[{"related_material":{"link":[{"relation":"software","url":"https://github.com/Christian-Offen/LagrangianShadowIntegration"}]},"abstract":[{"text":"The principle of least action is one of the most fundamental physical principle. It says that among all possible motions connecting two points in a phase space, the system will exhibit those motions which extremise an action functional. Many qualitative features of dynamical systems, such as the presence of conservation laws and energy balance equations, are related to the existence of an action functional. Incorporating variational structure into learning algorithms for dynamical systems is, therefore, crucial in order to make sure that the learned model shares important features with the exact physical system. In this paper we show how to incorporate variational principles into trajectory predictions of learned dynamical systems. The novelty of this work is that (1) our technique relies only on discrete position data of observed trajectories. Velocities or conjugate momenta do not need to be observed or approximated and no prior knowledge about the form of the variational principle is assumed. Instead, they are recovered using backward error analysis. (2) Moreover, our technique compensates discretisation errors when trajectories are computed from the learned system. This is important when moderate to large step-sizes are used and high accuracy is required. For this,\r\nwe introduce and rigorously analyse the concept of inverse modified Lagrangians by developing an inverse version of variational backward error analysis. (3) Finally, we introduce a method to perform system identification from position observations only, based on variational backward error analysis.","lang":"eng"}],"publication":"Journal of Computational and Applied Mathematics","type":"journal_article","keyword":["Lagrangian learning","variational backward error analysis","modified Lagrangian","variational integrators","physics informed learning"],"department":[{"_id":"636"}],"file":[{"access_level":"open_access","file_size":3640770,"file_name":"ShadowLagrangian_revision1_journal_style_arxiv.pdf","date_updated":"2022-06-28T15:25:50Z","relation":"main_file","content_type":"application/pdf","file_id":"32274","title":"Variational Learning of Euler–Lagrange Dynamics from Data","creator":"coffen","date_created":"2022-06-28T15:25:50Z","description":"The principle of least action is one of the most fundamental physical principle. It says that among all possible motions\nconnecting two points in a phase space, the system will exhibit those motions which extremise an action functional.\nMany qualitative features of dynamical systems, such as the presence of conservation laws and energy balance equa-\ntions, are related to the existence of an action functional. Incorporating variational structure into learning algorithms\nfor dynamical systems is, therefore, crucial in order to make sure that the learned model shares important features\nwith the exact physical system. In this paper we show how to incorporate variational principles into trajectory predic-\ntions of learned dynamical systems. The novelty of this work is that (1) our technique relies only on discrete position\ndata of observed trajectories. Velocities or conjugate momenta do not need to be observed or approximated and no\nprior knowledge about the form of the variational principle is assumed. Instead, they are recovered using backward\nerror analysis. (2) Moreover, our technique compensates discretisation errors when trajectories are computed from the\nlearned system. This is important when moderate to large step-sizes are used and high accuracy is required. For this,\nwe introduce and rigorously analyse the concept of inverse modified Lagrangians by developing an inverse version of\nvariational backward error analysis. (3) Finally, we introduce a method to perform system identification from position\nobservations only, based on variational backward error analysis."}],"date_created":"2022-01-11T13:24:00Z","date_updated":"2023-08-10T08:42:39Z","publication_status":"epub_ahead","intvolume":"       421","article_type":"original","year":"2023","title":"Variational Learning of Euler–Lagrange Dynamics from Data","author":[{"full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina","id":"16494"},{"id":"85279","orcid":"0000-0002-5940-8057","first_name":"Christian","last_name":"Offen","full_name":"Offen, Christian"}],"publication_identifier":{"issn":["0377-0427"]},"doi":"10.1016/j.cam.2022.114780","language":[{"iso":"eng"}],"quality_controlled":"1","file_date_updated":"2022-06-28T15:25:50Z","citation":{"ama":"Ober-Blöbaum S, Offen C. Variational Learning of Euler–Lagrange Dynamics from Data. <i>Journal of Computational and Applied Mathematics</i>. 2023;421:114780. doi:<a href=\"https://doi.org/10.1016/j.cam.2022.114780\">10.1016/j.cam.2022.114780</a>","bibtex":"@article{Ober-Blöbaum_Offen_2023, title={Variational Learning of Euler–Lagrange Dynamics from Data}, volume={421}, DOI={<a href=\"https://doi.org/10.1016/j.cam.2022.114780\">10.1016/j.cam.2022.114780</a>}, journal={Journal of Computational and Applied Mathematics}, publisher={Elsevier}, author={Ober-Blöbaum, Sina and Offen, Christian}, year={2023}, pages={114780} }","mla":"Ober-Blöbaum, Sina, and Christian Offen. “Variational Learning of Euler–Lagrange Dynamics from Data.” <i>Journal of Computational and Applied Mathematics</i>, vol. 421, Elsevier, 2023, p. 114780, doi:<a href=\"https://doi.org/10.1016/j.cam.2022.114780\">10.1016/j.cam.2022.114780</a>.","short":"S. Ober-Blöbaum, C. Offen, Journal of Computational and Applied Mathematics 421 (2023) 114780.","chicago":"Ober-Blöbaum, Sina, and Christian Offen. “Variational Learning of Euler–Lagrange Dynamics from Data.” <i>Journal of Computational and Applied Mathematics</i> 421 (2023): 114780. <a href=\"https://doi.org/10.1016/j.cam.2022.114780\">https://doi.org/10.1016/j.cam.2022.114780</a>.","apa":"Ober-Blöbaum, S., &#38; Offen, C. (2023). Variational Learning of Euler–Lagrange Dynamics from Data. <i>Journal of Computational and Applied Mathematics</i>, <i>421</i>, 114780. <a href=\"https://doi.org/10.1016/j.cam.2022.114780\">https://doi.org/10.1016/j.cam.2022.114780</a>","ieee":"S. Ober-Blöbaum and C. Offen, “Variational Learning of Euler–Lagrange Dynamics from Data,” <i>Journal of Computational and Applied Mathematics</i>, vol. 421, p. 114780, 2023, doi: <a href=\"https://doi.org/10.1016/j.cam.2022.114780\">10.1016/j.cam.2022.114780</a>."},"oa":"1","external_id":{"arxiv":["2112.12619"]},"has_accepted_license":"1","status":"public","ddc":["510"],"user_id":"85279","volume":421,"page":"114780","publisher":"Elsevier","_id":"29240"},{"volume":15,"user_id":"85279","ddc":["510"],"publisher":"AIMS Press","_id":"29236","page":"98-115","has_accepted_license":"1","status":"public","oa":"1","external_id":{"arxiv":["2201.03911"]},"quality_controlled":"1","citation":{"ieee":"R. McLachlan and C. Offen, “Backward error analysis for conjugate symplectic methods,” <i>Journal of Geometric Mechanics</i>, vol. 15, no. 1, pp. 98–115, 2023, doi: <a href=\"https://doi.org/10.3934/jgm.2023005\">10.3934/jgm.2023005</a>.","apa":"McLachlan, R., &#38; Offen, C. (2023). Backward error analysis for conjugate symplectic methods. <i>Journal of Geometric Mechanics</i>, <i>15</i>(1), 98–115. <a href=\"https://doi.org/10.3934/jgm.2023005\">https://doi.org/10.3934/jgm.2023005</a>","short":"R. McLachlan, C. Offen, Journal of Geometric Mechanics 15 (2023) 98–115.","chicago":"McLachlan, Robert, and Christian Offen. “Backward Error Analysis for Conjugate Symplectic Methods.” <i>Journal of Geometric Mechanics</i> 15, no. 1 (2023): 98–115. <a href=\"https://doi.org/10.3934/jgm.2023005\">https://doi.org/10.3934/jgm.2023005</a>.","mla":"McLachlan, Robert, and Christian Offen. “Backward Error Analysis for Conjugate Symplectic Methods.” <i>Journal of Geometric Mechanics</i>, vol. 15, no. 1, AIMS Press, 2023, pp. 98–115, doi:<a href=\"https://doi.org/10.3934/jgm.2023005\">10.3934/jgm.2023005</a>.","bibtex":"@article{McLachlan_Offen_2023, title={Backward error analysis for conjugate symplectic methods}, volume={15}, DOI={<a href=\"https://doi.org/10.3934/jgm.2023005\">10.3934/jgm.2023005</a>}, number={1}, journal={Journal of Geometric Mechanics}, publisher={AIMS Press}, author={McLachlan, Robert and Offen, Christian}, year={2023}, pages={98–115} }","ama":"McLachlan R, Offen C. Backward error analysis for conjugate symplectic methods. <i>Journal of Geometric Mechanics</i>. 