[{"status":"public","abstract":[{"lang":"eng","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."}],"type":"conference","language":[{"iso":"eng"}],"ddc":["510"],"department":[{"_id":"636"}],"user_id":"15694","_id":"30733","page":"1870-1875","citation":{"chicago":"Vertovec, Nikolaus, Sina Ober-Blöbaum, and Kostas Margellos. “Verification of Safety Critical Control Policies Using Kernel Methods,” 1870–75, 2022.","ieee":"N. Vertovec, S. Ober-Blöbaum, and K. Margellos, “Verification of safety critical control policies using kernel methods,” London, 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.","short":"N. Vertovec, S. Ober-Blöbaum, K. Margellos, in: 2022, pp. 1870–1875.","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} }","mla":"Vertovec, Nikolaus, et al. <i>Verification of Safety Critical Control Policies Using Kernel Methods</i>. 2022, pp. 1870–75.","apa":"Vertovec, N., Ober-Blöbaum, S., &#38; Margellos, K. (2022). <i>Verification of safety critical control policies using kernel methods</i>. 1870–1875."},"year":"2022","has_accepted_license":"1","conference":{"location":"London","end_date":"2022-07-15","start_date":"2022-07-12","name":"2022 European Control Conference (ECC)"},"title":"Verification of safety critical control policies using kernel methods","author":[{"first_name":"Nikolaus","full_name":"Vertovec, Nikolaus","id":"93930","last_name":"Vertovec"},{"id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"},{"first_name":"Kostas","last_name":"Margellos","full_name":"Margellos, Kostas"}],"date_created":"2022-03-31T11:14:13Z","date_updated":"2023-11-29T10:00:18Z"},{"publisher":"Springer","date_updated":"2023-05-08T09:04:26Z","date_created":"2023-05-08T09:04:06Z","author":[{"full_name":"Faulwasser, Timm","last_name":"Faulwasser","first_name":"Timm"},{"last_name":"Flaßkamp","full_name":"Flaßkamp, Kathrin","first_name":"Kathrin"},{"first_name":"Sina","last_name":"Ober-Blöbaum","id":"16494","full_name":"Ober-Blöbaum, Sina"},{"first_name":"Manuel","full_name":"Schaller, Manuel","last_name":"Schaller"},{"first_name":"Karl","last_name":"Worthmann","full_name":"Worthmann, Karl"}],"volume":34,"title":"Manifold turnpikes, trims, and symmetries","year":"2022","citation":{"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.","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.","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} }","short":"T. Faulwasser, K. Flaßkamp, S. Ober-Blöbaum, M. Schaller, K. Worthmann, Mathematics of Control, Signals, and Systems 34 (2022) 759–788.","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.","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.","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."},"intvolume":"        34","page":"759-788","_id":"44624","user_id":"15694","department":[{"_id":"636"}],"language":[{"iso":"eng"}],"type":"journal_article","publication":"Mathematics of Control, Signals, and Systems","status":"public"},{"external_id":{"arxiv":["2108.02492"]},"ddc":["510"],"language":[{"iso":"eng"}],"publication":"Chaos: An Interdisciplinary Journal of Nonlinear Science","abstract":[{"lang":"eng","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."}],"file":[{"file_size":2285059,"file_name":"SymplecticShadowIntegration_AIP.pdf","access_level":"open_access","file_id":"28734","date_updated":"2021-12-13T14:56:15Z","date_created":"2021-12-13T14:56:15Z","creator":"coffen","relation":"main_file","content_type":"application/pdf"}],"publisher":"AIP","date_created":"2021-08-11T08:24:02Z","title":"Symplectic integration of learned Hamiltonian systems","quality_controlled":"1","year":"2022","_id":"23382","department":[{"_id":"636"}],"user_id":"85279","article_type":"original","file_date_updated":"2021-12-13T14:56:15Z","type":"journal_article","status":"public","oa":"1","date_updated":"2023-08-10T08:48:14Z","volume":"32(1)","author":[{"id":"85279","full_name":"Offen, Christian","orcid":"0000-0002-5940-8057","last_name":"Offen","first_name":"Christian"},{"last_name":"Ober-Blöbaum","id":"16494","full_name":"Ober-Blöbaum, Sina","first_name":"Sina"}],"doi":"10.1063/5.0065913","main_file_link":[{"open_access":"1","url":"https://aip.scitation.org/doi/abs/10.1063/5.0065913"}],"has_accepted_license":"1","publication_status":"published","related_material":{"link":[{"url":"https://github.com/Christian-Offen/symplectic-shadow-integration","relation":"software","description":"GitHub"}]},"citation":{"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>","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>.","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} }","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>.","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>"}},{"user_id":"15694","department":[{"_id":"636"}],"_id":"29421","language":[{"iso":"eng"}],"type":"conference","publication":"7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC","status":"public","date_created":"2022-01-18T14:27:56Z","author":[{"last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","id":"16494","first_name":"Sina"},{"last_name":"Vermeeren","full_name":"Vermeeren, M.","first_name":"M."}],"volume":"54(19)","date_updated":"2022-01-21T13:36:53Z","title":"Superconvergence of galerkin variational integrators","citation":{"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.","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} }","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.","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).","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.","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.","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."