[{"year":"2020","title":"Deep model predictive flow control with limited sensor data and online learning","date_created":"2020-03-13T12:40:09Z","abstract":[{"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.","lang":"eng"}],"publication":"Theoretical and Computational Fluid Dynamics","language":[{"iso":"eng"}],"page":"577–591","intvolume":"        34","citation":{"short":"K. Bieker, S. Peitz, S.L. Brunton, J.N. Kutz, M. Dellnitz, Theoretical and Computational Fluid Dynamics 34 (2020) 577–591.","bibtex":"@article{Bieker_Peitz_Brunton_Kutz_Dellnitz_2020, title={Deep model predictive flow control with limited sensor data and online learning}, volume={34}, DOI={<a href=\"https://doi.org/10.1007/s00162-020-00520-4\">10.1007/s00162-020-00520-4</a>}, 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} }","mla":"Bieker, Katharina, et al. “Deep Model Predictive Flow Control with Limited Sensor Data and Online Learning.” <i>Theoretical and Computational Fluid Dynamics</i>, vol. 34, 2020, pp. 577–591, doi:<a href=\"https://doi.org/10.1007/s00162-020-00520-4\">10.1007/s00162-020-00520-4</a>.","apa":"Bieker, K., Peitz, S., Brunton, S. L., Kutz, J. N., &#38; Dellnitz, M. (2020). Deep model predictive flow control with limited sensor data and online learning. <i>Theoretical and Computational Fluid Dynamics</i>, <i>34</i>, 577–591. <a href=\"https://doi.org/10.1007/s00162-020-00520-4\">https://doi.org/10.1007/s00162-020-00520-4</a>","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.” <i>Theoretical and Computational Fluid Dynamics</i> 34 (2020): 577–591. <a href=\"https://doi.org/10.1007/s00162-020-00520-4\">https://doi.org/10.1007/s00162-020-00520-4</a>.","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,” <i>Theoretical and Computational Fluid Dynamics</i>, vol. 34, pp. 577–591, 2020.","ama":"Bieker K, Peitz S, Brunton SL, Kutz JN, Dellnitz M. Deep model predictive flow control with limited sensor data and online learning. <i>Theoretical and Computational Fluid Dynamics</i>. 2020;34:577–591. doi:<a href=\"https://doi.org/10.1007/s00162-020-00520-4\">10.1007/s00162-020-00520-4</a>"},"publication_identifier":{"issn":["0935-4964","1432-2250"]},"publication_status":"published","doi":"10.1007/s00162-020-00520-4","main_file_link":[{"open_access":"1","url":"https://link.springer.com/content/pdf/10.1007/s00162-020-00520-4.pdf"}],"date_updated":"2022-01-06T06:52:48Z","oa":"1","volume":34,"author":[{"last_name":"Bieker","id":"32829","full_name":"Bieker, Katharina","first_name":"Katharina"},{"orcid":"https://orcid.org/0000-0002-3389-793X","last_name":"Peitz","id":"47427","full_name":"Peitz, Sebastian","first_name":"Sebastian"},{"first_name":"Steven L.","full_name":"Brunton, Steven L.","last_name":"Brunton"},{"last_name":"Kutz","full_name":"Kutz, J. Nathan","first_name":"J. Nathan"},{"first_name":"Michael","last_name":"Dellnitz","full_name":"Dellnitz, Michael"}],"status":"public","type":"journal_article","article_type":"original","_id":"16290","project":[{"name":"Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"department":[{"_id":"101"}],"user_id":"47427"},{"language":[{"iso":"eng"}],"user_id":"47427","department":[{"_id":"101"}],"_id":"16309","status":"public","abstract":[{"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.","lang":"eng"}],"type":"journal_article","publication":"SIAM Journal on Applied Dynamical Systems","main_file_link":[{"url":"https://epubs.siam.org/doi/pdf/10.1137/20M1325678"}],"doi":"10.1137/20M1325678","title":"Data-Driven Model Predictive Control using Interpolated Koopman  Generators","date_created":"2020-03-17T09:53:01Z","author":[{"first_name":"Sebastian","last_name":"Peitz","orcid":"0000-0002-3389-793X","id":"47427","full_name":"Peitz, Sebastian"},{"last_name":"Otto","full_name":"Otto, Samuel E.","first_name":"Samuel E."},{"first_name":"Clarence W.","full_name":"Rowley, Clarence W.","last_name":"Rowley"}],"volume":19,"date_updated":"2022-01-06T06:52:48Z","citation":{"ama":"Peitz S, Otto SE, Rowley CW. Data-Driven Model Predictive Control using Interpolated Koopman  Generators. <i>SIAM Journal on Applied Dynamical Systems</i>. 2020;19(3):2162-2193. doi:<a href=\"https://doi.org/10.1137/20M1325678\">10.1137/20M1325678</a>","chicago":"Peitz, Sebastian, Samuel E. Otto, and Clarence W. Rowley. “Data-Driven Model Predictive Control Using Interpolated Koopman  Generators.” <i>SIAM Journal on Applied Dynamical Systems</i> 19, no. 3 (2020): 2162–93. <a href=\"https://doi.org/10.1137/20M1325678\">https://doi.org/10.1137/20M1325678</a>.","ieee":"S. Peitz, S. E. Otto, and C. W. Rowley, “Data-Driven Model Predictive Control using Interpolated Koopman  Generators,” <i>SIAM Journal on Applied Dynamical Systems</i>, vol. 19, no. 3, pp. 2162–2193, 2020.","apa":"Peitz, S., Otto, S. E., &#38; Rowley, C. W. (2020). Data-Driven Model Predictive Control using Interpolated Koopman  Generators. <i>SIAM Journal on Applied Dynamical Systems</i>, <i>19</i>(3), 2162–2193. <a href=\"https://doi.org/10.1137/20M1325678\">https://doi.org/10.1137/20M1325678</a>","short":"S. Peitz, S.E. Otto, C.W. Rowley, SIAM Journal on Applied Dynamical Systems 19 (2020) 2162–2193.","bibtex":"@article{Peitz_Otto_Rowley_2020, title={Data-Driven Model Predictive Control using Interpolated Koopman  Generators}, volume={19}, DOI={<a href=\"https://doi.org/10.1137/20M1325678\">10.1137/20M1325678</a>}, 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} }","mla":"Peitz, Sebastian, et al. “Data-Driven Model Predictive Control Using Interpolated Koopman  Generators.” <i>SIAM Journal on Applied Dynamical Systems</i>, vol. 19, no. 3, 2020, pp. 2162–93, doi:<a href=\"https://doi.org/10.1137/20M1325678\">10.1137/20M1325678</a>."