2023;15(1):98-115. doi:<a href=\"https://doi.org/10.3934/jgm.2023005\">10.3934/jgm.2023005</a>"},"file_date_updated":"2022-08-12T16:48:59Z","doi":"10.3934/jgm.2023005","language":[{"iso":"eng"}],"article_type":"original","intvolume":"        15","publication_status":"published","date_updated":"2023-08-10T08:40:30Z","author":[{"first_name":"Robert","last_name":"McLachlan","full_name":"McLachlan, Robert"},{"full_name":"Offen, Christian","first_name":"Christian","last_name":"Offen","orcid":"0000-0002-5940-8057","id":"85279"}],"year":"2023","title":"Backward error analysis for conjugate symplectic methods","department":[{"_id":"636"}],"type":"journal_article","keyword":["variational integrators","backward error analysis","Euler--Lagrange equations","multistep methods","conjugate symplectic methods"],"date_created":"2022-01-11T12:48:39Z","file":[{"creator":"coffen","date_created":"2022-08-12T16:48:59Z","description":"The numerical solution of an ordinary differential equation can be interpreted as the exact solution of a nearby modified equation. Investigating the behaviour of numerical solutions by analysing the modified equation is known as backward error analysis. If the original and modified equation share structural properties, then the exact and approximate solution share geometric features such as the existence of conserved quantities. Conjugate symplectic methods preserve a modified symplectic form and a modified Hamiltonian when applied to a Hamiltonian system. We show how a blended version of variational and symplectic techniques can be used to compute modified symplectic and Hamiltonian structures. In contrast to other approaches, our backward error analysis method does not rely on an ansatz but computes the structures systematically, provided that a variational formulation of the method is known. The technique is illustrated on the example of symmetric linear multistep methods with matrix coefficients.","file_size":827030,"access_level":"open_access","file_name":"BEA_MultiStep_Matrix.pdf","date_updated":"2022-08-12T16:48:59Z","relation":"main_file","content_type":"application/pdf","file_id":"32801","title":"Backward error analysis for conjugate symplectic methods"}],"abstract":[{"lang":"eng","text":"The numerical solution of an ordinary differential equation can be interpreted as the exact solution of a nearby modified equation. Investigating the behaviour of numerical solutions by analysing the modified equation is known as backward error analysis. If the original and modified equation share structural properties, then the exact and approximate solution share geometric features such as the existence of conserved quantities. Conjugate symplectic methods preserve a modified symplectic form and a modified Hamiltonian when applied to a Hamiltonian system. We show how a blended version of variational and symplectic techniques can be used to compute modified symplectic and Hamiltonian structures. In contrast to other approaches, our backward error analysis method does not rely on an ansatz but computes the structures systematically, provided that a variational formulation of the method is known. The technique is illustrated on the example of symmetric linear multistep methods with matrix coefficients."}],"related_material":{"link":[{"relation":"software","url":"https://github.com/Christian-Offen/BEAConjugateSymplectic"}]},"issue":"1","publication":"Journal of Geometric Mechanics"},{"language":[{"iso":"eng"}],"article_number":"063115","doi":"10.1063/5.0142969","publication_identifier":{"issn":["1054-1500"]},"author":[{"last_name":"Dierkes","first_name":"Eva","full_name":"Dierkes, Eva"},{"id":"85279","first_name":"Christian","orcid":"0000-0002-5940-8057","last_name":"Offen","full_name":"Offen, Christian"},{"id":"16494","full_name":"Ober-Blöbaum, Sina","first_name":"Sina","last_name":"Ober-Blöbaum"},{"last_name":"Flaßkamp","first_name":"Kathrin","full_name":"Flaßkamp, Kathrin"}],"title":"Hamiltonian Neural Networks with Automatic Symmetry Detection","year":"2023","article_type":"original","intvolume":"        33","publication_status":"published","date_updated":"2023-08-10T08:37:01Z","date_created":"2023-01-20T09:10:06Z","file":[{"title":"Hamiltonian Neural Networks with Automatic Symmetry Detection","file_id":"44205","content_type":"application/pdf","relation":"main_file","date_updated":"2023-04-26T16:20:56Z","file_name":"JournalPaper_main.pdf","access_level":"open_access","file_size":5200111,"description":"Incorporating physical system knowledge into data-driven\nsystem identification has been shown to be beneficial. The\napproach presented in this article combines learning of an\nenergy-conserving model from data with detecting a Lie\ngroup representation of the unknown system symmetry.\nThe proposed approach can improve the learned model\nand reveal underlying symmetry simultaneously.","date_created":"2023-04-26T16:20:56Z","creator":"coffen"}],"department":[{"_id":"636"}],"type":"journal_article","issue":"6","publication":"Chaos","abstract":[{"text":"Recently, Hamiltonian neural networks (HNN) have been introduced to incorporate prior physical knowledge when\r\nlearning the dynamical equations of Hamiltonian systems. Hereby, the symplectic system structure is preserved despite\r\nthe data-driven modeling approach. However, preserving symmetries requires additional attention. In this research, we\r\nenhance the HNN with a Lie algebra framework to detect and embed symmetries in the neural network. This approach\r\nallows to simultaneously learn the symmetry group action and the total energy of the system. As illustrating examples,\r\na pendulum on a cart and a two-body problem from astrodynamics are considered.","lang":"eng"}],"related_material":{"link":[{"description":"GitHub","url":"https://github.com/eva-dierkes/HNN_withSymmetries","relation":"software"}]},"publisher":"AIP Publishing","_id":"37654","volume":33,"user_id":"85279","ddc":["510"],"status":"public","has_accepted_license":"1","external_id":{"arxiv":["2301.07928"]},"oa":"1","citation":{"chicago":"Dierkes, Eva, Christian Offen, Sina Ober-Blöbaum, and Kathrin Flaßkamp. “Hamiltonian Neural Networks with Automatic Symmetry Detection.” <i>Chaos</i> 33, no. 6 (2023). <a href=\"https://doi.org/10.1063/5.0142969\">https://doi.org/10.1063/5.0142969</a>.","short":"E. Dierkes, C. Offen, S. Ober-Blöbaum, K. Flaßkamp, Chaos 33 (2023).","apa":"Dierkes, E., Offen, C., Ober-Blöbaum, S., &#38; Flaßkamp, K. (2023). Hamiltonian Neural Networks with Automatic Symmetry Detection. <i>Chaos</i>, <i>33</i>(6), Article 063115. <a href=\"https://doi.org/10.1063/5.0142969\">https://doi.org/10.1063/5.0142969</a>","ieee":"E. Dierkes, C. Offen, S. Ober-Blöbaum, and K. Flaßkamp, “Hamiltonian Neural Networks with Automatic Symmetry Detection,” <i>Chaos</i>, vol. 33, no. 6, Art. no. 063115, 2023, doi: <a href=\"https://doi.org/10.1063/5.0142969\">10.1063/5.0142969</a>.","ama":"Dierkes E, Offen C, Ober-Blöbaum S, Flaßkamp K. Hamiltonian Neural Networks with Automatic Symmetry Detection. <i>Chaos</i>. 2023;33(6). doi:<a href=\"https://doi.org/10.1063/5.0142969\">10.1063/5.0142969</a>","bibtex":"@article{Dierkes_Offen_Ober-Blöbaum_Flaßkamp_2023, title={Hamiltonian Neural Networks with Automatic Symmetry Detection}, volume={33}, DOI={<a href=\"https://doi.org/10.1063/5.0142969\">10.1063/5.0142969</a>}, number={6063115}, journal={Chaos}, publisher={AIP Publishing}, author={Dierkes, Eva and Offen, Christian and Ober-Blöbaum, Sina and Flaßkamp, Kathrin}, year={2023} }","mla":"Dierkes, Eva, et al. “Hamiltonian Neural Networks with Automatic Symmetry Detection.” <i>Chaos</i>, vol. 33, no. 6, 063115, AIP Publishing, 2023, doi:<a href=\"https://doi.org/10.1063/5.0142969\">10.1063/5.0142969</a>."