
Helge and Masbough, Niku}, year={2020}, pages={35–38} }'
chicago: 'Glöckner, Helge, and Niku Masbough. “Products of Regular Locally Compact
Spaces Are K_R-Spaces.” Topology Proceedings 55 (2020): 35–38.'
ieee: H. Glöckner and N. Masbough, “Products of regular locally compact spaces are
k_R-spaces,” Topology Proceedings, vol. 55, pp. 35–38, 2020.
mla: Glöckner, Helge, and Niku Masbough. “Products of Regular Locally Compact Spaces
Are K_R-Spaces.” Topology Proceedings, vol. 55, 2020, pp. 35–38.
short: H. Glöckner, N. Masbough, Topology Proceedings 55 (2020) 35–38.
date_created: 2022-12-21T19:06:45Z
date_updated: 2022-12-21T20:06:44Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
intvolume: ' 55'
keyword:
- 54B10
- 54D45
- 54D50
language:
- iso: eng
page: 35–38
publication: Topology Proceedings
publication_identifier:
issn:
- 0146-4124
quality_controlled: '1'
status: public
title: Products of regular locally compact spaces are k_R-spaces
type: journal_article
user_id: '178'
volume: 55
year: '2020'
...
---
_id: '34808'
abstract:
- lang: eng
text: "For suitable finite-dimensional smooth manifolds M (possibly with various\r\nkinds
of boundary or corners), locally convex topological vector spaces F and\r\nnon-negative
integers k, we construct continuous linear operators S_n from the\r\nspace of
F-valued k times continuously differentiable functions on M to the\r\ncorresponding
space of smooth functions such that S_n(f) converges to f in\r\nC^k(M,F) as n
tends to infinity, uniformly for f in compact subsets of\r\nC^k(M,F). We also
study the existence of continuous linear right inverses for\r\nrestriction maps
from C^k(M,F) to C^k(L,F) if L is a closed subset of M,\r\nendowed with a C^k-manifold
structure turning the inclusion map from L to M\r\ninto a C^k-map. Moreover, we
construct continuous linear right inverses for\r\nrestriction operators between
spaces of sections in vector bundles in many\r\nsituations, and smooth local right
inverses for restriction operators between\r\nmanifolds of mappings. We also obtain
smoothing results for sections in fibre\r\nbundles."
author:
- first_name: Helge
full_name: Glöckner, Helge
id: '178'
last_name: Glöckner
citation:
ama: Glöckner H. Smoothing operators for vector-valued functions and extension operators.
arXiv:200600254. Published online 2020.
apa: Glöckner, H. (2020). Smoothing operators for vector-valued functions and extension
operators. In arXiv:2006.00254.
bibtex: '@article{Glöckner_2020, title={Smoothing operators for vector-valued functions
and extension operators}, journal={arXiv:2006.00254}, author={Glöckner, Helge},
year={2020} }'
chicago: Glöckner, Helge. “Smoothing Operators for Vector-Valued Functions and Extension
Operators.” ArXiv:2006.00254, 2020.
ieee: H. Glöckner, “Smoothing operators for vector-valued functions and extension
operators,” arXiv:2006.00254. 2020.
mla: Glöckner, Helge. “Smoothing Operators for Vector-Valued Functions and Extension
Operators.” ArXiv:2006.00254, 2020.
short: H. Glöckner, ArXiv:2006.00254 (2020).
date_created: 2022-12-22T07:51:53Z
date_updated: 2022-12-22T07:52:42Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
external_id:
arxiv:
- '2006.00254'
language:
- iso: eng
publication: arXiv:2006.00254
status: public
title: Smoothing operators for vector-valued functions and extension operators
type: preprint
user_id: '178'
year: '2020'
...
---
_id: '29399'
author:
- first_name: D. J. N.
full_name: Limebeer, D. J. N.
last_name: Limebeer
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: F. H.
full_name: Farshi, F. H.
last_name: Farshi
citation:
ama: Limebeer DJN, Ober-Blöbaum S, Farshi FH. Variational integrators for dissipative
systems. IEEE Transactions on Automatic Control. 2020;65(4):1381-1396.
apa: Limebeer, D. J. N., Ober-Blöbaum, S., & Farshi, F. H. (2020). Variational
integrators for dissipative systems. IEEE Transactions on Automatic Control,
65(4), 1381–1396.
bibtex: '@article{Limebeer_Ober-Blöbaum_Farshi_2020, title={Variational integrators
for dissipative systems}, volume={65(4)}, journal={IEEE Transactions on Automatic
Control}, author={Limebeer, D. J. N. and Ober-Blöbaum, Sina and Farshi, F. H.},
year={2020}, pages={1381–1396} }'
chicago: 'Limebeer, D. J. N., Sina Ober-Blöbaum, and F. H. Farshi. “Variational
Integrators for Dissipative Systems.” IEEE Transactions on Automatic Control
65(4) (2020): 1381–96.'
ieee: D. J. N. Limebeer, S. Ober-Blöbaum, and F. H. Farshi, “Variational integrators
for dissipative systems,” IEEE Transactions on Automatic Control, vol.