},"page":"2162-2193","intvolume":"        19","year":"2020","issue":"3"},{"status":"public","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."}],"editor":[{"first_name":"Gert","last_name":"Kadunz","full_name":"Kadunz, Gert"}],"type":"book_chapter","publication":"Zeichen und Sprache im Mathematikunterricht","language":[{"iso":"ger"}],"user_id":"26809","department":[{"_id":"360"},{"_id":"98"}],"_id":"13108","citation":{"apa":"Schumacher, J., &#38; Rezat, S. (2020). Rekonstruktion diagrammatischen Schließens beim Erlernen der Subtraktion negativer Zahlen. Vergleich zweier methodischer Zugänge. In G. Kadunz (Ed.), <i>Zeichen und Sprache im Mathematikunterricht</i>. Springer. <a href=\"https://doi.org/10.1007/978-3-662-61194-4_5\">https://doi.org/10.1007/978-3-662-61194-4_5</a>","short":"J. Schumacher, S. Rezat, in: G. Kadunz (Ed.), Zeichen und Sprache im Mathematikunterricht, Springer, 2020.","bibtex":"@inbook{Schumacher_Rezat_2020, title={Rekonstruktion diagrammatischen Schließens beim Erlernen der Subtraktion negativer Zahlen. Vergleich zweier methodischer Zugänge}, DOI={<a href=\"https://doi.org/10.1007/978-3-662-61194-4_5\">10.1007/978-3-662-61194-4_5</a>}, booktitle={Zeichen und Sprache im Mathematikunterricht}, publisher={Springer}, author={Schumacher, Jan and Rezat, Sebastian}, editor={Kadunz, GertEditor}, year={2020} }","mla":"Schumacher, Jan, and Sebastian Rezat. “Rekonstruktion diagrammatischen Schließens beim Erlernen der Subtraktion negativer Zahlen. Vergleich zweier methodischer Zugänge.” <i>Zeichen und Sprache im Mathematikunterricht</i>, edited by Gert Kadunz, Springer, 2020, doi:<a href=\"https://doi.org/10.1007/978-3-662-61194-4_5\">10.1007/978-3-662-61194-4_5</a>.","ieee":"J. Schumacher and S. Rezat, “Rekonstruktion diagrammatischen Schließens beim Erlernen der Subtraktion negativer Zahlen. Vergleich zweier methodischer Zugänge,” in <i>Zeichen und Sprache im Mathematikunterricht</i>, G. Kadunz, Ed. Springer, 2020.","chicago":"Schumacher, Jan, and Sebastian Rezat. “Rekonstruktion diagrammatischen Schließens beim Erlernen der Subtraktion negativer Zahlen. Vergleich zweier methodischer Zugänge.” In <i>Zeichen und Sprache im Mathematikunterricht</i>, edited by Gert Kadunz. Springer, 2020. <a href=\"https://doi.org/10.1007/978-3-662-61194-4_5\">https://doi.org/10.1007/978-3-662-61194-4_5</a>.","ama":"Schumacher J, Rezat S. Rekonstruktion diagrammatischen Schließens beim Erlernen der Subtraktion negativer Zahlen. Vergleich zweier methodischer Zugänge. In: Kadunz G, ed. <i>Zeichen und Sprache im Mathematikunterricht</i>. Springer; 2020. doi:<a href=\"https://doi.org/10.1007/978-3-662-61194-4_5\">10.1007/978-3-662-61194-4_5</a>"},"year":"2020","publication_status":"published","quality_controlled":"1","doi":"10.1007/978-3-662-61194-4_5","title":"Rekonstruktion diagrammatischen Schließens beim Erlernen der Subtraktion negativer Zahlen. Vergleich zweier methodischer Zugänge","author":[{"last_name":"Schumacher","orcid":"0000-0002-6676-9774","full_name":"Schumacher, Jan","id":"26809","first_name":"Jan"},{"first_name":"Sebastian","full_name":"Rezat, Sebastian","last_name":"Rezat"}],"date_created":"2019-08-30T12:00:51Z","date_updated":"2022-01-06T06:51:28Z","publisher":"Springer"},{"_id":"31873","user_id":"26809","department":[{"_id":"360"},{"_id":"98"}],"language":[{"iso":"eng"}],"type":"conference","status":"public","date_updated":"2022-06-14T07:15:34Z","publisher":"LibreCat University","date_created":"2022-06-14T07:10:29Z","author":[{"last_name":"Schumacher","orcid":"0000-0002-6676-9774","id":"26809","full_name":"Schumacher, Jan","first_name":"Jan"}],"title":"Deduktion und Abduktion beim diagrammatischen Schließen – das didaktische Potential der Peirceschen Semiotik","doi":"10.17877/DE290R-21555","publication_status":"published","year":"2020","citation":{"apa":"Schumacher, J. (2020). <i>Deduktion und Abduktion beim diagrammatischen Schließen – das didaktische Potential der Peirceschen Semiotik</i>. <a href=\"https://doi.org/10.17877/DE290R-21555\">https://doi.org/10.17877/DE290R-21555</a>","bibtex":"@inproceedings{Schumacher_2020, title={Deduktion und Abduktion beim diagrammatischen Schließen – das didaktische Potential der Peirceschen Semiotik}, DOI={<a href=\"https://doi.org/10.17877/DE290R-21555\">10.17877/DE290R-21555</a>}, publisher={LibreCat University}, author={Schumacher, Jan}, year={2020} }","mla":"Schumacher, Jan. <i>Deduktion Und Abduktion Beim Diagrammatischen Schließen – Das Didaktische Potential Der Peirceschen Semiotik</i>. LibreCat University, 2020, doi:<a href=\"https://doi.org/10.17877/DE290R-21555\">10.17877/DE290R-21555</a>.","short":"J. Schumacher, in: LibreCat University, 2020.","chicago":"Schumacher, Jan. “Deduktion Und Abduktion Beim Diagrammatischen Schließen – Das Didaktische Potential Der Peirceschen Semiotik.” LibreCat University, 2020. <a href=\"https://doi.org/10.17877/DE290R-21555\">https://doi.org/10.17877/DE290R-21555</a>.","ieee":"J. Schumacher, “Deduktion und Abduktion beim diagrammatischen Schließen – das didaktische Potential der Peirceschen Semiotik,” 2020, doi: <a href=\"https://doi.org/10.17877/DE290R-21555\">10.17877/DE290R-21555</a>.","ama":"Schumacher J. Deduktion und Abduktion beim diagrammatischen Schließen – das didaktische Potential der Peirceschen Semiotik. In: LibreCat University; 2020. doi:<a href=\"https://doi.org/10.17877/DE290R-21555\">10.17877/DE290R-21555</a>"}},{"status":"public","type":"journal_article","publication":"Archivum Mathematicum","language":[{"iso":"eng"}],"article_type":"original","keyword":["22A22","22E65","22E67","46T10","47H30","58D15","58H05"],"user_id":"178","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"_id":"34789","citation":{"apa":"Amiri, H., Glöckner, H., &#38; Schmeding, A. (2020). Lie