},"file_date_updated":"2023-04-26T16:20:56Z"},{"main_file_link":[{"url":"https://epubs.siam.org/doi/reader/10.1137/21M1412682"}],"language":[{"iso":"eng"}],"doi":"10.1137/21M1412682","title":"Efficient time stepping for numerical integration using reinforcement  learning","year":"2023","author":[{"first_name":"Michael","last_name":"Dellnitz","full_name":"Dellnitz, Michael"},{"id":"48129","full_name":"Hüllermeier, Eyke","last_name":"Hüllermeier","first_name":"Eyke"},{"first_name":"Marvin","last_name":"Lücke","full_name":"Lücke, Marvin"},{"id":"16494","first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina"},{"id":"85279","last_name":"Offen","orcid":"0000-0002-5940-8057","first_name":"Christian","full_name":"Offen, Christian"},{"full_name":"Peitz, Sebastian","first_name":"Sebastian","orcid":"0000-0002-3389-793X","last_name":"Peitz","id":"47427"},{"last_name":"Pfannschmidt","orcid":"0000-0001-9407-7903","first_name":"Karlson","full_name":"Pfannschmidt, Karlson","id":"13472"}],"publication_status":"published","date_updated":"2023-08-25T09:24:50Z","intvolume":"        45","date_created":"2021-04-09T07:59:19Z","type":"journal_article","department":[{"_id":"101"},{"_id":"636"},{"_id":"355"},{"_id":"655"}],"publication":"SIAM Journal on Scientific Computing","issue":"2","related_material":{"link":[{"description":"GitHub","url":"https://github.com/lueckem/quadrature-ML","relation":"software"}]},"abstract":[{"text":"Many problems in science and engineering require an efficient numerical approximation of integrals or solutions to differential equations. For systems with rapidly changing dynamics, an equidistant discretization is often inadvisable as it results in prohibitively large errors or computational effort. To this end, adaptive schemes, such as solvers based on Runge–Kutta pairs, have been developed which adapt the step size based on local error estimations at each step. While the classical schemes apply very generally and are highly efficient on regular systems, they can behave suboptimally when an inefficient step rejection mechanism is triggered by structurally complex systems such as chaotic systems. To overcome these issues, we propose a method to tailor numerical schemes to the problem class at hand. This is achieved by combining simple, classical quadrature rules or ODE solvers with data-driven time-stepping controllers. Compared with learning solution operators to ODEs directly, it generalizes better to unseen initial data as our approach employs classical numerical schemes as base methods. At the same time it can make use of identified structures of a problem class and, therefore, outperforms state-of-the-art adaptive schemes. Several examples demonstrate superior efficiency. Source code is available at https://github.com/lueckem/quadrature-ML.","lang":"eng"}],"page":"A579-A595","_id":"21600","user_id":"47427","ddc":["510"],"volume":45,"status":"public","has_accepted_license":"1","external_id":{"arxiv":["arXiv:2104.03562"]},"citation":{"short":"M. Dellnitz, E. Hüllermeier, M. Lücke, S. Ober-Blöbaum, C. Offen, S. Peitz, K. Pfannschmidt, SIAM Journal on Scientific Computing 45 (2023) A579–A595.","chicago":"Dellnitz, Michael, Eyke Hüllermeier, Marvin Lücke, Sina Ober-Blöbaum, Christian Offen, Sebastian Peitz, and Karlson Pfannschmidt. “Efficient Time Stepping for Numerical Integration Using Reinforcement  Learning.” <i>SIAM Journal on Scientific Computing</i> 45, no. 2 (2023): A579–95. <a href=\"https://doi.org/10.1137/21M1412682\">https://doi.org/10.1137/21M1412682</a>.","apa":"Dellnitz, M., Hüllermeier, E., Lücke, M., Ober-Blöbaum, S., Offen, C., Peitz, S., &#38; Pfannschmidt, K. (2023). Efficient time stepping for numerical integration using reinforcement  learning. <i>SIAM Journal on Scientific Computing</i>, <i>45</i>(2), A579–A595. <a href=\"https://doi.org/10.1137/21M1412682\">https://doi.org/10.1137/21M1412682</a>","ieee":"M. Dellnitz <i>et al.</i>, “Efficient time stepping for numerical integration using reinforcement  learning,” <i>SIAM Journal on Scientific Computing</i>, vol. 45, no. 2, pp. A579–A595, 2023, doi: <a href=\"https://doi.org/10.1137/21M1412682\">10.1137/21M1412682</a>.","ama":"Dellnitz M, Hüllermeier E, Lücke M, et al. Efficient time stepping for numerical integration using reinforcement  learning. <i>SIAM Journal on Scientific Computing</i>. 2023;45(2):A579-A595. doi:<a href=\"https://doi.org/10.1137/21M1412682\">10.1137/21M1412682</a>","bibtex":"@article{Dellnitz_Hüllermeier_Lücke_Ober-Blöbaum_Offen_Peitz_Pfannschmidt_2023, title={Efficient time stepping for numerical integration using reinforcement  learning}, volume={45}, DOI={<a href=\"https://doi.org/10.1137/21M1412682\">10.1137/21M1412682</a>}, number={2}, journal={SIAM Journal on Scientific Computing}, author={Dellnitz, Michael and Hüllermeier, Eyke and Lücke, Marvin and Ober-Blöbaum, Sina and Offen, Christian and Peitz, Sebastian and Pfannschmidt, Karlson}, year={2023}, pages={A579–A595} }","mla":"Dellnitz, Michael, et al. “Efficient Time Stepping for Numerical Integration Using Reinforcement  Learning.” <i>SIAM Journal on Scientific Computing</i>, vol. 45, no. 2, 2023, pp. A579–95, doi:<a href=\"https://doi.org/10.1137/21M1412682\">10.1137/21M1412682</a>."}},{"alternative_title":["GAMM Rundbriefe"],"user_id":"15694","_id":"47147","publisher":"Invited Mathematical Magazine Article","language":[{"iso":"eng"}],"date_updated":"2023-09-21T07:27:15Z","author":[{"first_name":"Yana","last_name":"Lishkova","full_name":"Lishkova, Yana"},{"full_name":"Ober-Blöbaum, Sina","first_name":"Sina","last_name":"Ober-Blöbaum","id":"16494"},{"first_name":"Sigrid","last_name":"Leyendecker","full_name":"Leyendecker, Sigrid"}],"title":"Multirate Discrete Mechanics and Optimal Control for a Flexible Satelite Model ","status":"public","year":"2023","type":"report","date_created":"2023-09-21T07:20:43Z","citation":{"apa":"Lishkova, Y., Ober-Blöbaum, S., &#38; Leyendecker, S. (2023). <i>Multirate Discrete Mechanics and Optimal Control for a Flexible Satelite Model </i>. Invited Mathematical Magazine Article.","ieee":"Y. Lishkova, S. Ober-Blöbaum, and S. Leyendecker, <i>Multirate Discrete Mechanics and Optimal Control for a Flexible Satelite Model </i>. Invited Mathematical Magazine Article, 2023.","chicago":"Lishkova, Yana, Sina Ober-Blöbaum, and Sigrid Leyendecker. <i>Multirate Discrete Mechanics and Optimal Control for a Flexible Satelite Model </i>. Invited Mathematical Magazine Article, 2023.","short":"Y. Lishkova, S. Ober-Blöbaum, S. Leyendecker, Multirate Discrete Mechanics and Optimal Control for a Flexible Satelite Model , Invited Mathematical Magazine Article, 2023.","mla":"Lishkova, Yana, et al. <i>Multirate Discrete Mechanics and Optimal Control for a Flexible Satelite Model </i>. Invited Mathematical Magazine Article, 2023.","ama":"Lishkova Y, Ober-Blöbaum S, Leyendecker S. <i>Multirate Discrete Mechanics and Optimal Control for a Flexible Satelite Model </i>. Invited Mathematical Magazine Article; 2023.","bibtex":"@book{Lishkova_Ober-Blöbaum_Leyendecker_2023, title={Multirate Discrete Mechanics and Optimal Control for a Flexible Satelite Model }, publisher={Invited Mathematical Magazine Article}, author={Lishkova, Yana and Ober-Blöbaum, Sina and Leyendecker, Sigrid}, year={2023} }"}},{"user_id":"15694","publisher":"Accepted for the 74th International Astronautical Concress (IAC)","_id":"47148","language":[{"iso":"eng"}],"date_updated":"2023-09-21T07:27:21Z","author":[{"last_name":"Lishkova","first_name":"Y.","full_name":"Lishkova, Y."},{"last_name":"Bando","first_name":"M.","full_name":"Bando, M."},{"id":"16494","first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina"}],"status":"public","title":"Variational approach for modelling and optimal control of electrodynamic tether motion","year":"2023","type":"conference","date_created":"2023-09-21T07:25:40Z","citation":{"mla":"Lishkova, Y., et al. <i>Variational Approach for Modelling and Optimal Control of Electrodynamic Tether Motion</i>. Accepted for the 74th International Astronautical Concress (IAC), 2023.","bibtex":"@inproceedings{Lishkova_Bando_Ober-Blöbaum_2023, title={Variational approach for modelling and optimal control of electrodynamic tether motion}, publisher={Accepted for the 74th International Astronautical Concress (IAC)}, author={Lishkova, Y. and Bando, M. and Ober-Blöbaum, Sina}, year={2023} }","ama":"Lishkova Y, Bando M, Ober-Blöbaum S. Variational approach for modelling and optimal control of electrodynamic tether motion. In: Accepted for the 74th International Astronautical Concress (IAC); 2023.","ieee":"Y. Lishkova, M. Bando, and S. Ober-Blöbaum, “Variational approach for modelling and optimal control of electrodynamic tether motion,” 2023.","apa":"Lishkova, Y., Bando, M., &#38; Ober-Blöbaum, S. (2023). <i>Variational approach for modelling and optimal control of electrodynamic tether motion</i>.","chicago":"Lishkova, Y., M. Bando, and Sina Ober-Blöbaum. “Variational Approach for Modelling and Optimal Control of Electrodynamic Tether Motion.” Accepted for the 74th International Astronautical Concress (IAC), 2023.","short":"Y. Lishkova, M. Bando, S. Ober-Blöbaum, in: Accepted for the 74th International Astronautical Concress (IAC), 2023."}},{"_id":"30490","language":[{"iso":"eng"}],"page":"57-89","volume":"14(1)","user_id":"15694","author":[{"full_name":"Cresson, Jacky","last_name":"Cresson","first_name":"Jacky"},{"first_name":"Fernando","last_name":"Jiménez","full_name":"Jiménez, Fernando"},{"id":"16494","last_name":"Ober-Blöbaum","first_name":"Sina","full_name":"Ober-Blöbaum, Sina"}],"title":"Continuous and discrete Noether's fractional conserved quantities for restricted calculus of variations","status":"public","year":"2022","date_updated":"2022-03-24T12:26:32Z","date_created":"2022-03-24T12:26:10Z","department":[{"_id":"636"}],"type":"journal_article","citation":{"ama":"Cresson J, Jiménez F, Ober-Blöbaum S. Continuous and discrete Noether’s fractional conserved quantities for restricted calculus of variations. <i>AIMS</i>. 