65(4), pp. 1381–1396, 2020.
mla: Limebeer, D. J. N., et al. “Variational Integrators for Dissipative Systems.”
IEEE Transactions on Automatic Control, vol. 65(4), 2020, pp. 1381–96.
short: D.J.N. Limebeer, S. Ober-Blöbaum, F.H. Farshi, IEEE Transactions on Automatic
Control 65(4) (2020) 1381–1396.
date_created: 2022-01-18T11:17:25Z
date_updated: 2022-01-21T08:26:46Z
department:
- _id: '636'
language:
- iso: eng
page: 1381-1396
publication: IEEE Transactions on Automatic Control
status: public
title: Variational integrators for dissipative systems
type: journal_article
user_id: '15694'
volume: 65(4)
year: '2020'
...
---
_id: '16297'
abstract:
- lang: eng
text: "In real-world problems, uncertainties (e.g., errors in the measurement,\r\nprecision
errors) often lead to poor performance of numerical algorithms when\r\nnot explicitly
taken into account. This is also the case for control problems,\r\nwhere optimal
solutions can degrade in quality or even become infeasible. Thus,\r\nthere is
the need to design methods that can handle uncertainty. In this work,\r\nwe consider
nonlinear multi-objective optimal control problems with uncertainty\r\non the
initial conditions, and in particular their incorporation into a\r\nfeedback loop
via model predictive control (MPC). In multi-objective optimal\r\ncontrol, an
optimal compromise between multiple conflicting criteria has to be\r\nfound. For
such problems, not much has been reported in terms of uncertainties.\r\nTo address
this problem class, we design an offline/online framework to compute\r\nan approximation
of efficient control strategies. This approach is closely\r\nrelated to explicit
MPC for nonlinear systems, where the potentially expensive\r\noptimization problem
is solved in an offline phase in order to enable fast\r\nsolutions in the online
phase. In order to reduce the numerical cost of the\r\noffline phase, we exploit
symmetries in the control problems. Furthermore, in\r\norder to ensure optimality
of the solutions, we include an additional online\r\noptimization step, which
is considerably cheaper than the original\r\nmulti-objective optimization problem.
We test our framework on a car\r\nmaneuvering problem where safety and speed are
the objectives. The\r\nmulti-objective framework allows for online adaptations
of the desired\r\nobjective. Alternatively, an automatic scalarizing procedure
yields very\r\nefficient feedback controls. Our results show that the method is
capable of\r\ndesigning driving strategies that deal better with uncertainties
in the initial\r\nconditions, which translates into potentially safer and faster
driving\r\nstrategies."
author:
- first_name: Carlos Ignacio
full_name: Hernández Castellanos, Carlos Ignacio
last_name: Hernández Castellanos
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
citation:
ama: Hernández Castellanos CI, Ober-Blöbaum S, Peitz S. Explicit Multi-objective
Model Predictive Control for Nonlinear Systems Under Uncertainty. International
Journal of Robust and Nonlinear Control. 2020;30(17):7593-7618. doi:10.1002/rnc.5197
apa: Hernández Castellanos, C. I., Ober-Blöbaum, S., & Peitz, S. (2020). Explicit
Multi-objective Model Predictive Control for Nonlinear Systems Under Uncertainty.
International Journal of Robust and Nonlinear Control, 30(17), 7593–7618.
https://doi.org/10.1002/rnc.5197
bibtex: '@article{Hernández Castellanos_Ober-Blöbaum_Peitz_2020, title={Explicit
Multi-objective Model Predictive Control for Nonlinear Systems Under Uncertainty},
volume={30(17)}, DOI={10.1002/rnc.5197},
journal={International Journal of Robust and Nonlinear Control}, author={Hernández
Castellanos, Carlos Ignacio and Ober-Blöbaum, Sina and Peitz, Sebastian}, year={2020},
pages={7593–7618} }'
chicago: 'Hernández Castellanos, Carlos Ignacio, Sina Ober-Blöbaum, and Sebastian
Peitz. “Explicit Multi-Objective Model Predictive Control for Nonlinear Systems
Under Uncertainty.” International Journal of Robust and Nonlinear Control
30(17) (2020): 7593–7618. https://doi.org/10.1002/rnc.5197.'
ieee: 'C. I. Hernández Castellanos, S. Ober-Blöbaum, and S. Peitz, “Explicit Multi-objective
Model Predictive Control for Nonlinear Systems Under Uncertainty,” International
Journal of Robust and Nonlinear Control, vol. 30(17), pp. 7593–7618, 2020,
doi: 10.1002/rnc.5197.'
mla: Hernández Castellanos, Carlos Ignacio, et al. “Explicit Multi-Objective Model
Predictive Control for Nonlinear Systems Under Uncertainty.” International
Journal of Robust and Nonlinear Control, vol. 30(17), 2020, pp. 7593–618,
doi:10.1002/rnc.5197.
short: C.I. Hernández Castellanos, S. Ober-Blöbaum, S. Peitz, International Journal
of Robust and Nonlinear Control 30(17) (2020) 7593–7618.
date_created: 2020-03-13T12:45:56Z
date_updated: 2022-01-21T09:55:39Z
department:
- _id: '101'
doi: 10.1002/rnc.5197
language:
- iso: eng
page: 7593-7618
publication: International Journal of Robust and Nonlinear Control
status: public
title: Explicit Multi-objective Model Predictive Control for Nonlinear Systems Under
Uncertainty
type: journal_article
user_id: '15694'
volume: 30(17)
year: '2020'
...