groupoids of mappings taking values in a Lie groupoid. <i>Archivum Mathematicum</i>, <i>56</i>(5), 307–356. <a href=\"https://doi.org/10.5817/AM2020-5-307\">https://doi.org/10.5817/AM2020-5-307</a>","bibtex":"@article{Amiri_Glöckner_Schmeding_2020, title={Lie groupoids of mappings taking values in a Lie groupoid}, volume={56}, DOI={<a href=\"https://doi.org/10.5817/AM2020-5-307\">10.5817/AM2020-5-307</a>}, number={5}, journal={Archivum Mathematicum}, author={Amiri, Habib and Glöckner, Helge and Schmeding, Alexander}, year={2020}, pages={307–356} }","short":"H. Amiri, H. Glöckner, A. Schmeding, Archivum Mathematicum 56 (2020) 307–356.","mla":"Amiri, Habib, et al. “Lie Groupoids of Mappings Taking Values in a Lie Groupoid.” <i>Archivum Mathematicum</i>, vol. 56, no. 5, 2020, pp. 307–356, doi:<a href=\"https://doi.org/10.5817/AM2020-5-307\">10.5817/AM2020-5-307</a>.","ama":"Amiri H, Glöckner H, Schmeding A. Lie groupoids of mappings taking values in a Lie groupoid. <i>Archivum Mathematicum</i>. 2020;56(5):307–356. doi:<a href=\"https://doi.org/10.5817/AM2020-5-307\">10.5817/AM2020-5-307</a>","ieee":"H. Amiri, H. Glöckner, and A. Schmeding, “Lie groupoids of mappings taking values in a Lie groupoid,” <i>Archivum Mathematicum</i>, vol. 56, no. 5, pp. 307–356, 2020, doi: <a href=\"https://doi.org/10.5817/AM2020-5-307\">10.5817/AM2020-5-307</a>.","chicago":"Amiri, Habib, Helge Glöckner, and Alexander Schmeding. “Lie Groupoids of Mappings Taking Values in a Lie Groupoid.” <i>Archivum Mathematicum</i> 56, no. 5 (2020): 307–356. <a href=\"https://doi.org/10.5817/AM2020-5-307\">https://doi.org/10.5817/AM2020-5-307</a>."},"intvolume":"        56","page":"307–356","year":"2020","issue":"5","quality_controlled":"1","publication_identifier":{"issn":["0044-8753"]},"doi":"10.5817/AM2020-5-307","title":"Lie groupoids of mappings taking values in a Lie groupoid","date_created":"2022-12-21T19:13:24Z","author":[{"full_name":"Amiri, Habib","last_name":"Amiri","first_name":"Habib"},{"first_name":"Helge","last_name":"Glöckner","id":"178","full_name":"Glöckner, Helge"},{"first_name":"Alexander","full_name":"Schmeding, Alexander","last_name":"Schmeding"}],"volume":56,"date_updated":"2022-12-21T19:15:59Z"},{"author":[{"id":"178","full_name":"Glöckner, Helge","last_name":"Glöckner","first_name":"Helge"},{"first_name":"Niku","full_name":"Masbough, Niku","last_name":"Masbough"}],"date_created":"2022-12-21T19:06:45Z","volume":55,"date_updated":"2022-12-21T20:06:44Z","title":"Products of regular locally compact spaces are k_R-spaces","publication_identifier":{"issn":["0146-4124"]},"quality_controlled":"1","citation":{"chicago":"Glöckner, Helge, and Niku Masbough. “Products of Regular Locally Compact Spaces Are K_R-Spaces.” <i>Topology Proceedings</i> 55 (2020): 35–38.","ieee":"H. Glöckner and N. Masbough, “Products of regular locally compact spaces are k_R-spaces,” <i>Topology Proceedings</i>, vol. 55, pp. 35–38, 2020.","ama":"Glöckner H, Masbough N. Products of regular locally compact spaces are k_R-spaces. <i>Topology Proceedings</i>. 2020;55:35–38.","short":"H. Glöckner, N. Masbough, Topology Proceedings 55 (2020) 35–38.","mla":"Glöckner, Helge, and Niku Masbough. “Products of Regular Locally Compact Spaces Are K_R-Spaces.” <i>Topology Proceedings</i>, vol. 55, 2020, pp. 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} }","apa":"Glöckner, H., &#38; Masbough, N. (2020). Products of regular locally compact spaces are k_R-spaces. <i>Topology Proceedings</i>, <i>55</i>, 35–38."},"intvolume":"        55","page":"35–38","year":"2020","user_id":"178","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"_id":"34787","language":[{"iso":"eng"}],"article_type":"original","keyword":["54B10","54D45","54D50"],"type":"journal_article","publication":"Topology Proceedings","status":"public"},{"title":"Smoothing operators for vector-valued functions and extension operators","date_updated":"2022-12-22T07:52:42Z","author":[{"id":"178","full_name":"Glöckner, Helge","last_name":"Glöckner","first_name":"Helge"}],"date_created":"2022-12-22T07:51:53Z","year":"2020","citation":{"chicago":"Glöckner, Helge. “Smoothing Operators for Vector-Valued Functions and Extension Operators.” <i>ArXiv:2006.00254</i>, 2020.","ieee":"H. Glöckner, “Smoothing operators for vector-valued functions and extension operators,” <i>arXiv:2006.00254</i>. 2020.","ama":"Glöckner H. Smoothing operators for vector-valued functions and extension operators. <i>arXiv:200600254</i>. Published online 2020.","apa":"Glöckner, H. (2020). Smoothing operators for vector-valued functions and extension operators. In <i>arXiv:2006.00254</i>.","mla":"Glöckner, Helge. “Smoothing Operators for Vector-Valued Functions and Extension Operators.” <i>ArXiv:2006.00254</i>, 2020.","bibtex":"@article{Glöckner_2020, title={Smoothing operators for vector-valued functions and extension operators}, journal={arXiv:2006.00254}, author={Glöckner, Helge}, year={2020} }","short":"H. Glöckner, ArXiv:2006.00254 (2020)."},"language":[{"iso":"eng"}],"_id":"34808","external_id":{"arxiv":["2006.00254"]},"department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"user_id":"178","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."}],"status":"public","publication":"arXiv:2006.00254","type":"preprint"},{"_id":"29399","user_id":"15694","department":[{"_id":"636"}],"language":[{"iso":"eng"}],"type":"journal_article","publication":"IEEE Transactions on Automatic Control","status":"public","date_updated":"2022-01-21T08:26:46Z","author":[{"last_name":"Limebeer","full_name":"Limebeer, D. J. N.","first_name":"D. J. N."