2022;14(1):57-89.","short":"J. Cresson, F. Jiménez, S. Ober-Blöbaum, AIMS 14(1) (2022) 57–89.","chicago":"Cresson, Jacky, Fernando Jiménez, and Sina Ober-Blöbaum. “Continuous and Discrete Noether’s Fractional Conserved Quantities for Restricted Calculus of Variations.” <i>AIMS</i> 14(1) (2022): 57–89.","bibtex":"@article{Cresson_Jiménez_Ober-Blöbaum_2022, title={Continuous and discrete Noether’s fractional conserved quantities for restricted calculus of variations}, volume={14(1)}, journal={AIMS}, author={Cresson, Jacky and Jiménez, Fernando and Ober-Blöbaum, Sina}, year={2022}, pages={57–89} }","apa":"Cresson, J., Jiménez, F., &#38; Ober-Blöbaum, S. (2022). Continuous and discrete Noether’s fractional conserved quantities for restricted calculus of variations. <i>AIMS</i>, <i>14(1)</i>, 57–89.","mla":"Cresson, Jacky, et al. “Continuous and Discrete Noether’s Fractional Conserved Quantities for Restricted Calculus of Variations.” <i>AIMS</i>, vol. 14(1), 2022, pp. 57–89.","ieee":"J. Cresson, F. Jiménez, and S. Ober-Blöbaum, “Continuous and discrete Noether’s fractional conserved quantities for restricted calculus of variations,” <i>AIMS</i>, vol. 14(1), pp. 57–89, 2022."},"publication":"AIMS"},{"user_id":"87909","doi":"10.1007/s10957-022-02023-0","language":[{"iso":"eng"}],"_id":"30861","publisher":"Springer Science and Business Media LLC","publication_status":"published","date_updated":"2022-04-08T18:23:02Z","title":"Turnpike Property in Optimal Microbial Metabolite Production","status":"public","year":"2022","author":[{"first_name":"Jean-Baptiste","last_name":"Caillau","full_name":"Caillau, Jean-Baptiste"},{"full_name":"Djema, Walid","last_name":"Djema","first_name":"Walid"},{"first_name":"Jean-Luc","last_name":"Gouzé","full_name":"Gouzé, Jean-Luc"},{"full_name":"Maslovskaya, Sofya","first_name":"Sofya","last_name":"Maslovskaya","id":"87909"},{"full_name":"Pomet, Jean-Baptiste","last_name":"Pomet","first_name":"Jean-Baptiste"}],"publication_identifier":{"issn":["0022-3239","1573-2878"]},"keyword":["Applied Mathematics","Management Science and Operations Research","Control and Optimization"],"type":"journal_article","department":[{"_id":"636"}],"date_created":"2022-04-08T17:23:13Z","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>We consider the problem of maximization of metabolite production in bacterial cells formulated as a dynamical optimal control problem (DOCP). According to Pontryagin’s maximum principle, optimal solutions are concatenations of singular and bang arcs and exhibit the chattering or <jats:italic>Fuller</jats:italic> phenomenon, which is problematic for applications. To avoid chattering, we introduce a reduced model which is still biologically relevant and retains the important structural features of the original problem. Using a combination of analytical and numerical methods, we show that the singular arc is dominant in the studied DOCPs and exhibits the <jats:italic>turnpike</jats:italic> property. This property is further used in order to design simple and realistic suboptimal control strategies.</jats:p>","lang":"eng"}],"publication":"Journal of Optimization Theory and Applications","citation":{"mla":"Caillau, Jean-Baptiste, et al. “Turnpike Property in Optimal Microbial Metabolite Production.” <i>Journal of Optimization Theory and Applications</i>, Springer Science and Business Media LLC, 2022, doi:<a href=\"https://doi.org/10.1007/s10957-022-02023-0\">10.1007/s10957-022-02023-0</a>.","ama":"Caillau J-B, Djema W, Gouzé J-L, Maslovskaya S, Pomet J-B. Turnpike Property in Optimal Microbial Metabolite Production. <i>Journal of Optimization Theory and Applications</i>. Published online 2022. doi:<a href=\"https://doi.org/10.1007/s10957-022-02023-0\">10.1007/s10957-022-02023-0</a>","bibtex":"@article{Caillau_Djema_Gouzé_Maslovskaya_Pomet_2022, title={Turnpike Property in Optimal Microbial Metabolite Production}, DOI={<a href=\"https://doi.org/10.1007/s10957-022-02023-0\">10.1007/s10957-022-02023-0</a>}, journal={Journal of Optimization Theory and Applications}, publisher={Springer Science and Business Media LLC}, author={Caillau, Jean-Baptiste and Djema, Walid and Gouzé, Jean-Luc and Maslovskaya, Sofya and Pomet, Jean-Baptiste}, year={2022} }","apa":"Caillau, J.-B., Djema, W., Gouzé, J.-L., Maslovskaya, S., &#38; Pomet, J.-B. (2022). Turnpike Property in Optimal Microbial Metabolite Production. <i>Journal of Optimization Theory and Applications</i>. <a href=\"https://doi.org/10.1007/s10957-022-02023-0\">https://doi.org/10.1007/s10957-022-02023-0</a>","ieee":"J.-B. Caillau, W. Djema, J.-L. Gouzé, S. Maslovskaya, and J.-B. Pomet, “Turnpike Property in Optimal Microbial Metabolite Production,” <i>Journal of Optimization Theory and Applications</i>, 2022, doi: <a href=\"https://doi.org/10.1007/s10957-022-02023-0\">10.1007/s10957-022-02023-0</a>.","short":"J.-B. Caillau, W. Djema, J.-L. Gouzé, S. Maslovskaya, J.-B. Pomet, Journal of Optimization Theory and Applications (2022).","chicago":"Caillau, Jean-Baptiste, Walid Djema, Jean-Luc Gouzé, Sofya Maslovskaya, and Jean-Baptiste Pomet. “Turnpike Property in Optimal Microbial Metabolite Production.” <i>Journal of Optimization Theory and Applications</i>, 2022. <a href=\"https://doi.org/10.1007/s10957-022-02023-0\">https://doi.org/10.1007/s10957-022-02023-0</a>."}},{"has_accepted_license":"1","date_updated":"2023-11-29T10:00:18Z","author":[{"full_name":"Vertovec, Nikolaus","last_name":"Vertovec","first_name":"Nikolaus","id":"93930"},{"id":"16494","full_name":"Ober-Blöbaum, Sina","first_name":"Sina","last_name":"Ober-Blöbaum"},{"last_name":"Margellos","first_name":"Kostas","full_name":"Margellos, Kostas"}],"conference":{"name":"2022 European Control Conference (ECC)","start_date":"2022-07-12","location":"London","end_date":"2022-07-15"},"year":"2022","status":"public","title":"Verification of safety critical control policies using kernel methods","user_id":"15694","ddc":["510"],"language":[{"iso":"eng"}],"_id":"30733","page":"1870-1875","abstract":[{"text":"Hamilton-Jacobi reachability methods for safety-critical control have been well studied, but the safety guarantees derived rely on the accuracy of the numerical computation. Thus, it is crucial to understand and account for any inaccuracies that occur due to uncertainty in the underlying dynamics and environment as well as the induced numerical errors. To this end, we propose a framework for modeling the error of the value function inherent in Hamilton-Jacobi reachability using a Gaussian process. The derived safety controller can be used in conjuncture with arbitrary controllers to provide a safe hybrid control law. The marginal likelihood of the Gaussian process then provides a confidence metric used to determine switches between a least restrictive controller and a safety controller. We test both the prediction as well as the correction capabilities of the presented method in a classical pursuit-evasion example.","lang":"eng"}],"citation":{"ieee":"N. Vertovec, S. Ober-Blöbaum, and K. Margellos, “Verification of safety critical control policies using kernel methods,” London, 2022, pp. 1870–1875.","apa":"Vertovec, N., Ober-Blöbaum, S., &#38; Margellos, K. (2022). <i>Verification of safety critical control policies using kernel methods</i>. 1870–1875.","mla":"Vertovec, Nikolaus, et al. <i>Verification of Safety Critical Control Policies Using Kernel Methods</i>. 2022, pp. 1870–75.","bibtex":"@inproceedings{Vertovec_Ober-Blöbaum_Margellos_2022, title={Verification of safety critical control policies using kernel methods}, author={Vertovec, Nikolaus and Ober-Blöbaum, Sina and Margellos, Kostas}, year={2022}, pages={1870–1875} }","chicago":"Vertovec, Nikolaus, Sina Ober-Blöbaum, and Kostas Margellos. “Verification of Safety Critical Control Policies Using Kernel Methods,” 1870–75, 2022.","short":"N. Vertovec, S. Ober-Blöbaum, K. Margellos, in: 2022, pp. 1870–1875.","ama":"Vertovec N, Ober-Blöbaum S, Margellos K. Verification of safety critical control policies using kernel methods. In: ; 2022:1870-1875."