---
_id: '29398'
author:
- first_name: C. I. O.
full_name: Hernández Castellanos, C. I. O.
last_name: Hernández Castellanos
- first_name: G.
full_name: Schütze, G.
last_name: Schütze
- first_name: J.-Q.
full_name: Sun, J.-Q.
last_name: Sun
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: G.
full_name: Morales-Luna, G.
last_name: Morales-Luna
citation:
ama: Hernández Castellanos CIO, Schütze G, Sun J-Q, Ober-Blöbaum S, Morales-Luna
G. Numerical computation of lightly multi-objective robust optimal solutions by
means of generalized cell mapping. Mathematics. 2020;8(11):1959.
apa: Hernández Castellanos, C. I. O., Schütze, G., Sun, J.-Q., Ober-Blöbaum, S.,
& Morales-Luna, G. (2020). Numerical computation of lightly multi-objective
robust optimal solutions by means of generalized cell mapping. Mathematics,
8(11):1959.
bibtex: '@article{Hernández Castellanos_Schütze_Sun_Ober-Blöbaum_Morales-Luna_2020,
title={Numerical computation of lightly multi-objective robust optimal solutions
by means of generalized cell mapping}, volume={8(11):1959}, journal={Mathematics},
author={Hernández Castellanos, C. I. O. and Schütze, G. and Sun, J.-Q. and Ober-Blöbaum,
Sina and Morales-Luna, G.}, year={2020} }'
chicago: Hernández Castellanos, C. I. O., G. Schütze, J.-Q. Sun, Sina Ober-Blöbaum,
and G. Morales-Luna. “Numerical Computation of Lightly Multi-Objective Robust
Optimal Solutions by Means of Generalized Cell Mapping.” Mathematics 8(11):1959
(2020).
ieee: C. I. O. Hernández Castellanos, G. Schütze, J.-Q. Sun, S. Ober-Blöbaum, and
G. Morales-Luna, “Numerical computation of lightly multi-objective robust optimal
solutions by means of generalized cell mapping,” Mathematics, vol. 8(11):1959,
2020.
mla: Hernández Castellanos, C. I. O., et al. “Numerical Computation of Lightly Multi-Objective
Robust Optimal Solutions by Means of Generalized Cell Mapping.” Mathematics,
vol. 8(11):1959, 2020.
short: C.I.O. Hernández Castellanos, G. Schütze, J.-Q. Sun, S. Ober-Blöbaum, G.
Morales-Luna, Mathematics 8(11):1959 (2020).
date_created: 2022-01-18T11:08:28Z
date_updated: 2022-01-21T09:57:35Z
department:
- _id: '636'
language:
- iso: eng
publication: Mathematics
status: public
title: Numerical computation of lightly multi-objective robust optimal solutions by
means of generalized cell mapping
type: journal_article
user_id: '15694'
volume: 8(11):1959
year: '2020'
...
---
_id: '29422'
author:
- first_name: Y.
full_name: Lishkova, Y.
last_name: Lishkova
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: M.
full_name: Cannon, M.
last_name: Cannon
- first_name: S.
full_name: Leyendecker, S.
last_name: Leyendecker
citation:
ama: 'Lishkova Y, Ober-Blöbaum S, Cannon M, Leyendecker S. A multirate variational
approach to simulation and optimal control for flexible spacecraft. In: Accepted
for Publication in Proceedings of 2020 AAS/AIAA Astrodynamics Specialist Conference
- Lake Tahoe. ; 2020.'
apa: Lishkova, Y., Ober-Blöbaum, S., Cannon, M., & Leyendecker, S. (2020). A
multirate variational approach to simulation and optimal control for flexible
spacecraft. Accepted for Publication in Proceedings of 2020 AAS/AIAA Astrodynamics
Specialist Conference - Lake Tahoe.
bibtex: '@inproceedings{Lishkova_Ober-Blöbaum_Cannon_Leyendecker_2020, title={A
multirate variational approach to simulation and optimal control for flexible
spacecraft}, booktitle={Accepted for publication in Proceedings of 2020 AAS/AIAA
Astrodynamics Specialist Conference - Lake Tahoe}, author={Lishkova, Y. and Ober-Blöbaum,
Sina and Cannon, M. and Leyendecker, S.}, year={2020} }'
chicago: Lishkova, Y., Sina Ober-Blöbaum, M. Cannon, and S. Leyendecker. “A Multirate
Variational Approach to Simulation and Optimal Control for Flexible Spacecraft.”