},{"id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"},{"last_name":"Farshi","full_name":"Farshi, F. H.","first_name":"F. H."}],"date_created":"2022-01-18T11:17:25Z","volume":"65(4)","title":"Variational integrators for dissipative systems","year":"2020","citation":{"ama":"Limebeer DJN, Ober-Blöbaum S, Farshi FH. Variational integrators for dissipative systems. <i>IEEE Transactions on Automatic Control</i>. 2020;65(4):1381-1396.","ieee":"D. J. N. Limebeer, S. Ober-Blöbaum, and F. H. Farshi, “Variational integrators for dissipative systems,” <i>IEEE Transactions on Automatic Control</i>, vol. 65(4), pp. 1381–1396, 2020.","chicago":"Limebeer, D. J. N., Sina Ober-Blöbaum, and F. H. Farshi. “Variational Integrators for Dissipative Systems.” <i>IEEE Transactions on Automatic Control</i> 65(4) (2020): 1381–96.","apa":"Limebeer, D. J. N., Ober-Blöbaum, S., &#38; Farshi, F. H. (2020). Variational integrators for dissipative systems. <i>IEEE Transactions on Automatic Control</i>, <i>65(4)</i>, 1381–1396.","short":"D.J.N. Limebeer, S. Ober-Blöbaum, F.H. Farshi, IEEE Transactions on Automatic Control 65(4) (2020) 1381–1396.","mla":"Limebeer, D. J. N., et al. “Variational Integrators for Dissipative Systems.” <i>IEEE Transactions on Automatic Control</i>, vol. 65(4), 2020, pp. 1381–96.","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} }"},"page":"1381-1396"},{"page":"7593-7618","citation":{"ama":"Hernández Castellanos CI, Ober-Blöbaum S, Peitz S. Explicit Multi-objective Model Predictive Control for Nonlinear Systems  Under Uncertainty. <i>International Journal of Robust and Nonlinear Control</i>. 2020;30(17):7593-7618. doi:<a href=\"https://doi.org/10.1002/rnc.5197\">10.1002/rnc.5197</a>","ieee":"C. I. Hernández Castellanos, S. Ober-Blöbaum, and S. Peitz, “Explicit Multi-objective Model Predictive Control for Nonlinear Systems  Under Uncertainty,” <i>International Journal of Robust and Nonlinear Control</i>, vol. 30(17), pp. 7593–7618, 2020, doi: <a href=\"https://doi.org/10.1002/rnc.5197\">10.1002/rnc.5197</a>.","chicago":"Hernández Castellanos, Carlos Ignacio, Sina Ober-Blöbaum, and Sebastian Peitz. “Explicit Multi-Objective Model Predictive Control for Nonlinear Systems  Under Uncertainty.” <i>International Journal of Robust and Nonlinear Control</i> 30(17) (2020): 7593–7618. <a href=\"https://doi.org/10.1002/rnc.5197\">https://doi.org/10.1002/rnc.5197</a>.","apa":"Hernández Castellanos, C. I., Ober-Blöbaum, S., &#38; Peitz, S. (2020). Explicit Multi-objective Model Predictive Control for Nonlinear Systems  Under Uncertainty. <i>International Journal of Robust and Nonlinear Control</i>, <i>30(17)</i>, 7593–7618. <a href=\"https://doi.org/10.1002/rnc.5197\">https://doi.org/10.1002/rnc.5197</a>","short":"C.I. Hernández Castellanos, S. Ober-Blöbaum, S. Peitz, International Journal of Robust and Nonlinear Control 30(17) (2020) 7593–7618.","mla":"Hernández Castellanos, Carlos Ignacio, et al. “Explicit Multi-Objective Model Predictive Control for Nonlinear Systems  Under Uncertainty.” <i>International Journal of Robust and Nonlinear Control</i>, vol. 30(17), 2020, pp. 7593–618, doi:<a href=\"https://doi.org/10.1002/rnc.5197\">10.1002/rnc.5197</a>.","bibtex":"@article{Hernández Castellanos_Ober-Blöbaum_Peitz_2020, title={Explicit Multi-objective Model Predictive Control for Nonlinear Systems  Under Uncertainty}, volume={30(17)}, DOI={<a href=\"https://doi.org/10.1002/rnc.5197\">10.1002/rnc.5197</a>}, 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} }"},"year":"2020","volume":"30(17)","date_created":"2020-03-13T12:45:56Z","author":[{"full_name":"Hernández Castellanos, Carlos Ignacio","last_name":"Hernández Castellanos","first_name":"Carlos Ignacio"},{"first_name":"Sina","id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum"},{"orcid":"https://orcid.org/0000-0002-3389-793X","last_name":"Peitz","id":"47427","full_name":"Peitz, Sebastian","first_name":"Sebastian"}],"date_updated":"2022-01-21T09:55:39Z","doi":"10.1002/rnc.5197","title":"Explicit Multi-objective Model Predictive Control for Nonlinear Systems  Under Uncertainty","publication":"International Journal of Robust and Nonlinear Control","type":"journal_article","status":"public","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."}],"department":[{"_id":"101"}],"user_id":"15694","_id":"16297","language":[{"iso":"eng"}]},{"title":"Numerical computation of lightly multi-objective robust optimal solutions by means of generalized cell mapping","date_updated":"2022-01-21T09:57:35Z","author":[{"last_name":"Hernández Castellanos","full_name":"Hernández Castellanos, C. I. O.","first_name":"C. I. O."},{"last_name":"Schütze","full_name":"Schütze, G.","first_name":"G."},{"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"},{"full_name":"Morales-Luna, G.","last_name":"Morales-Luna","first_name":"G."}],"date_created":"2022-01-18T11:08:28Z","volume":"8(11):1959","year":"2020","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. <i>Mathematics</i>. 2020;8(11):1959.","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,” <i>Mathematics</i>, vol. 8(11):1959, 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.” <i>Mathematics</i> 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).","mla":"Hernández Castellanos, C. I. O., et al. “Numerical Computation of Lightly Multi-Objective Robust Optimal Solutions by Means of Generalized Cell Mapping.” <i>Mathematics</i>, vol. 8(11):1959, 2020.","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} }","apa":"Hernández Castellanos, C. I. O., Schütze, G., Sun, J.