},"department":[{"_id":"636"}],"type":"conference","date_created":"2022-03-31T11:14:13Z"},{"page":"759-788","_id":"44624","publisher":"Springer","language":[{"iso":"eng"}],"user_id":"15694","volume":34,"status":"public","year":"2022","title":"Manifold turnpikes, trims, and symmetries","author":[{"full_name":"Faulwasser, Timm","last_name":"Faulwasser","first_name":"Timm"},{"last_name":"Flaßkamp","first_name":"Kathrin","full_name":"Flaßkamp, Kathrin"},{"first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","id":"16494"},{"full_name":"Schaller, Manuel","last_name":"Schaller","first_name":"Manuel"},{"full_name":"Worthmann, Karl","first_name":"Karl","last_name":"Worthmann"}],"date_updated":"2023-05-08T09:04:26Z","intvolume":"        34","date_created":"2023-05-08T09:04:06Z","type":"journal_article","department":[{"_id":"636"}],"publication":"Mathematics of Control, Signals, and Systems","citation":{"bibtex":"@article{Faulwasser_Flaßkamp_Ober-Blöbaum_Schaller_Worthmann_2022, title={Manifold turnpikes, trims, and symmetries}, volume={34}, journal={Mathematics of Control, Signals, and Systems}, publisher={Springer}, author={Faulwasser, Timm and Flaßkamp, Kathrin and Ober-Blöbaum, Sina and Schaller, Manuel and Worthmann, Karl}, year={2022}, pages={759–788} }","ama":"Faulwasser T, Flaßkamp K, Ober-Blöbaum S, Schaller M, Worthmann K. Manifold turnpikes, trims, and symmetries. <i>Mathematics of Control, Signals, and Systems</i>. 2022;34:759-788.","mla":"Faulwasser, Timm, et al. “Manifold Turnpikes, Trims, and Symmetries.” <i>Mathematics of Control, Signals, and Systems</i>, vol. 34, Springer, 2022, pp. 759–88.","short":"T. Faulwasser, K. Flaßkamp, S. Ober-Blöbaum, M. Schaller, K. Worthmann, Mathematics of Control, Signals, and Systems 34 (2022) 759–788.","chicago":"Faulwasser, Timm, Kathrin Flaßkamp, Sina Ober-Blöbaum, Manuel Schaller, and Karl Worthmann. “Manifold Turnpikes, Trims, and Symmetries.” <i>Mathematics of Control, Signals, and Systems</i> 34 (2022): 759–88.","ieee":"T. Faulwasser, K. Flaßkamp, S. Ober-Blöbaum, M. Schaller, and K. Worthmann, “Manifold turnpikes, trims, and symmetries,” <i>Mathematics of Control, Signals, and Systems</i>, vol. 34, pp. 759–788, 2022.","apa":"Faulwasser, T., Flaßkamp, K., Ober-Blöbaum, S., Schaller, M., &#38; Worthmann, K. (2022). Manifold turnpikes, trims, and symmetries. <i>Mathematics of Control, Signals, and Systems</i>, <i>34</i>, 759–788."}},{"year":"2022","title":"Backward error analysis for variational discretisations of partial  differential equations","author":[{"full_name":"McLachlan, Robert I","first_name":"Robert I","last_name":"McLachlan"},{"full_name":"Offen, Christian","first_name":"Christian","last_name":"Offen","orcid":"https://orcid.org/0000-0002-5940-8057","id":"85279"}],"date_updated":"2023-08-10T08:44:55Z","publication_status":"published","intvolume":"        14","article_type":"original","language":[{"iso":"eng"}],"doi":"10.3934/jgm.2022014","issue":"3","publication":"Journal of Geometric Mechanics","related_material":{"link":[{"relation":"software","url":"https://github.com/Christian-Offen/multisymplectic"}]},"abstract":[{"text":"In backward error analysis, an approximate solution to an equation is compared to the exact solution to a nearby ‘modified’ equation. In numerical ordinary differential equations, the two agree up to any power of the step size. If the differential equation has a geometric property then the modified equation may share it. In this way, known properties of differential equations can be applied to the approximation. But for partial differential equations, the known modified equations are of higher order, limiting applicability of the theory. Therefore, we study symmetric solutions of discretized\r\npartial differential equations that arise from a discrete variational principle. These symmetric solutions obey infinite-dimensional functional equations. We show that these equations admit second-order modified equations which are Hamiltonian and also possess first-order Lagrangians in modified coordinates. The modified equation and its associated structures are computed explicitly for the case of rotating travelling waves in the nonlinear wave equation.","lang":"eng"}],"file":[{"date_created":"2022-06-13T09:11:38Z","description":"In backward error analysis, an approximate solution to an equa-\ntion is compared to the exact solution to a nearby ‘modified’ equation. In\nnumerical ordinary differential equations, the two agree up to any power of\nthe step size. If the differential equation has a geometric property then the\nmodified equation may share it. In this way, known properties of differential\nequations can be applied to the approximation. But for partial differential\nequations, the known modified equations are of higher order, limiting appli-\ncability of the theory. Therefore, we study symmetric solutions of discretized\npartial differential equations that arise from a discrete variational principle.\nThese symmetric solutions obey infinite-dimensional functional equations. We\nshow that these equations admit second-order modified equations which are\nHamiltonian and also possess first-order Lagrangians in modified coordinates.\nThe modified equation and its associated structures are computed explicitly\nfor the case of rotating travelling waves in the nonlinear wave equation.","creator":"coffen","file_id":"31859","content_type":"application/pdf","title":"Backward error analysis for variational discretisations of PDEs","file_name":"2_BlendedBEASymmPDE.pdf","access_level":"open_access","file_size":1507248,"relation":"main_file","date_updated":"2022-06-13T09:11:38Z"}],"date_created":"2020-10-06T16:33:19Z","type":"journal_article","department":[{"_id":"636"}],"status":"public","has_accepted_license":"1","page":"447 - 471","publisher":"AIMS","_id":"19941","ddc":["510"],"user_id":"85279","volume":14,"file_date_updated":"2022-06-13T09:11:38Z","citation":{"mla":"McLachlan, Robert I., and Christian Offen. “Backward Error Analysis for Variational Discretisations of Partial  Differential Equations.” <i>Journal of Geometric Mechanics</i>, vol. 14, no. 3, AIMS, 2022, pp. 447–71, doi:<a href=\"https://doi.org/10.3934/jgm.2022014\">10.3934/jgm.2022014</a>.","ama":"McLachlan RI, Offen C. Backward error analysis for variational discretisations of partial  differential equations. <i>Journal of Geometric Mechanics</i>. 2022;14(3):447-471. doi:<a href=\"https://doi.org/10.3934/jgm.2022014\">10.3934/jgm.2022014</a>","bibtex":"@article{McLachlan_Offen_2022, title={Backward error analysis for variational discretisations of partial  differential equations}, volume={14}, DOI={<a href=\"https://doi.org/10.3934/jgm.2022014\">10.3934/jgm.2022014</a>}, number={3}, journal={Journal of Geometric Mechanics}, publisher={AIMS}, author={McLachlan, Robert I and Offen, Christian}, year={2022}, pages={447–471} }","apa":"McLachlan, R. I., &#38; Offen, C. (2022). Backward error analysis for variational discretisations of partial  differential equations. <i>Journal of Geometric Mechanics</i>, <i>14</i>(3), 447–471. <a href=\"https://doi.org/10.3934/jgm.2022014\">https://doi.org/10.3934/jgm.2022014</a>","ieee":"R. I. McLachlan and C. Offen, “Backward error analysis for variational discretisations of partial  differential equations,” <i>Journal of Geometric Mechanics</i>, vol. 14, no. 3, pp. 447–471, 2022, doi: <a href=\"https://doi.org/10.3934/jgm.2022014\">10.3934/jgm.2022014</a>.","short":"R.I. McLachlan, C. Offen, Journal of Geometric Mechanics 14 (2022) 447–471.","chicago":"McLachlan, Robert I, and Christian Offen. “Backward Error Analysis for Variational Discretisations of Partial  Differential Equations.” <i>Journal of Geometric Mechanics</i> 14, no. 3 (2022): 447–71. <a href=\"https://doi.org/10.3934/jgm.2022014\">https://doi.org/10.3934/jgm.2022014</a>."},"external_id":{"arxiv":["2006.14172"]},"oa":"1"},{"file":[{"access_level":"open_access","file_size":2285059,"file_name":"SymplecticShadowIntegration_AIP.pdf","date_updated":"2021-12-13T14:56:15Z","relation":"main_file","content_type":"application/pdf","file_id":"28734","creator":"coffen","date_created":"2021-12-13T14:56:15Z"}],"date_created":"2021-08-11T08:24:02Z","type":"journal_article","department":[{"_id":"636"}],"publication":"Chaos: An Interdisciplinary Journal of Nonlinear Science","abstract":[{"text":"Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation laws. To predict Hamiltonian dynamics based on discrete trajectory observations, incorporation of prior knowledge about Hamiltonian structure greatly improves predictions. This is typically done by learning the system's Hamiltonian and then integrating the Hamiltonian vector field with a symplectic integrator. For this, however, Hamiltonian data needs to be approximated based on the trajectory observations. Moreover, the numerical integrator introduces an additional discretisation error. In this paper, we show that an inverse modified Hamiltonian structure adapted to the geometric integrator can be learned directly from observations. A separate approximation step for the Hamiltonian data avoided. The inverse modified data compensates for the discretisation error such that the discretisation