In Accepted for Publication in Proceedings of 2020 AAS/AIAA Astrodynamics Specialist
Conference - Lake Tahoe, 2020.
ieee: Y. Lishkova, S. Ober-Blöbaum, M. Cannon, and S. Leyendecker, “A multirate
variational approach to simulation and optimal control for flexible spacecraft,”
2020.
mla: Lishkova, Y., et al. “A Multirate Variational Approach to Simulation and Optimal
Control for Flexible Spacecraft.” Accepted for Publication in Proceedings of
2020 AAS/AIAA Astrodynamics Specialist Conference - Lake Tahoe, 2020.
short: 'Y. Lishkova, S. Ober-Blöbaum, M. Cannon, S. Leyendecker, in: Accepted for
Publication in Proceedings of 2020 AAS/AIAA Astrodynamics Specialist Conference
- Lake Tahoe, 2020.'
date_created: 2022-01-18T14:37:53Z
date_updated: 2022-01-21T13:45:40Z
department:
- _id: '636'
language:
- iso: eng
publication: Accepted for publication in Proceedings of 2020 AAS/AIAA Astrodynamics
Specialist Conference - Lake Tahoe
status: public
title: A multirate variational approach to simulation and optimal control for flexible
spacecraft
type: conference
user_id: '15694'
year: '2020'
...
---
_id: '29423'
author:
- first_name: T.
full_name: Faulwasser, T.
last_name: Faulwasser
- first_name: K.
full_name: Flaßkamp, K.
last_name: Flaßkamp
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: 'K. '
full_name: 'Worthmann, K. '
last_name: Worthmann
citation:
ama: 'Faulwasser T, Flaßkamp K, Ober-Blöbaum S, Worthmann K. A dissipativity characterization
of velocity turnpikes in optimal control problems for mechanical systems. In:
24th International Symposium on Mathematical Theory of Networks and Systems.
; 2020.'
apa: Faulwasser, T., Flaßkamp, K., Ober-Blöbaum, S., & Worthmann, K. (2020).
A dissipativity characterization of velocity turnpikes in optimal control problems
for mechanical systems. 24th International Symposium on Mathematical Theory
of Networks and Systems.
bibtex: '@inproceedings{Faulwasser_Flaßkamp_Ober-Blöbaum_Worthmann_2020, title={A
dissipativity characterization of velocity turnpikes in optimal control problems
for mechanical systems}, booktitle={24th International Symposium on Mathematical
Theory of Networks and Systems}, author={Faulwasser, T. and Flaßkamp, K. and Ober-Blöbaum,
Sina and Worthmann, K. }, year={2020} }'
chicago: Faulwasser, T., K. Flaßkamp, Sina Ober-Blöbaum, and K. Worthmann. “A Dissipativity
Characterization of Velocity Turnpikes in Optimal Control Problems for Mechanical
Systems.” In 24th International Symposium on Mathematical Theory of Networks
and Systems, 2020.
ieee: T. Faulwasser, K. Flaßkamp, S. Ober-Blöbaum, and K. Worthmann, “A dissipativity
characterization of velocity turnpikes in optimal control problems for mechanical
systems,” 2020.
mla: Faulwasser, T., et al. “A Dissipativity Characterization of Velocity Turnpikes
in Optimal Control Problems for Mechanical Systems.” 24th International Symposium
on Mathematical Theory of Networks and Systems, 2020.
short: 'T. Faulwasser, K. Flaßkamp, S. Ober-Blöbaum, K. Worthmann, in: 24th International
Symposium on Mathematical Theory of Networks and Systems, 2020.'
date_created: 2022-01-18T14:42:07Z
date_updated: 2022-01-21T13:46:57Z
department:
- _id: '636'
language:
- iso: eng
publication: 24th International Symposium on Mathematical Theory of Networks and Systems
status: public
title: A dissipativity characterization of velocity turnpikes in optimal control problems
for mechanical systems
type: conference
user_id: '15694'
year: '2020'
...
---
_id: '29424'
author:
- first_name: 'J. '
full_name: 'Cresson, J. '
last_name: Cresson
- first_name: F.
full_name: Jiménez, F.
last_name: Jiménez
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
citation:
ama: 'Cresson J, Jiménez F, Ober-Blöbaum S. Modelling of the convection-diffusion
equation through fractional restricted calculus of variations. In: 24th International
Symposium on Mathematical Theory of Networks and Systems. ; 2020.'
apa: Cresson, J., Jiménez, F., & Ober-Blöbaum, S. (2020). Modelling of the convection-diffusion
equation through fractional restricted calculus of variations. 24th International
Symposium on Mathematical Theory of Networks and Systems.
bibtex: '@inproceedings{Cresson_Jiménez_Ober-Blöbaum_2020, title={Modelling of the
convection-diffusion equation through fractional restricted calculus of variations},
booktitle={24th International Symposium on Mathematical Theory of Networks and
Systems}, author={Cresson, J. and Jiménez, F. and Ober-Blöbaum, Sina}, year={2020}
}'
chicago: Cresson, J. , F. Jiménez, and Sina Ober-Blöbaum. “Modelling of the Convection-Diffusion
Equation through Fractional Restricted Calculus of Variations.” In 24th International
Symposium on Mathematical Theory of Networks and Systems, 2020.
ieee: J. Cresson, F. Jiménez, and S. Ober-Blöbaum, “Modelling of the convection-diffusion
equation through fractional restricted calculus of variations,” 2020.
mla: Cresson, J., et al. “Modelling of the Convection-Diffusion Equation through
Fractional Restricted Calculus of Variations.” 24th International Symposium
on Mathematical Theory of Networks and Systems, 2020.
short: 'J. Cresson, F. Jiménez, S. Ober-Blöbaum, in: 24th International Symposium
on Mathematical Theory of Networks and Systems, 2020.'
date_created: 2022-01-18T14:45:22Z
date_updated: 2022-01-21T13:47:49Z
department:
- _id: '636'
language:
- iso: eng
publication: 24th International Symposium on Mathematical Theory of Networks and Systems
status: public
title: Modelling of the convection-diffusion equation through fractional restricted
calculus of variations
type: conference
user_id: '15694'
year: '2020'
...