-Q., Ober-Blöbaum, S., &#38; Morales-Luna, G. (2020). Numerical computation of lightly multi-objective robust optimal solutions by means of generalized cell mapping. <i>Mathematics</i>, <i>8(11):1959</i>."},"language":[{"iso":"eng"}],"_id":"29398","user_id":"15694","department":[{"_id":"636"}],"status":"public","type":"journal_article","publication":"Mathematics"},{"type":"conference","publication":"Accepted for publication in Proceedings of 2020 AAS/AIAA Astrodynamics Specialist Conference - Lake Tahoe","status":"public","user_id":"15694","department":[{"_id":"636"}],"_id":"29422","language":[{"iso":"eng"}],"citation":{"apa":"Lishkova, Y., Ober-Blöbaum, S., Cannon, M., &#38; Leyendecker, S. (2020). A multirate variational approach to simulation and optimal control for flexible spacecraft. <i>Accepted for Publication in Proceedings of 2020 AAS/AIAA Astrodynamics Specialist Conference - Lake Tahoe</i>.","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.","mla":"Lishkova, Y., et al. “A Multirate Variational Approach to Simulation and Optimal Control for Flexible Spacecraft.” <i>Accepted for Publication in Proceedings of 2020 AAS/AIAA Astrodynamics Specialist Conference - Lake Tahoe</i>, 2020.","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} }","ama":"Lishkova Y, Ober-Blöbaum S, Cannon M, Leyendecker S. A multirate variational approach to simulation and optimal control for flexible spacecraft. In: <i>Accepted for Publication in Proceedings of 2020 AAS/AIAA Astrodynamics Specialist Conference - Lake Tahoe</i>. ; 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 <i>Accepted for Publication in Proceedings of 2020 AAS/AIAA Astrodynamics Specialist Conference - Lake Tahoe</i>, 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."},"year":"2020","author":[{"full_name":"Lishkova, Y.","last_name":"Lishkova","first_name":"Y."},{"first_name":"Sina","last_name":"Ober-Blöbaum","id":"16494","full_name":"Ober-Blöbaum, Sina"},{"full_name":"Cannon, M.","last_name":"Cannon","first_name":"M."},{"first_name":"S.","full_name":"Leyendecker, S.","last_name":"Leyendecker"}],"date_created":"2022-01-18T14:37:53Z","date_updated":"2022-01-21T13:45:40Z","title":"A multirate variational approach to simulation and optimal control for flexible spacecraft"},{"language":[{"iso":"eng"}],"_id":"29423","department":[{"_id":"636"}],"user_id":"15694","status":"public","publication":"24th International Symposium on Mathematical Theory of Networks and Systems","type":"conference","title":"A dissipativity characterization of velocity turnpikes in optimal control problems for mechanical systems","date_updated":"2022-01-21T13:46:57Z","date_created":"2022-01-18T14:42:07Z","author":[{"first_name":"T.","last_name":"Faulwasser","full_name":"Faulwasser, T."},{"last_name":"Flaßkamp","full_name":"Flaßkamp, K.","first_name":"K."},{"full_name":"Ober-Blöbaum, Sina","id":"16494","last_name":"Ober-Blöbaum","first_name":"Sina"},{"last_name":"Worthmann","full_name":"Worthmann, K. ","first_name":"K. "}],"year":"2020","citation":{"apa":"Faulwasser, T., Flaßkamp, K., Ober-Blöbaum, S., &#38; Worthmann, K. (2020). A dissipativity characterization of velocity turnpikes in optimal control problems for mechanical systems. <i>24th International Symposium on Mathematical Theory of Networks and Systems</i>.","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} }","short":"T. Faulwasser, K. Flaßkamp, S. Ober-Blöbaum, K. Worthmann, in: 24th International Symposium on Mathematical Theory of Networks and Systems, 2020.","mla":"Faulwasser, T., et al. “A Dissipativity Characterization of Velocity Turnpikes in Optimal Control Problems for Mechanical Systems.” <i>24th International Symposium on Mathematical Theory of Networks and Systems</i>, 2020.","ama":"Faulwasser T, Flaßkamp K, Ober-Blöbaum S, Worthmann K. A dissipativity characterization of velocity turnpikes in optimal control problems for mechanical systems. In: <i>24th International Symposium on Mathematical Theory of Networks and Systems</i>. ; 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.","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 <i>24th International Symposium on Mathematical Theory of Networks and Systems</i>, 2020."}},{"publication":"24th International Symposium on Mathematical Theory of Networks and Systems","type":"conference","status":"public","_id":"29424","department":[{"_id":"636"}],"user_id":"15694","language":[{"iso":"eng"}],"year":"2020","citation":{"ama":"Cresson J, Jiménez F, Ober-Blöbaum S. Modelling of the convection-diffusion equation through fractional restricted calculus of variations. In: <i>24th International Symposium on Mathematical Theory of Networks and Systems</i>. ; 2020.","ieee":"J. Cresson, F. Jiménez, and S. Ober-Blöbaum, “Modelling of the convection-diffusion equation through fractional restricted calculus of variations,” 2020.","chicago":"Cresson, J. , F. Jiménez, and Sina Ober-Blöbaum. “Modelling of the Convection-Diffusion Equation through Fractional Restricted Calculus of Variations.” In <i>24th International Symposium on Mathematical Theory of Networks and Systems</i>, 2020.","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} }","mla":"Cresson, J., et al. “Modelling of the Convection-Diffusion Equation through Fractional Restricted Calculus of Variations.” <i>24th International Symposium on Mathematical Theory of Networks and Systems</i>, 2020.","short":"J. Cresson, F. Jiménez, S. Ober-Blöbaum, in: 24th International Symposium on Mathematical Theory of Networks and Systems, 2020.","apa":"Cresson, J., Jiménez, F., &#38; Ober-Blöbaum, S. (2020). Modelling of the convection-diffusion equation through fractional restricted calculus of variations. <i>24th International Symposium on Mathematical Theory of Networks and Systems</i>."