error is eliminated. The technique is developed for Gaussian Processes.","lang":"eng"}],"related_material":{"link":[{"url":"https://github.com/Christian-Offen/symplectic-shadow-integration","relation":"software","description":"GitHub"}]},"main_file_link":[{"open_access":"1","url":"https://aip.scitation.org/doi/abs/10.1063/5.0065913"}],"language":[{"iso":"eng"}],"doi":"10.1063/5.0065913","title":"Symplectic integration of learned Hamiltonian systems","year":"2022","author":[{"id":"85279","orcid":"0000-0002-5940-8057","first_name":"Christian","last_name":"Offen","full_name":"Offen, Christian"},{"last_name":"Ober-Blöbaum","first_name":"Sina","full_name":"Ober-Blöbaum, Sina","id":"16494"}],"date_updated":"2023-08-10T08:48:14Z","publication_status":"published","article_type":"original","external_id":{"arxiv":["2108.02492"]},"oa":"1","file_date_updated":"2021-12-13T14:56:15Z","citation":{"bibtex":"@article{Offen_Ober-Blöbaum_2022, title={Symplectic integration of learned Hamiltonian systems}, volume={32(1)}, DOI={<a href=\"https://doi.org/10.1063/5.0065913\">10.1063/5.0065913</a>}, journal={Chaos: An Interdisciplinary Journal of Nonlinear Science}, publisher={AIP}, author={Offen, Christian and Ober-Blöbaum, Sina}, year={2022} }","chicago":"Offen, Christian, and Sina Ober-Blöbaum. “Symplectic Integration of Learned Hamiltonian Systems.” <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i> 32(1) (2022). <a href=\"https://doi.org/10.1063/5.0065913\">https://doi.org/10.1063/5.0065913</a>.","ama":"Offen C, Ober-Blöbaum S. Symplectic integration of learned Hamiltonian systems. <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i>. 2022;32(1). doi:<a href=\"https://doi.org/10.1063/5.0065913\">10.1063/5.0065913</a>","short":"C. Offen, S. Ober-Blöbaum, Chaos: An Interdisciplinary Journal of Nonlinear Science 32(1) (2022).","ieee":"C. Offen and S. Ober-Blöbaum, “Symplectic integration of learned Hamiltonian systems,” <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i>, vol. 32(1), 2022, doi: <a href=\"https://doi.org/10.1063/5.0065913\">10.1063/5.0065913</a>.","mla":"Offen, Christian, and Sina Ober-Blöbaum. “Symplectic Integration of Learned Hamiltonian Systems.” <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i>, vol. 32(1), AIP, 2022, doi:<a href=\"https://doi.org/10.1063/5.0065913\">10.1063/5.0065913</a>.","apa":"Offen, C., &#38; Ober-Blöbaum, S. (2022). Symplectic integration of learned Hamiltonian systems. <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i>, <i>32(1)</i>. <a href=\"https://doi.org/10.1063/5.0065913\">https://doi.org/10.1063/5.0065913</a>"},"quality_controlled":"1","_id":"23382","publisher":"AIP","ddc":["510"],"user_id":"85279","volume":"32(1)","status":"public","has_accepted_license":"1"},{"_id":"29421","language":[{"iso":"eng"}],"page":"327-333","volume":"54(19)","user_id":"15694","author":[{"id":"16494","full_name":"Ober-Blöbaum, Sina","first_name":"Sina","last_name":"Ober-Blöbaum"},{"full_name":"Vermeeren, M.","first_name":"M.","last_name":"Vermeeren"}],"corporate_editor":["IFAC-PapersOnLine"],"status":"public","year":"2021","title":"Superconvergence of galerkin variational integrators","date_updated":"2022-01-21T13:36:53Z","date_created":"2022-01-18T14:27:56Z","department":[{"_id":"636"}],"type":"conference","citation":{"apa":"Ober-Blöbaum, S., &#38; Vermeeren, M. (2021). Superconvergence of galerkin variational integrators. In IFAC-PapersOnLine (Ed.), <i>7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC: Vol. 54(19)</i> (pp. 327–333).","ieee":"S. Ober-Blöbaum and M. Vermeeren, “Superconvergence of galerkin variational integrators,” in <i>7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC</i>, 2021, vol. 54(19), pp. 327–333.","short":"S. Ober-Blöbaum, M. Vermeeren, in: IFAC-PapersOnLine (Ed.), 7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC, 2021, pp. 327–333.","chicago":"Ober-Blöbaum, Sina, and M. Vermeeren. “Superconvergence of Galerkin Variational Integrators.” In <i>7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC</i>, edited by IFAC-PapersOnLine, 54(19):327–33, 2021.","mla":"Ober-Blöbaum, Sina, and M. Vermeeren. “Superconvergence of Galerkin Variational Integrators.” <i>7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC</i>, edited by IFAC-PapersOnLine, vol. 54(19), 2021, pp. 327–33.","ama":"Ober-Blöbaum S, Vermeeren M. Superconvergence of galerkin variational integrators. In: IFAC-PapersOnLine, ed. <i>7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC</i>. Vol 54(19). ; 2021:327-333.","bibtex":"@inproceedings{Ober-Blöbaum_Vermeeren_2021, title={Superconvergence of galerkin variational integrators}, volume={54(19)}, booktitle={7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC}, author={Ober-Blöbaum, Sina and Vermeeren, M.}, editor={IFAC-PapersOnLine}, year={2021}, pages={327–333} }"},"publication":"7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC"},{"date_created":"2020-03-13T12:44:36Z","type":"journal_article","oa":"1","department":[{"_id":"101"}],"publication":"International Journal of Robust and Nonlinear Control","citation":{"ieee":"S. Ober-Blöbaum and S. Peitz, “Explicit multiobjective model predictive control for nonlinear systems  with symmetries,” <i>International Journal of Robust and Nonlinear Control</i>, vol. 31(2), pp. 380–403, 2021, doi: <a href=\"https://doi.org/10.1002/rnc.5281\">10.1002/rnc.5281</a>.","apa":"Ober-Blöbaum, S., &#38; Peitz, S. (2021). Explicit multiobjective model predictive control for nonlinear systems  with symmetries. <i>International Journal of Robust and Nonlinear Control</i>, <i>31(2)</i>, 380–403. <a href=\"https://doi.org/10.1002/rnc.5281\">https://doi.org/10.1002/rnc.5281</a>","short":"S. Ober-Blöbaum, S. Peitz, International Journal of Robust and Nonlinear Control 31(2) (2021) 380–403.","chicago":"Ober-Blöbaum, Sina, and Sebastian Peitz. “Explicit Multiobjective Model Predictive Control for Nonlinear Systems  with Symmetries.” <i>International Journal of Robust and Nonlinear Control</i> 31(2) (2021): 380–403. <a href=\"https://doi.org/10.1002/rnc.5281\">https://doi.org/10.1002/rnc.5281</a>.","mla":"Ober-Blöbaum, Sina, and Sebastian Peitz. “Explicit Multiobjective Model Predictive Control for Nonlinear Systems  with Symmetries.” <i>International Journal of Robust and Nonlinear Control</i>, vol. 31(2), 2021, pp. 380–403, doi:<a href=\"https://doi.org/10.1002/rnc.5281\">10.1002/rnc.5281</a>.","bibtex":"@article{Ober-Blöbaum_Peitz_2021, title={Explicit multiobjective model predictive control for nonlinear systems  with symmetries}, volume={31(2)}, DOI={<a href=\"https://doi.org/10.1002/rnc.5281\">10.1002/rnc.5281</a>}, journal={International Journal of Robust and Nonlinear Control}, author={Ober-Blöbaum, Sina and Peitz, Sebastian}, year={2021}, pages={380–403} }","ama":"Ober-Blöbaum S, Peitz S. Explicit multiobjective model predictive control for nonlinear systems  with symmetries. <i>International Journal of Robust and Nonlinear Control</i>. 2021;31(2):380-403. doi:<a href=\"https://doi.org/10.1002/rnc.5281\">10.1002/rnc.5281</a>"},"abstract":[{"lang":"eng","text":"Model predictive control is a prominent approach to construct a feedback\r\ncontrol loop for dynamical systems. Due to real-time constraints, the major\r\nchallenge in MPC is to solve model-based optimal control problems in a very\r\nshort amount of time. For linear-quadratic problems, Bemporad et al. have\r\nproposed an explicit formulation where the underlying optimization problems are\r\nsolved a priori in an offline phase. In this article, we present an extension\r\nof this concept in two significant ways. We consider nonlinear problems and -\r\nmore importantly - problems with multiple conflicting objective functions. In\r\nthe offline phase, we build a library of Pareto optimal solutions from which we\r\nthen obtain a valid compromise solution in the online phase according to a\r\ndecision maker's preference. Since the standard multi-parametric programming\r\napproach is no longer valid in this situation, we instead use interpolation\r\nbetween different entries of the library. To reduce the number of problems that\r\nhave to be solved in the offline phase, we exploit symmetries in the dynamical\r\nsystem and the corresponding multiobjective optimal control problem. The\r\nresults are verified using two different examples from autonomous driving."