---
_id: '29545'
author:
- first_name: Frédéric
full_name: Jean, Frédéric
last_name: Jean
- first_name: Sofya
full_name: Maslovskaya, Sofya
id: '87909'
last_name: Maslovskaya
- first_name: Igor
full_name: Zelenko, Igor
last_name: Zelenko
citation:
ama: Jean F, Maslovskaya S, Zelenko I. On Weyl’s type theorems and genericity of
projective rigidity in sub-Riemannian geometry. Geometriae Dedicata. 2020;213(1):295-314.
doi:10.1007/s10711-020-00581-z
apa: Jean, F., Maslovskaya, S., & Zelenko, I. (2020). On Weyl’s type theorems
and genericity of projective rigidity in sub-Riemannian geometry. Geometriae
Dedicata, 213(1), 295–314. https://doi.org/10.1007/s10711-020-00581-z
bibtex: '@article{Jean_Maslovskaya_Zelenko_2020, title={On Weyl’s type theorems
and genericity of projective rigidity in sub-Riemannian geometry}, volume={213},
DOI={10.1007/s10711-020-00581-z},
number={1}, journal={Geometriae Dedicata}, publisher={Springer Science and Business
Media LLC}, author={Jean, Frédéric and Maslovskaya, Sofya and Zelenko, Igor},
year={2020}, pages={295–314} }'
chicago: 'Jean, Frédéric, Sofya Maslovskaya, and Igor Zelenko. “On Weyl’s Type Theorems
and Genericity of Projective Rigidity in Sub-Riemannian Geometry.” Geometriae
Dedicata 213, no. 1 (2020): 295–314. https://doi.org/10.1007/s10711-020-00581-z.'
ieee: 'F. Jean, S. Maslovskaya, and I. Zelenko, “On Weyl’s type theorems and genericity
of projective rigidity in sub-Riemannian geometry,” Geometriae Dedicata,
vol. 213, no. 1, pp. 295–314, 2020, doi: 10.1007/s10711-020-00581-z.'
mla: Jean, Frédéric, et al. “On Weyl’s Type Theorems and Genericity of Projective
Rigidity in Sub-Riemannian Geometry.” Geometriae Dedicata, vol. 213, no.
1, Springer Science and Business Media LLC, 2020, pp. 295–314, doi:10.1007/s10711-020-00581-z.
short: F. Jean, S. Maslovskaya, I. Zelenko, Geometriae Dedicata 213 (2020) 295–314.
date_created: 2022-01-26T13:19:18Z
date_updated: 2022-01-26T13:19:39Z
department:
- _id: '636'
doi: 10.1007/s10711-020-00581-z
intvolume: ' 213'
issue: '1'
keyword:
- Geometry and Topology
language:
- iso: eng
page: 295-314
publication: Geometriae Dedicata
publication_identifier:
issn:
- 0046-5755
- 1572-9168
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: On Weyl’s type theorems and genericity of projective rigidity in sub-Riemannian
geometry
type: journal_article
user_id: '87909'
volume: 213
year: '2020'
...
---
_id: '29546'
author:
- first_name: Sofya
full_name: Maslovskaya, Sofya
id: '87909'
last_name: Maslovskaya
- first_name: Jean-Baptiste
full_name: Caillau, Jean-Baptiste
last_name: Caillau
- first_name: Walid
full_name: Djema, Walid
last_name: Djema
- first_name: Laetitia
full_name: Giraldi, Laetitia
last_name: Giraldi
- first_name: Jean-Luc
full_name: Jean-Luc, Jean-Luc
last_name: Jean-Luc
- first_name: Jean-Baptiste
full_name: Pomet, Jean-Baptiste
last_name: Pomet
citation:
ama: 'Maslovskaya S, Caillau J-B, Djema W, Giraldi L, Jean-Luc J-L, Pomet J-B. The
turnpike property in maximization of microbial metabolite production. In: ; 2020.'
apa: Maslovskaya, S., Caillau, J.-B., Djema, W., Giraldi, L., Jean-Luc, J.-L., &
Pomet, J.-B. (2020). The turnpike property in maximization of microbial metabolite
production. IFAC 2020 - 21rst IFAC World Congress.
bibtex: '@inproceedings{Maslovskaya_Caillau_Djema_Giraldi_Jean-Luc_Pomet_2020, title={The
turnpike property in maximization of microbial metabolite production}, author={Maslovskaya,
Sofya and Caillau, Jean-Baptiste and Djema, Walid and Giraldi, Laetitia and Jean-Luc,
Jean-Luc and Pomet, Jean-Baptiste}, year={2020} }'
chicago: Maslovskaya, Sofya, Jean-Baptiste Caillau, Walid Djema, Laetitia Giraldi,
Jean-Luc Jean-Luc, and Jean-Baptiste Pomet. “The Turnpike Property in Maximization
of Microbial Metabolite Production,” 2020.
ieee: S. Maslovskaya, J.-B. Caillau, W. Djema, L. Giraldi, J.-L. Jean-Luc, and J.-B.