},"date_updated":"2022-01-21T13:47:49Z","author":[{"full_name":"Cresson, J. ","last_name":"Cresson","first_name":"J. "},{"last_name":"Jiménez","full_name":"Jiménez, F.","first_name":"F."},{"last_name":"Ober-Blöbaum","id":"16494","full_name":"Ober-Blöbaum, Sina","first_name":"Sina"}],"date_created":"2022-01-18T14:45:22Z","title":"Modelling of the convection-diffusion equation through fractional restricted calculus of variations"},{"date_created":"2022-01-26T13:19:18Z","publisher":"Springer Science and Business Media LLC","title":"On Weyl’s type theorems and genericity of projective rigidity in sub-Riemannian geometry","issue":"1","year":"2020","language":[{"iso":"eng"}],"keyword":["Geometry and Topology"],"publication":"Geometriae Dedicata","author":[{"first_name":"Frédéric","full_name":"Jean, Frédéric","last_name":"Jean"},{"last_name":"Maslovskaya","full_name":"Maslovskaya, Sofya","id":"87909","first_name":"Sofya"},{"full_name":"Zelenko, Igor","last_name":"Zelenko","first_name":"Igor"}],"volume":213,"date_updated":"2022-01-26T13:19:39Z","doi":"10.1007/s10711-020-00581-z","publication_status":"published","publication_identifier":{"issn":["0046-5755","1572-9168"]},"citation":{"apa":"Jean, F., Maslovskaya, S., &#38; Zelenko, I. (2020). On Weyl’s type theorems and genericity of projective rigidity in sub-Riemannian geometry. <i>Geometriae Dedicata</i>, <i>213</i>(1), 295–314. <a href=\"https://doi.org/10.1007/s10711-020-00581-z\">https://doi.org/10.1007/s10711-020-00581-z</a>","short":"F. Jean, S. Maslovskaya, I. Zelenko, Geometriae Dedicata 213 (2020) 295–314.","mla":"Jean, Frédéric, et al. “On Weyl’s Type Theorems and Genericity of Projective Rigidity in Sub-Riemannian Geometry.” <i>Geometriae Dedicata</i>, vol. 213, no. 1, Springer Science and Business Media LLC, 2020, pp. 295–314, doi:<a href=\"https://doi.org/10.1007/s10711-020-00581-z\">10.1007/s10711-020-00581-z</a>.","bibtex":"@article{Jean_Maslovskaya_Zelenko_2020, title={On Weyl’s type theorems and genericity of projective rigidity in sub-Riemannian geometry}, volume={213}, DOI={<a href=\"https://doi.org/10.1007/s10711-020-00581-z\">10.1007/s10711-020-00581-z</a>}, 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.” <i>Geometriae Dedicata</i> 213, no. 1 (2020): 295–314. <a href=\"https://doi.org/10.1007/s10711-020-00581-z\">https://doi.org/10.1007/s10711-020-00581-z</a>.","ieee":"F. Jean, S. Maslovskaya, and I. Zelenko, “On Weyl’s type theorems and genericity of projective rigidity in sub-Riemannian geometry,” <i>Geometriae Dedicata</i>, vol. 213, no. 1, pp. 295–314, 2020, doi: <a href=\"https://doi.org/10.1007/s10711-020-00581-z\">10.1007/s10711-020-00581-z</a>.","ama":"Jean F, Maslovskaya S, Zelenko I. On Weyl’s type theorems and genericity of projective rigidity in sub-Riemannian geometry. <i>Geometriae Dedicata</i>. 2020;213(1):295-314. doi:<a href=\"https://doi.org/10.1007/s10711-020-00581-z\">10.1007/s10711-020-00581-z</a>"},"intvolume":"       213","page":"295-314","user_id":"87909","department":[{"_id":"636"}],"_id":"29545","type":"journal_article","status":"public"},{"quality_controlled":"1","citation":{"apa":"Maslovskaya, S., Caillau, J.-B., Djema, W., Giraldi, L., Jean-Luc, J.-L., &#38; Pomet, J.-B. (2020). <i>The turnpike property in maximization of microbial metabolite production</i>. IFAC 2020 - 21rst IFAC World Congress.","mla":"Maslovskaya, Sofya, et al. <i>The Turnpike Property in Maximization of Microbial Metabolite Production</i>. 2020.","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} }","short":"S. Maslovskaya, J.-B. Caillau, W. Djema, L. Giraldi, J.-L. Jean-Luc, J.-B. Pomet, in: 2020.","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.","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.","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."},"year":"2020","date_created":"2022-01-26T13:26:36Z","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"},{"full_name":"Djema, Walid","last_name":"Djema","first_name":"Walid"},{"last_name":"Giraldi","full_name":"Giraldi, Laetitia","first_name":"Laetitia"},{"first_name":"Jean-Luc","full_name":"Jean-Luc, Jean-Luc","last_name":"Jean-Luc"},{"last_name":"Pomet","full_name":"Pomet, Jean-Baptiste","first_name":"Jean-Baptiste"}],"date_updated":"2022-01-26T13:39:01Z","oa":"1","main_file_link":[{"url":"https://hal.archives-ouvertes.fr/hal-02916081/document","open_access":"1"}],"conference":{"name":"IFAC 2020 - 21rst IFAC World Congress"},"title":"The turnpike property in maximization of microbial metabolite production","type":"conference_abstract","status":"public","user_id":"87909","department":[{"_id":"636"}],"_id":"29546","extern":"1","language":[{"iso":"eng"}]},{"publication_status":"published","publication_identifier":{"issn":["0010-3616","1432-0916"]},"citation":{"ieee":"B. Küster and T. Weich, “Pollicott-Ruelle Resonant States and Betti Numbers,” <i>Communications in Mathematical Physics</i>, vol. 378, no. 2, pp. 917–941, 2020, doi: <a href=\"https://doi.org/10.1007/s00220-020-03793-2\">10.1007/s00220-020-03793-2</a>.","chicago":"Küster, Benjamin, and Tobias Weich. “Pollicott-Ruelle Resonant States and Betti Numbers.” <i>Communications in Mathematical Physics</i> 378, no. 2 (2020): 917–41. <a href=\"https://doi.org/10.1007/s00220-020-03793-2\">https://doi.org/10.1007/s00220-020-03793-2</a>.","ama":"Küster B, Weich T. Pollicott-Ruelle Resonant States and Betti Numbers. <i>Communications in Mathematical Physics</i>. 