}],"project":[{"name":"Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"main_file_link":[{"url":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/rnc.5281","open_access":"1"}],"page":"380-403","language":[{"iso":"eng"}],"_id":"16294","doi":"10.1002/rnc.5281","user_id":"15694","volume":"31(2)","status":"public","year":"2021","title":"Explicit multiobjective model predictive control for nonlinear systems  with symmetries","author":[{"id":"16494","first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina"},{"full_name":"Peitz, Sebastian","first_name":"Sebastian","last_name":"Peitz","orcid":"https://orcid.org/0000-0002-3389-793X","id":"47427"}],"date_updated":"2022-01-24T13:27:50Z"},{"language":[{"iso":"eng"}],"article_number":"109804","doi":"10.1016/j.automatica.2021.109804","publication_identifier":{"issn":["0005-1098"]},"author":[{"full_name":"Djema, Walid","last_name":"Djema","first_name":"Walid"},{"full_name":"Giraldi, Laetitia","last_name":"Giraldi","first_name":"Laetitia"},{"first_name":"Sofya","last_name":"Maslovskaya","full_name":"Maslovskaya, Sofya","id":"87909"},{"first_name":"Olivier","last_name":"Bernard","full_name":"Bernard, Olivier"}],"title":"Turnpike features in optimal selection of species represented by quota models","year":"2021","intvolume":"       132","publication_status":"published","date_updated":"2022-01-26T13:15:33Z","date_created":"2022-01-26T13:13:06Z","department":[{"_id":"636"}],"type":"journal_article","keyword":["Electrical and Electronic Engineering","Control and Systems Engineering"],"publication":"Automatica","_id":"29543","publisher":"Elsevier BV","volume":132,"user_id":"87909","status":"public","citation":{"chicago":"Djema, Walid, Laetitia Giraldi, Sofya Maslovskaya, and Olivier Bernard. “Turnpike Features in Optimal Selection of Species Represented by Quota Models.” <i>Automatica</i> 132 (2021). <a href=\"https://doi.org/10.1016/j.automatica.2021.109804\">https://doi.org/10.1016/j.automatica.2021.109804</a>.","ama":"Djema W, Giraldi L, Maslovskaya S, Bernard O. Turnpike features in optimal selection of species represented by quota models. <i>Automatica</i>. 2021;132. doi:<a href=\"https://doi.org/10.1016/j.automatica.2021.109804\">10.1016/j.automatica.2021.109804</a>","short":"W. Djema, L. Giraldi, S. Maslovskaya, O. Bernard, Automatica 132 (2021).","bibtex":"@article{Djema_Giraldi_Maslovskaya_Bernard_2021, title={Turnpike features in optimal selection of species represented by quota models}, volume={132}, DOI={<a href=\"https://doi.org/10.1016/j.automatica.2021.109804\">10.1016/j.automatica.2021.109804</a>}, number={109804}, journal={Automatica}, publisher={Elsevier BV}, author={Djema, Walid and Giraldi, Laetitia and Maslovskaya, Sofya and Bernard, Olivier}, year={2021} }","mla":"Djema, Walid, et al. “Turnpike Features in Optimal Selection of Species Represented by Quota Models.” <i>Automatica</i>, vol. 132, 109804, Elsevier BV, 2021, doi:<a href=\"https://doi.org/10.1016/j.automatica.2021.109804\">10.1016/j.automatica.2021.109804</a>.","apa":"Djema, W., Giraldi, L., Maslovskaya, S., &#38; Bernard, O. (2021). Turnpike features in optimal selection of species represented by quota models. <i>Automatica</i>, <i>132</i>, Article 109804. <a href=\"https://doi.org/10.1016/j.automatica.2021.109804\">https://doi.org/10.1016/j.automatica.2021.109804</a>","ieee":"W. Djema, L. Giraldi, S. Maslovskaya, and O. Bernard, “Turnpike features in optimal selection of species represented by quota models,” <i>Automatica</i>, vol. 132, Art. no. 109804, 2021, doi: <a href=\"https://doi.org/10.1016/j.automatica.2021.109804\">10.1016/j.automatica.2021.109804</a>."}},{"date_created":"2021-07-29T09:38:32Z","file":[{"date_created":"2021-07-29T09:37:49Z","creator":"coffen","file_id":"22895","content_type":"application/pdf","file_name":"ifacconf.pdf","access_level":"open_access","file_size":3125220,"relation":"main_file","date_updated":"2021-07-29T09:37:49Z"}],"department":[{"_id":"636"}],"type":"conference","keyword":["optimal control","catastrophe theory","bifurcations","variational methods","symplectic integrators"],"abstract":[{"lang":"eng","text":"The first order optimality conditions of optimal control problems (OCPs) can\r\nbe regarded as boundary value problems for Hamiltonian systems. Variational or\r\nsymplectic discretisation methods are classically known for their excellent\r\nlong term behaviour. As boundary value problems are posed on intervals of\r\nfixed, moderate length, it is not immediately clear whether methods can profit\r\nfrom structure preservation in this context. When parameters are present,\r\nsolutions can undergo bifurcations, for instance, two solutions can merge and\r\nannihilate one another as parameters are varied. We will show that generic\r\nbifurcations of an OCP are preserved under discretisation when the OCP is\r\neither directly discretised to a discrete OCP (direct method) or translated\r\ninto a Hamiltonian boundary value problem using first order necessary\r\nconditions of optimality which is then solved using a symplectic integrator\r\n(indirect method). Moreover, certain bifurcations break when a non-symplectic\r\nscheme is used. The general phenomenon is illustrated on the example of a cut\r\nlocus of an ellipsoid."}],"related_material":{"link":[{"description":"GitHub/Zenodo","relation":"software","url":"https://doi.org/10.5281/zenodo.4562664"}]},"series_title":"IFAC-PapersOnLine","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://www.sciencedirect.com/science/article/pii/S2405896321021236"}],"doi":"https://doi.org/10.1016/j.ifacol.2021.11.099","publication_identifier":{"issn":["2405-8963"]},"author":[{"id":"85279","full_name":"Offen, Christian","first_name":"Christian","last_name":"Offen","orcid":"0000-0002-5940-8057"},{"id":"16494","full_name":"Ober-Blöbaum, Sina","first_name":"Sina","last_name":"Ober-Blöbaum"}],"year":"2021","title":"Bifurcation preserving discretisations of optimal control problems","publication_status":"published","date_updated":"2023-11-29T10:19:41Z","external_id":{"arxiv":["2107.13853"]},"oa":"1","citation":{"bibtex":"@article{Offen_Ober-Blöbaum_2021, series={IFAC-PapersOnLine}, title={Bifurcation preserving discretisations of optimal control problems}, volume={54(19)}, DOI={<a href=\"https://doi.org/10.1016/j.ifacol.2021.11.099\">https://doi.org/10.1016/j.ifacol.2021.11.099</a>}, author={Offen, Christian and Ober-Blöbaum, Sina}, year={2021}, pages={334–339}, collection={IFAC-PapersOnLine} }","ama":"Offen C, Ober-Blöbaum S. Bifurcation preserving discretisations of optimal control problems. 2021;54(19):334-339. doi:<a href=\"https://doi.org/10.1016/j.ifacol.2021.11.099\">https://doi.org/10.1016/j.ifacol.2021.11.099</a>","mla":"Offen, Christian, and Sina Ober-Blöbaum. <i>Bifurcation Preserving Discretisations of Optimal Control Problems</i>. 2021, pp. 334–39, doi:<a href=\"https://doi.org/10.1016/j.ifacol.2021.11.099\">https://doi.org/10.1016/j.ifacol.2021.11.099</a>.","short":"C. Offen, S. Ober-Blöbaum, 54(19) (2021) 334–339.","chicago":"Offen, Christian, and Sina Ober-Blöbaum. “Bifurcation Preserving Discretisations of Optimal Control Problems.” IFAC-PapersOnLine, 2021. <a href=\"https://doi.org/10.1016/j.ifacol.2021.11.099\">https://doi.org/10.1016/j.ifacol.2021.11.099</a>.","ieee":"C. Offen and S. Ober-Blöbaum, “Bifurcation preserving discretisations of optimal control problems,” vol. 54(19). pp. 334–339, 2021, doi: <a href=\"https://doi.org/10.1016/j.ifacol.2021.11.099\">https://doi.org/10.1016/j.ifacol.2021.11.099</a>.","apa":"Offen, C., &#38; Ober-Blöbaum, S. (2021). <i>Bifurcation preserving discretisations of optimal control problems: Vol. 54(19)</i> (pp. 334–339). <a href=\"https://doi.org/10.1016/j.ifacol.2021.11.099\">https://doi.org/10.1016/j.ifacol.2021.11.099</a>"},"file_date_updated":"2021-07-29T09:37:49Z","quality_controlled":"1","_id":"22894","page":"334-339","volume":"54(19)","user_id":"15694","ddc":["510"],"conference":{"end_date":"2021-10-13","start_date":"2021-10-11","name":"7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, LHMNC 2021","location":"Berlin, Germany"},"status":"public","has_accepted_license":"1"},{"page":"2896","_id":"21572","publisher":"IEEE","user_id":"15694","status":"public","conference":{"start_date":"2021-12-14","name":"60th IEEE Conference on Decision and Control (CDC)","location":"Austin, TX, USA","end_date":"2021-12-17"},"external_id":{"arxiv":["2011.05364"]},"citation":{"bibtex":"@inproceedings{Ridderbusch_Offen_Ober-Blöbaum_Goulart_2021, title={Learning ODE Models with Qualitative Structure Using Gaussian Processes }, DOI={<a href=\"https://doi.org/10.1109/CDC45484.2021.9683426\">10.1109/CDC45484.2021.9683426</a>}, booktitle={2021 60th IEEE Conference on Decision and Control (CDC)}, publisher={IEEE}, author={Ridderbusch, Steffen and Offen, Christian and Ober-Blöbaum, Sina and Goulart, Paul}, year={2021}, pages={2896} }","ama":"Ridderbusch S, Offen C, Ober-Blöbaum S, Goulart P. Learning ODE Models with Qualitative Structure Using Gaussian Processes . In: <i>2021 