Pomet, “The turnpike property in maximization of microbial metabolite production,”
presented at the IFAC 2020 - 21rst IFAC World Congress, 2020.
mla: Maslovskaya, Sofya, et al. The Turnpike Property in Maximization of Microbial
Metabolite Production. 2020.
short: 'S. Maslovskaya, J.-B. Caillau, W. Djema, L. Giraldi, J.-L. Jean-Luc, J.-B.
Pomet, in: 2020.'
conference:
name: IFAC 2020 - 21rst IFAC World Congress
date_created: 2022-01-26T13:26:36Z
date_updated: 2022-01-26T13:39:01Z
department:
- _id: '636'
extern: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://hal.archives-ouvertes.fr/hal-02916081/document
oa: '1'
quality_controlled: '1'
status: public
title: The turnpike property in maximization of microbial metabolite production
type: conference_abstract
user_id: '87909'
year: '2020'
...
---
_id: '31264'
abstract:
- lang: eng
text: "AbstractGiven a closed orientable hyperbolic
manifold of dimension $$\\ne
3$$\r\n
\ \r\n ≠\r\n 3\r\n
\ \r\n
we prove that the multiplicity of the Pollicott-Ruelle resonance of the geodesic
flow on perpendicular one-forms at zero agrees with the first Betti number of
the manifold. Additionally, we prove that this equality is stable under small
perturbations of the Riemannian metric and simultaneous small perturbations of
the geodesic vector field within the class of contact vector fields. For more
general perturbations we get bounds on the multiplicity of the resonance zero
on all one-forms in terms of the first and zeroth Betti numbers. Furthermore,
we identify for hyperbolic manifolds further resonance spaces whose multiplicities
are given by higher Betti numbers.\r\n"
author:
- first_name: Benjamin
full_name: Küster, Benjamin
last_name: Küster
- first_name: Tobias
full_name: Weich, Tobias
id: '49178'
last_name: Weich
orcid: 0000-0002-9648-6919
citation:
ama: Küster B, Weich T. Pollicott-Ruelle Resonant States and Betti Numbers. Communications
in Mathematical Physics. 2020;378(2):917-941. doi:10.1007/s00220-020-03793-2
apa: Küster, B., & Weich, T. (2020). Pollicott-Ruelle Resonant States and Betti
Numbers. Communications in Mathematical Physics, 378(2), 917–941.
https://doi.org/10.1007/s00220-020-03793-2
bibtex: '@article{Küster_Weich_2020, title={Pollicott-Ruelle Resonant States and
Betti Numbers}, volume={378}, DOI={10.1007/s00220-020-03793-2},
number={2}, journal={Communications in Mathematical Physics}, publisher={Springer
Science and Business Media LLC}, author={Küster, Benjamin and Weich, Tobias},
year={2020}, pages={917–941} }'
chicago: 'Küster, Benjamin, and Tobias Weich. “Pollicott-Ruelle Resonant States
and Betti Numbers.” Communications in Mathematical Physics 378, no. 2 (2020):
917–41. https://doi.org/10.1007/s00220-020-03793-2.'
ieee: 'B. Küster and T. Weich, “Pollicott-Ruelle Resonant States and Betti Numbers,”
Communications in Mathematical Physics, vol. 378, no. 2, pp. 917–941, 2020,
doi: 10.1007/s00220-020-03793-2.'
mla: Küster, Benjamin, and Tobias Weich. “Pollicott-Ruelle Resonant States and Betti
Numbers.” Communications in Mathematical Physics, vol. 378, no. 2, Springer
Science and Business Media LLC, 2020, pp. 917–41, doi:10.1007/s00220-020-03793-2.
short: B. Küster, T. Weich, Communications in Mathematical Physics 378 (2020) 917–941.
date_created: 2022-05-17T12:06:06Z
date_updated: 2022-05-19T10:13:48Z
department:
- _id: '10'
- _id: '623'
- _id: '548'
doi: 10.1007/s00220-020-03793-2
intvolume: ' 378'
issue: '2'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
page: 917-941
publication: Communications in Mathematical Physics
publication_identifier:
issn:
- 0010-3616
- 1432-0916
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Pollicott-Ruelle Resonant States and Betti Numbers
type: journal_article
user_id: '49178'
volume: 378
year: '2020'
...
---
_id: '31372'
author:
- first_name: Max
full_name: Hoffmann, Max
id: '32202'
last_name: Hoffmann
citation:
ama: 'Hoffmann M. Schnittstellenaktivitäten zum Kongruenzsatz WSW. In: Siller H-S,
Weigel W, Wörler JF, eds. Beiträge zum Mathematikunterricht 2020. WTM-Verlag;
2020:1353-1356. doi:10.17877/DE290R-21368'
apa: Hoffmann, M. (2020). Schnittstellenaktivitäten zum Kongruenzsatz WSW. In H.-S.