2020;378(2):917-941. doi:<a href=\"https://doi.org/10.1007/s00220-020-03793-2\">10.1007/s00220-020-03793-2</a>","mla":"Küster, Benjamin, and Tobias Weich. “Pollicott-Ruelle Resonant States and Betti Numbers.” <i>Communications in Mathematical Physics</i>, vol. 378, no. 2, Springer Science and Business Media LLC, 2020, pp. 917–41, doi:<a href=\"https://doi.org/10.1007/s00220-020-03793-2\">10.1007/s00220-020-03793-2</a>.","bibtex":"@article{Küster_Weich_2020, title={Pollicott-Ruelle Resonant States and Betti Numbers}, volume={378}, DOI={<a href=\"https://doi.org/10.1007/s00220-020-03793-2\">10.1007/s00220-020-03793-2</a>}, 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} }","short":"B. Küster, T. Weich, Communications in Mathematical Physics 378 (2020) 917–941.","apa":"Küster, B., &#38; Weich, T. (2020). Pollicott-Ruelle Resonant States and Betti Numbers. <i>Communications in Mathematical Physics</i>, <i>378</i>(2), 917–941. <a href=\"https://doi.org/10.1007/s00220-020-03793-2\">https://doi.org/10.1007/s00220-020-03793-2</a>"},"intvolume":"       378","page":"917-941","author":[{"first_name":"Benjamin","full_name":"Küster, Benjamin","last_name":"Küster"},{"orcid":"0000-0002-9648-6919","last_name":"Weich","full_name":"Weich, Tobias","id":"49178","first_name":"Tobias"}],"volume":378,"date_updated":"2022-05-19T10:13:48Z","doi":"10.1007/s00220-020-03793-2","type":"journal_article","status":"public","user_id":"49178","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"_id":"31264","issue":"2","year":"2020","date_created":"2022-05-17T12:06:06Z","publisher":"Springer Science and Business Media LLC","title":"Pollicott-Ruelle Resonant States and Betti Numbers","publication":"Communications in Mathematical Physics","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>Given a closed orientable hyperbolic manifold of dimension <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\ne 3$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mo>≠</mml:mo>\r\n                    <mml:mn>3</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula> 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</jats:p>","lang":"eng"}],"language":[{"iso":"eng"}],"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"]},{"language":[{"iso":"ger"}],"user_id":"32202","department":[{"_id":"97"}],"_id":"31372","status":"public","editor":[{"first_name":"Hans-Stefan","last_name":"Siller","full_name":"Siller, Hans-Stefan"},{"full_name":"Weigel, Wolfgang","last_name":"Weigel","first_name":"Wolfgang"},{"last_name":"Wörler","full_name":"Wörler, Jan Franz","first_name":"Jan Franz"}],"type":"conference","publication":"Beiträge zum Mathematikunterricht 2020","main_file_link":[{"open_access":"1","url":"https://eldorado.tu-dortmund.de/handle/2003/39476"}],"doi":"10.17877/DE290R-21368","title":"Schnittstellenaktivitäten zum Kongruenzsatz WSW","author":[{"first_name":"Max","full_name":"Hoffmann, Max","id":"32202","last_name":"Hoffmann"}],"date_created":"2022-05-22T14:41:16Z","publisher":"WTM-Verlag","date_updated":"2022-05-22T14:44:17Z","oa":"1","citation":{"apa":"Hoffmann, M. (2020). Schnittstellenaktivitäten zum Kongruenzsatz WSW. In H.-S. Siller, W. Weigel, &#38; J. F. Wörler (Eds.), <i>Beiträge zum Mathematikunterricht 2020</i> (pp. 1353–1356). WTM-Verlag. <a href=\"https://doi.org/10.17877/DE290R-21368\">https://doi.org/10.17877/DE290R-21368</a>","bibtex":"@inproceedings{Hoffmann_2020, place={Münster}, title={Schnittstellenaktivitäten zum Kongruenzsatz WSW}, DOI={<a href=\"https://doi.org/10.17877/DE290R-21368\">10.17877/DE290R-21368</a>}, 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} }","mla":"Hoffmann, Max. “Schnittstellenaktivitäten zum Kongruenzsatz WSW.” <i>Beiträge zum Mathematikunterricht 2020</i>, edited by Hans-Stefan Siller et al., WTM-Verlag, 2020, pp. 1353–56, doi:<a href=\"https://doi.org/10.17877/DE290R-21368\">10.17877/DE290R-21368</a>.","short":"M. Hoffmann, in: H.-S. Siller, W. Weigel, J.F. Wörler (Eds.), Beiträge zum Mathematikunterricht 2020, WTM-Verlag, Münster, 2020, pp. 1353–1356.","ama":"Hoffmann M. Schnittstellenaktivitäten zum Kongruenzsatz WSW. In: Siller H-S, Weigel W, Wörler JF, eds. <i>Beiträge zum Mathematikunterricht 2020</i>. WTM-Verlag; 2020:1353-1356. doi:<a href=\"https://doi.org/10.17877/DE290R-21368\">10.17877/DE290R-21368</a>","chicago":"Hoffmann, Max. “Schnittstellenaktivitäten zum Kongruenzsatz WSW.” In <i>Beiträge zum Mathematikunterricht 2020</i>, edited by Hans-Stefan Siller, Wolfgang Weigel, and Jan Franz Wörler, 1353–56. Münster: WTM-Verlag, 2020. <a href=\"https://doi.org/10.17877/DE290R-21368\">https://doi.org/10.17877/DE290R-21368</a>.","ieee":"M. Hoffmann, “Schnittstellenaktivitäten zum Kongruenzsatz WSW,” in <i>Beiträge zum Mathematikunterricht 2020</i>, 2020, pp. 1353–1356, doi: <a href=\"https://doi.org/10.17877/DE290R-21368\">10.17877/DE290R-21368</a>."},"page":"1353-1356","place":"Münster","year":"2020","publication_status":"published"},{"publication_status":"published","citation":{"ieee":"M. Hoffmann, “Rezension: Andrew Granville und Jenniver Granville: Prime Supects: The Anatomy of Integers and Permutations,” <i>Mathematische Semesterberichte</i>, vol. 67. pp. 119–121, 2020, doi: <a href=\"https://doi.org/10.1007/s00591-019-00269-w\">10.1007/s00591-019-00269-w</a>.","chicago":"Hoffmann, Max. “Rezension: Andrew Granville und Jenniver Granville: Prime Supects: The Anatomy of Integers and Permutations.” <i>Mathematische Semesterberichte</i>, 2020. <a href=\"https://doi.org/10.1007/s00591-019-00269-w\">https://doi.org/10.1007/s00591-019-00269-w</a>.","ama":"Hoffmann M. Rezension: Andrew Granville und Jenniver Granville: Prime Supects: The Anatomy of Integers and Permutations. <i>Mathematische Semesterberichte</i>. 