60th IEEE Conference on Decision and Control (CDC)</i>. IEEE; 2021:2896. doi:<a href=\"https://doi.org/10.1109/CDC45484.2021.9683426\">10.1109/CDC45484.2021.9683426</a>","mla":"Ridderbusch, Steffen, et al. “Learning ODE Models with Qualitative Structure Using Gaussian Processes .” <i>2021 60th IEEE Conference on Decision and Control (CDC)</i>, IEEE, 2021, p. 2896, doi:<a href=\"https://doi.org/10.1109/CDC45484.2021.9683426\">10.1109/CDC45484.2021.9683426</a>.","short":"S. Ridderbusch, C. Offen, S. Ober-Blöbaum, P. Goulart, in: 2021 60th IEEE Conference on Decision and Control (CDC), IEEE, 2021, p. 2896.","chicago":"Ridderbusch, Steffen, Christian Offen, Sina Ober-Blöbaum, and Paul Goulart. “Learning ODE Models with Qualitative Structure Using Gaussian Processes .” In <i>2021 60th IEEE Conference on Decision and Control (CDC)</i>, 2896. IEEE, 2021. <a href=\"https://doi.org/10.1109/CDC45484.2021.9683426\">https://doi.org/10.1109/CDC45484.2021.9683426</a>.","ieee":"S. Ridderbusch, C. Offen, S. Ober-Blöbaum, and P. Goulart, “Learning ODE Models with Qualitative Structure Using Gaussian Processes ,” in <i>2021 60th IEEE Conference on Decision and Control (CDC)</i>, Austin, TX, USA, 2021, p. 2896, doi: <a href=\"https://doi.org/10.1109/CDC45484.2021.9683426\">10.1109/CDC45484.2021.9683426</a>.","apa":"Ridderbusch, S., Offen, C., Ober-Blöbaum, S., &#38; Goulart, P. (2021). Learning ODE Models with Qualitative Structure Using Gaussian Processes . <i>2021 60th IEEE Conference on Decision and Control (CDC)</i>, 2896. <a href=\"https://doi.org/10.1109/CDC45484.2021.9683426\">https://doi.org/10.1109/CDC45484.2021.9683426</a>"},"language":[{"iso":"eng"}],"doi":"10.1109/CDC45484.2021.9683426","year":"2021","title":"Learning ODE Models with Qualitative Structure Using Gaussian Processes ","author":[{"last_name":"Ridderbusch","first_name":"Steffen","full_name":"Ridderbusch, Steffen"},{"id":"85279","full_name":"Offen, Christian","orcid":"0000-0002-5940-8057","first_name":"Christian","last_name":"Offen"},{"id":"16494","last_name":"Ober-Blöbaum","first_name":"Sina","full_name":"Ober-Blöbaum, Sina"},{"full_name":"Goulart, Paul","first_name":"Paul","last_name":"Goulart"}],"publication_identifier":{"eisbn":["978-1-6654-3659-5"]},"publication_status":"published","date_updated":"2023-11-29T10:24:55Z","date_created":"2021-03-30T10:27:44Z","type":"conference","department":[{"_id":"636"}],"publication":"2021 60th IEEE Conference on Decision and Control (CDC)","related_material":{"link":[{"description":"GitHub","url":"https://github.com/Crown421/StructureGPs-paper","relation":"software"}]}},{"page":"1975-1980","language":[{"iso":"eng"}],"_id":"21592","user_id":"15694","year":"2021","status":"public","title":"Multi-objective minimum time optimal control for low-thrust trajectory design","conference":{"location":"Rotterdam, the Netherlands","start_date":"2021-06-29","name":"2021 European Control Conference (ECC)","end_date":"2021-07-02"},"author":[{"last_name":"Vertovec","first_name":"Nikolaus","full_name":"Vertovec, Nikolaus","id":"87056"},{"first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","id":"16494"},{"full_name":"Margellos, Kostas","last_name":"Margellos","first_name":"Kostas"}],"date_updated":"2023-11-29T10:26:49Z","publication_status":"accepted","external_id":{"arxiv":["2103.08813"]},"date_created":"2021-04-03T03:00:35Z","type":"conference","department":[{"_id":"636"}],"citation":{"chicago":"Vertovec, Nikolaus, Sina Ober-Blöbaum, and Kostas Margellos. “Multi-Objective Minimum Time Optimal Control for Low-Thrust Trajectory Design,” 1975–80, n.d.","short":"N. Vertovec, S. Ober-Blöbaum, K. Margellos, in: n.d., pp. 1975–1980.","ama":"Vertovec N, Ober-Blöbaum S, Margellos K. Multi-objective minimum time optimal control for low-thrust trajectory design. In: ; :1975-1980.","bibtex":"@inproceedings{Vertovec_Ober-Blöbaum_Margellos, title={Multi-objective minimum time optimal control for low-thrust trajectory design}, author={Vertovec, Nikolaus and Ober-Blöbaum, Sina and Margellos, Kostas}, pages={1975–1980} }","apa":"Vertovec, N., Ober-Blöbaum, S., &#38; Margellos, K. (n.d.). <i>Multi-objective minimum time optimal control for low-thrust trajectory design</i>. 1975–1980.","mla":"Vertovec, Nikolaus, et al. <i>Multi-Objective Minimum Time Optimal Control for Low-Thrust Trajectory Design</i>. pp. 1975–80.","ieee":"N. Vertovec, S. Ober-Blöbaum, and K. Margellos, “Multi-objective minimum time optimal control for low-thrust trajectory design,” Rotterdam, the Netherlands, pp. 1975–1980."},"abstract":[{"lang":"eng","text":"We propose a reachability approach for infinite and finite horizon multi-objective optimization problems for low-thrust spacecraft trajectory design. The main advantage of the proposed method is that the Pareto front can be efficiently constructed from the zero level set of the solution to a Hamilton-Jacobi-Bellman equation. We demonstrate the proposed method by applying it to a low-thrust spacecraft trajectory design problem. By deriving the analytic expression for the Hamiltonian and the optimal control policy, we are able to efficiently compute the backward reachable set and reconstruct the optimal trajectories. Furthermore, we show that any reconstructed trajectory will be guaranteed to be weakly Pareto optimal. The proposed method can be used as a benchmark for future research of applying reachability analysis to low-thrust spacecraft trajectory design."}]},{"date_created":"2022-02-17T07:28:47Z","department":[{"_id":"636"}],"type":"conference","citation":{"short":"F. Jiménez, S. Ober-Blöbaum, in: Nichtlineare Sci 31, 2021.","chicago":"Jiménez, F., and Sina Ober-Blöbaum. “Fractional Damping Through Restricted Calculus of Variations.” In <i>Nichtlineare Sci 31</i>, Vol. 46. J Nonlinear Sci , 2021.","apa":"Jiménez, F., &#38; Ober-Blöbaum, S. (2021). Fractional Damping Through Restricted Calculus of Variations. <i>Nichtlineare Sci 31</i>, <i>46</i>.","ieee":"F. Jiménez and S. Ober-Blöbaum, “Fractional Damping Through Restricted Calculus of Variations,” in <i>Nichtlineare Sci 31</i>, 2021, vol. 46.","ama":"Jiménez F, Ober-Blöbaum S. Fractional Damping Through Restricted Calculus of Variations. In: <i>Nichtlineare Sci 31</i>. Vol 46. J Nonlinear Sci . ; 2021.","bibtex":"@inproceedings{Jiménez_Ober-Blöbaum_2021, series={J Nonlinear Sci }, title={Fractional Damping Through Restricted Calculus of Variations}, volume={46}, booktitle={Nichtlineare Sci 31}, author={Jiménez, F. and Ober-Blöbaum, Sina}, year={2021}, collection={J Nonlinear Sci } }","mla":"Jiménez, F., and Sina Ober-Blöbaum. “Fractional Damping Through Restricted Calculus of Variations.” <i>Nichtlineare Sci 31</i>, vol. 46, 2021."},"publication":"Nichtlineare Sci 31","series_title":"J Nonlinear Sci ","_id":"29868","language":[{"iso":"eng"}],"volume":46,"user_id":"15694","author":[{"last_name":"Jiménez","first_name":"F.","full_name":"Jiménez, F."},{"id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"}],"status":"public","year":"2021","title":"Fractional Damping Through Restricted Calculus of Variations","intvolume":"        46","date_updated":"2023-11-29T10:23:46Z"},{"citation":{"bibtex":"@inproceedings{Lishkova_Cannon_Ober-Blöbaum_2021, title={A multirate variational approach to Nonlinear MPC}, publisher={European Control Conference (ECC), IEEE}, author={Lishkova, Y. and Cannon, M. and Ober-Blöbaum, Sina}, year={2021} }","ama":"Lishkova Y, Cannon M, Ober-Blöbaum S. A multirate variational approach to Nonlinear MPC. In: European Control Conference (ECC), IEEE; 2021.","mla":"Lishkova, Y., et al. <i>A Multirate Variational Approach to Nonlinear MPC</i>. European Control Conference (ECC), IEEE, 2021.","chicago":"Lishkova, Y., M. Cannon, and Sina Ober-Blöbaum. “A Multirate Variational Approach to Nonlinear MPC.” European Control Conference (ECC), IEEE, 2021.","short":"Y. Lishkova, M. Cannon, S. Ober-Blöbaum, in: European Control Conference (ECC), IEEE, 2021.","ieee":"Y. Lishkova, M. Cannon, and S. Ober-Blöbaum, “A multirate variational approach to Nonlinear MPC,” 2021.","apa":"Lishkova, Y., Cannon, M., &#38; Ober-Blöbaum, S. (2021). <i>A multirate variational approach to Nonlinear MPC</i>."},"type":"conference","date_created":"2023-09-21T07:14:57Z","date_updated":"2023-09-21T07:27:30Z","author":[{"full_name":"Lishkova, Y.","first_name":"Y.","last_name":"Lishkova"},{"last_name":"Cannon","first_name":"M.","full_name":"Cannon, M."},{"id":"16494","full_name":"Ober-Blöbaum, Sina","first_name":"Sina","last_name":"Ober-Blöbaum"}],"status":"public","title":"A multirate variational approach to Nonlinear MPC","year":"2021","user_id":"15694","_id":"47146","language":[{"iso":"eng"}],"publisher":"European Control Conference (ECC), IEEE"}]