Siller, W. Weigel, & J. F. Wörler (Eds.), Beiträge zum Mathematikunterricht
2020 (pp. 1353–1356). WTM-Verlag. https://doi.org/10.17877/DE290R-21368
bibtex: '@inproceedings{Hoffmann_2020, place={Münster}, title={Schnittstellenaktivitäten
zum Kongruenzsatz WSW}, DOI={10.17877/DE290R-21368},
booktitle={Beiträge zum Mathematikunterricht 2020}, publisher={WTM-Verlag}, author={Hoffmann,
Max}, editor={Siller, Hans-Stefan and Weigel, Wolfgang and Wörler, Jan Franz},
year={2020}, pages={1353–1356} }'
chicago: 'Hoffmann, Max. “Schnittstellenaktivitäten zum Kongruenzsatz WSW.” In Beiträge
zum Mathematikunterricht 2020, edited by Hans-Stefan Siller, Wolfgang Weigel,
and Jan Franz Wörler, 1353–56. Münster: WTM-Verlag, 2020. https://doi.org/10.17877/DE290R-21368.'
ieee: 'M. Hoffmann, “Schnittstellenaktivitäten zum Kongruenzsatz WSW,” in Beiträge
zum Mathematikunterricht 2020, 2020, pp. 1353–1356, doi: 10.17877/DE290R-21368.'
mla: Hoffmann, Max. “Schnittstellenaktivitäten zum Kongruenzsatz WSW.” Beiträge
zum Mathematikunterricht 2020, edited by Hans-Stefan Siller et al., WTM-Verlag,
2020, pp. 1353–56, doi:10.17877/DE290R-21368.
short: 'M. Hoffmann, in: H.-S. Siller, W. Weigel, J.F. Wörler (Eds.), Beiträge zum
Mathematikunterricht 2020, WTM-Verlag, Münster, 2020, pp. 1353–1356.'
date_created: 2022-05-22T14:41:16Z
date_updated: 2022-05-22T14:44:17Z
department:
- _id: '97'
doi: 10.17877/DE290R-21368
editor:
- first_name: Hans-Stefan
full_name: Siller, Hans-Stefan
last_name: Siller
- first_name: Wolfgang
full_name: Weigel, Wolfgang
last_name: Weigel
- first_name: Jan Franz
full_name: Wörler, Jan Franz
last_name: Wörler
language:
- iso: ger
main_file_link:
- open_access: '1'
url: https://eldorado.tu-dortmund.de/handle/2003/39476
oa: '1'
page: 1353-1356
place: Münster
publication: Beiträge zum Mathematikunterricht 2020
publication_status: published
publisher: WTM-Verlag
status: public
title: Schnittstellenaktivitäten zum Kongruenzsatz WSW
type: conference
user_id: '32202'
year: '2020'
...
---
_id: '31386'
author:
- first_name: Max
full_name: Hoffmann, Max
id: '32202'
last_name: Hoffmann
citation:
ama: 'Hoffmann M. Rezension: Andrew Granville und Jenniver Granville: Prime Supects:
The Anatomy of Integers and Permutations. Mathematische Semesterberichte.
2020;67:119–121. doi:10.1007/s00591-019-00269-w'
apa: 'Hoffmann, M. (2020). Rezension: Andrew Granville und Jenniver Granville: Prime
Supects: The Anatomy of Integers and Permutations. In Mathematische Semesterberichte
(Vol. 67, pp. 119–121). https://doi.org/10.1007/s00591-019-00269-w'
bibtex: '@article{Hoffmann_2020, title={Rezension: Andrew Granville und Jenniver
Granville: Prime Supects: The Anatomy of Integers and Permutations}, volume={67},
DOI={10.1007/s00591-019-00269-w},
journal={Mathematische Semesterberichte}, author={Hoffmann, Max}, year={2020},
pages={119–121} }'
chicago: 'Hoffmann, Max. “Rezension: Andrew Granville und Jenniver Granville: Prime
Supects: The Anatomy of Integers and Permutations.” Mathematische Semesterberichte,
2020. https://doi.org/10.1007/s00591-019-00269-w.'
ieee: 'M. Hoffmann, “Rezension: Andrew Granville und Jenniver Granville: Prime Supects:
The Anatomy of Integers and Permutations,” Mathematische Semesterberichte,
vol. 67. pp. 119–121, 2020, doi: 10.1007/s00591-019-00269-w.'
mla: 'Hoffmann, Max. “Rezension: Andrew Granville und Jenniver Granville: Prime
Supects: The Anatomy of Integers and Permutations.” Mathematische Semesterberichte,
vol. 67, 2020, pp. 119–121, doi:10.1007/s00591-019-00269-w.'
short: M. Hoffmann, Mathematische Semesterberichte 67 (2020) 119–121.
date_created: 2022-05-22T15:23:04Z
date_updated: 2022-05-22T15:58:26Z
department:
- _id: '97'
doi: 10.1007/s00591-019-00269-w
intvolume: ' 67'
language:
- iso: ger
main_file_link:
- url: https://link.springer.com/article/10.1007/s00591-019-00269-w
page: 119–121
publication: Mathematische Semesterberichte
publication_status: published
status: public
title: 'Rezension: Andrew Granville und Jenniver Granville: Prime Supects: The Anatomy
of Integers and Permutations'
type: review
user_id: '32202'
volume: 67
year: '2020'
...