2020;67:119–121. doi:<a href=\"https://doi.org/10.1007/s00591-019-00269-w\">10.1007/s00591-019-00269-w</a>","apa":"Hoffmann, M. (2020). Rezension: Andrew Granville und Jenniver Granville: Prime Supects: The Anatomy of Integers and Permutations. In <i>Mathematische Semesterberichte</i> (Vol. 67, pp. 119–121). <a href=\"https://doi.org/10.1007/s00591-019-00269-w\">https://doi.org/10.1007/s00591-019-00269-w</a>","bibtex":"@article{Hoffmann_2020, title={Rezension: Andrew Granville und Jenniver Granville: Prime Supects: The Anatomy of Integers and Permutations}, volume={67}, DOI={<a href=\"https://doi.org/10.1007/s00591-019-00269-w\">10.1007/s00591-019-00269-w</a>}, journal={Mathematische Semesterberichte}, author={Hoffmann, Max}, year={2020}, pages={119–121} }","mla":"Hoffmann, Max. “Rezension: Andrew Granville und Jenniver Granville: Prime Supects: The Anatomy of Integers and Permutations.” <i>Mathematische Semesterberichte</i>, vol. 67, 2020, pp. 119–121, doi:<a href=\"https://doi.org/10.1007/s00591-019-00269-w\">10.1007/s00591-019-00269-w</a>.","short":"M. Hoffmann, Mathematische Semesterberichte 67 (2020) 119–121."},"intvolume":"        67","page":"119–121","year":"2020","author":[{"first_name":"Max","last_name":"Hoffmann","full_name":"Hoffmann, Max","id":"32202"}],"date_created":"2022-05-22T15:23:04Z","volume":67,"date_updated":"2022-05-22T15:58:26Z","main_file_link":[{"url":"https://link.springer.com/article/10.1007/s00591-019-00269-w"}],"doi":"10.1007/s00591-019-00269-w","title":"Rezension: Andrew Granville und Jenniver Granville: Prime Supects: The Anatomy of Integers and Permutations","type":"review","publication":"Mathematische Semesterberichte","status":"public","user_id":"32202","department":[{"_id":"97"}],"_id":"31386","language":[{"iso":"ger"}]},{"type":"review","publication":"Mathematische Semesterberichte","status":"public","user_id":"32202","department":[{"_id":"97"}],"_id":"31384","language":[{"iso":"ger"}],"publication_status":"published","citation":{"ama":"Hoffmann M. Rezension: Ehrhard Behrends: Parkettierungen der Ebene – Von Escher über Möbius zu Penrose. <i>Mathematische Semesterberichte</i>. 2020;67:115–116. doi:<a href=\"https://doi.org/10.1007/s00591-019-00264-1\">10.1007/s00591-019-00264-1</a>","ieee":"M. Hoffmann, “Rezension: Ehrhard Behrends: Parkettierungen der Ebene – Von Escher über Möbius zu Penrose,” <i>Mathematische Semesterberichte</i>, vol. 67. pp. 115–116, 2020, doi: <a href=\"https://doi.org/10.1007/s00591-019-00264-1\">10.1007/s00591-019-00264-1</a>.","chicago":"Hoffmann, Max. “Rezension: Ehrhard Behrends: Parkettierungen der Ebene – Von Escher über Möbius zu Penrose.” <i>Mathematische Semesterberichte</i>, 2020. <a href=\"https://doi.org/10.1007/s00591-019-00264-1\">https://doi.org/10.1007/s00591-019-00264-1</a>.","mla":"Hoffmann, Max. “Rezension: Ehrhard Behrends: Parkettierungen der Ebene – Von Escher über Möbius zu Penrose.” <i>Mathematische Semesterberichte</i>, vol. 67, 2020, pp. 115–116, doi:<a href=\"https://doi.org/10.1007/s00591-019-00264-1\">10.1007/s00591-019-00264-1</a>.","bibtex":"@article{Hoffmann_2020, title={Rezension: Ehrhard Behrends: Parkettierungen der Ebene – Von Escher über Möbius zu Penrose}, volume={67}, DOI={<a href=\"https://doi.org/10.1007/s00591-019-00264-1\">10.1007/s00591-019-00264-1</a>}, journal={Mathematische Semesterberichte}, author={Hoffmann, Max}, year={2020}, pages={115–116} }","short":"M. Hoffmann, Mathematische Semesterberichte 67 (2020) 115–116.","apa":"Hoffmann, M. (2020). Rezension: Ehrhard Behrends: Parkettierungen der Ebene – Von Escher über Möbius zu Penrose. In <i>Mathematische Semesterberichte</i> (Vol. 67, pp. 115–116). <a href=\"https://doi.org/10.1007/s00591-019-00264-1\">https://doi.org/10.1007/s00591-019-00264-1</a>"},"intvolume":"        67","page":"115–116","year":"2020","author":[{"last_name":"Hoffmann","full_name":"Hoffmann, Max","id":"32202","first_name":"Max"}],"date_created":"2022-05-22T15:18:37Z","volume":67,"date_updated":"2022-05-22T15:58:39Z","main_file_link":[{"url":"https://link.springer.com/article/10.1007/s00591-019-00264-1"}],"doi":"10.1007/s00591-019-00264-1","title":"Rezension: Ehrhard Behrends: Parkettierungen der Ebene – Von Escher über Möbius zu Penrose"},{"citation":{"mla":"Hoffmann, Max, editor. <i>Der Mathematikunterricht 66 (6): Geometrie in Schule und Lehramtsausbildung – ein Nachwuchsheft</i>. 2020.","bibtex":"@book{Hoffmann_2020, title={Der Mathematikunterricht 66 (6): Geometrie in Schule und Lehramtsausbildung – ein Nachwuchsheft}, year={2020} }","short":"M. Hoffmann, ed., Der Mathematikunterricht 66 (6): Geometrie in Schule und Lehramtsausbildung – ein Nachwuchsheft, 2020.","apa":"Hoffmann, M. (Ed.). (2020). <i>Der Mathematikunterricht 66 (6): Geometrie in Schule und Lehramtsausbildung – ein Nachwuchsheft</i>.","ama":"Hoffmann M, ed. <i>Der Mathematikunterricht 66 (6): Geometrie in Schule und Lehramtsausbildung – ein Nachwuchsheft</i>.; 2020.","ieee":"M. Hoffmann, Ed., <i>Der Mathematikunterricht 66 (6): Geometrie in Schule und Lehramtsausbildung – ein Nachwuchsheft</i>. 2020.","chicago":"Hoffmann, Max, ed. <i>Der Mathematikunterricht 66 (6): Geometrie in Schule und Lehramtsausbildung – ein Nachwuchsheft</i>, 2020."},"year":"2020","related_material":{"link":[{"url":"https://www.friedrich-verlag.de/shop/geometrie-in-schule-und-lehramtsausbildung-ein-nachwuchsheft-524216","relation":"table_of_contents"}]},"publication_status":"published","title":"Der Mathematikunterricht 66 (6): Geometrie in Schule und Lehramtsausbildung – ein Nachwuchsheft","date_created":"2022-05-22T15:08:51Z","date_updated":"2022-05-22T16:00:26Z","status":"public","editor":[{"first_name":"Max","last_name":"Hoffmann","full_name":"Hoffmann, Max","id":"32202"}],"type":"book_editor","language":[{"iso":"ger"}],"department":[{"_id":"97"}],"user_id":"32202","_id":"31381"}]