---
_id: '31384'
author:
- first_name: Max
full_name: Hoffmann, Max
id: '32202'
last_name: Hoffmann
citation:
ama: 'Hoffmann M. Rezension: Ehrhard Behrends: Parkettierungen der Ebene – Von Escher
über Möbius zu Penrose. Mathematische Semesterberichte. 2020;67:115–116.
doi:10.1007/s00591-019-00264-1'
apa: 'Hoffmann, M. (2020). Rezension: Ehrhard Behrends: Parkettierungen der Ebene
– Von Escher über Möbius zu Penrose. In Mathematische Semesterberichte
(Vol. 67, pp. 115–116). https://doi.org/10.1007/s00591-019-00264-1'
bibtex: '@article{Hoffmann_2020, title={Rezension: Ehrhard Behrends: Parkettierungen
der Ebene – Von Escher über Möbius zu Penrose}, volume={67}, DOI={10.1007/s00591-019-00264-1},
journal={Mathematische Semesterberichte}, author={Hoffmann, Max}, year={2020},
pages={115–116} }'
chicago: 'Hoffmann, Max. “Rezension: Ehrhard Behrends: Parkettierungen der Ebene
– Von Escher über Möbius zu Penrose.” Mathematische Semesterberichte, 2020.
https://doi.org/10.1007/s00591-019-00264-1.'
ieee: 'M. Hoffmann, “Rezension: Ehrhard Behrends: Parkettierungen der Ebene – Von
Escher über Möbius zu Penrose,” Mathematische Semesterberichte, vol. 67.
pp. 115–116, 2020, doi: 10.1007/s00591-019-00264-1.'
mla: 'Hoffmann, Max. “Rezension: Ehrhard Behrends: Parkettierungen der Ebene – Von
Escher über Möbius zu Penrose.” Mathematische Semesterberichte, vol. 67,
2020, pp. 115–116, doi:10.1007/s00591-019-00264-1.'
short: M. Hoffmann, Mathematische Semesterberichte 67 (2020) 115–116.
date_created: 2022-05-22T15:18:37Z
date_updated: 2022-05-22T15:58:39Z
department:
- _id: '97'
doi: 10.1007/s00591-019-00264-1
intvolume: ' 67'
language:
- iso: ger
main_file_link:
- url: https://link.springer.com/article/10.1007/s00591-019-00264-1
page: 115–116
publication: Mathematische Semesterberichte
publication_status: published
status: public
title: 'Rezension: Ehrhard Behrends: Parkettierungen der Ebene – Von Escher über Möbius
zu Penrose'
type: review
user_id: '32202'
volume: 67
year: '2020'
...
---
_id: '31381'
citation:
ama: 'Hoffmann M, ed. Der Mathematikunterricht 66 (6): Geometrie in Schule und
Lehramtsausbildung – ein Nachwuchsheft.; 2020.'
apa: 'Hoffmann, M. (Ed.). (2020). Der Mathematikunterricht 66 (6): Geometrie
in Schule und Lehramtsausbildung – ein Nachwuchsheft.'
bibtex: '@book{Hoffmann_2020, title={Der Mathematikunterricht 66 (6): Geometrie
in Schule und Lehramtsausbildung – ein Nachwuchsheft}, year={2020} }'
chicago: 'Hoffmann, Max, ed. Der Mathematikunterricht 66 (6): Geometrie in Schule
und Lehramtsausbildung – ein Nachwuchsheft, 2020.'
ieee: 'M. Hoffmann, Ed., Der Mathematikunterricht 66 (6): Geometrie in Schule
und Lehramtsausbildung – ein Nachwuchsheft. 2020.'
mla: 'Hoffmann, Max, editor. Der Mathematikunterricht 66 (6): Geometrie in Schule
und Lehramtsausbildung – ein Nachwuchsheft. 2020.'
short: 'M. Hoffmann, ed., Der Mathematikunterricht 66 (6): Geometrie in Schule und
Lehramtsausbildung – ein Nachwuchsheft, 2020.'
date_created: 2022-05-22T15:08:51Z
date_updated: 2022-05-22T16:00:26Z
department:
- _id: '97'
editor:
- first_name: Max
full_name: Hoffmann, Max
id: '32202'
last_name: Hoffmann
language:
- iso: ger
publication_status: published
related_material:
link:
- relation: table_of_contents
url: https://www.friedrich-verlag.de/shop/geometrie-in-schule-und-lehramtsausbildung-ein-nachwuchsheft-524216
status: public
title: 'Der Mathematikunterricht 66 (6): Geometrie in Schule und Lehramtsausbildung
– ein Nachwuchsheft'
type: book_editor
user_id: '32202'
year: '2020'
...