},"corporate_editor":["IFAC-PapersOnLine"],"page":"327-333","year":"2021"},{"publication":"International Journal of Robust and Nonlinear Control","type":"journal_article","status":"public","abstract":[{"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.","lang":"eng"}],"department":[{"_id":"101"}],"user_id":"15694","_id":"16294","project":[{"_id":"52","name":"Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"language":[{"iso":"eng"}],"page":"380-403","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>.","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>.","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>","short":"S. Ober-Blöbaum, S. Peitz, International Journal of Robust and Nonlinear Control 31(2) (2021) 380–403.","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} }","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>.","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>"},"year":"2021","volume":"31(2)","author":[{"first_name":"Sina","last_name":"Ober-Blöbaum","id":"16494","full_name":"Ober-Blöbaum, Sina"},{"first_name":"Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X","last_name":"Peitz","id":"47427","full_name":"Peitz, Sebastian"}],"date_created":"2020-03-13T12:44:36Z","oa":"1","date_updated":"2022-01-24T13:27:50Z","doi":"10.1002/rnc.5281","main_file_link":[{"open_access":"1","url":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/rnc.5281"}],"title":"Explicit multiobjective model predictive control for nonlinear systems  with symmetries"},{"external_id":{"arxiv":["2107.13853"]},"language":[{"iso":"eng"}],"keyword":["optimal control","catastrophe theory","bifurcations","variational methods","symplectic integrators"],"ddc":["510"],"file":[{"file_size":3125220,"file_id":"22895","file_name":"ifacconf.pdf","access_level":"open_access","date_updated":"2021-07-29T09:37:49Z","date_created":"2021-07-29T09:37:49Z","creator":"coffen","relation":"main_file","content_type":"application/pdf"}],"abstract":[{"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.","lang":"eng"}],"date_created":"2021-07-29T09:38:32Z","title":"Bifurcation preserving discretisations of optimal control problems","quality_controlled":"1","year":"2021","department":[{"_id":"636"}],"user_id":"15694","series_title":"IFAC-PapersOnLine","_id":"22894","file_date_updated":"2021-07-29T09:37:49Z","type":"conference","status":"public","volume":"54(19)","author":[{"last_name":"Offen","orcid":"0000-0002-5940-8057","id":"85279","full_name":"Offen, Christian","first_name":"Christian"},{"first_name":"Sina","full_name":"Ober-Blöbaum, Sina","id":"16494","last_name":"Ober-Blöbaum"}],"date_updated":"2023-11-29T10:19:41Z","oa":"1","conference":{"name":"7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, LHMNC 2021","start_date":"2021-10-11","end_date":"2021-10-13","location":"Berlin, Germany"},"doi":"https://doi.org/10.1016/j.ifacol.2021.11.099","main_file_link":[{"open_access":"1","url":"https://www.sciencedirect.com/science/article/pii/S2405896321021236"}],"related_material":{"link":[{"description":"GitHub/Zenodo","relation":"software","url":"https://doi.org/10.5281/zenodo.4562664"}]},"has_accepted_license":"1","publication_identifier":{"issn":["2405-8963"]},"publication_status":"published","page":"334-339","citation":{"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>","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>.","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>.","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>","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} }","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."}},{"page":"2896","citation":{"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>","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} }","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.","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>","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>."},"related_material":{"link":[{"description":"GitHub","relation":"software","url":"https://github.com/Crown421/StructureGPs-paper"}]},"publication_identifier":{"eisbn":["978-1-6654-3659-5"]},"publication_status":"published","doi":"10.1109/CDC45484.2021.9683426","conference":{"location":"Austin, TX, USA","end_date":"2021-12-17","start_date":"2021-12-14","name":"60th IEEE Conference on Decision and Control (CDC)"},"author":[{"first_name":"Steffen","full_name":"Ridderbusch, Steffen","last_name":"Ridderbusch"},{"first_name":"Christian","full_name":"Offen, Christian","id":"85279","last_name":"Offen","orcid":"0000-0002-5940-8057"},{"first_name":"Sina","last_name":"Ober-Blöbaum","id":"16494","full_name":"Ober-Blöbaum, Sina"},{"first_name":"Paul","full_name":"Goulart, Paul","last_name":"Goulart"}],"date_updated":"2023-11-29T10:24:55Z","status":"public","type":"conference","department":[{"_id":"636"}],"user_id":"15694","_id":"21572","year":"2021","title":"Learning ODE Models with Qualitative Structure Using Gaussian Processes ","date_created":"2021-03-30T10:27:44Z","publisher":"IEEE","publication":"2021 60th IEEE Conference on Decision and Control (CDC)","language":[{"iso":"eng"}],"external_id":{"arxiv":["2011.05364"]}},{"type":"conference","abstract":[{"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.","lang":"eng"}],"status":"public","_id":"21592","external_id":{"arxiv":["2103.08813"]},"department":[{"_id":"636"}],"user_id":"15694","language":[{"iso":"eng"}],"publication_status":"accepted","year":"2021","page":"1975-1980","citation":{"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.","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} }","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.","chicago":"Vertovec, Nikolaus, Sina Ober-Blöbaum, and Kostas Margellos. “Multi-Objective Minimum Time Optimal Control for Low-Thrust Trajectory Design,” 1975–80, n.d.","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."},"date_updated":"2023-11-29T10:26:49Z","date_created":"2021-04-03T03:00:35Z","author":[{"last_name":"Vertovec","id":"87056","full_name":"Vertovec, Nikolaus","first_name":"Nikolaus"},{"first_name":"Sina","id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum"},{"first_name":"Kostas","last_name":"Margellos","full_name":"Margellos, Kostas"}],"title":"Multi-objective minimum time optimal control for low-thrust trajectory design","conference":{"name":"2021 European Control Conference (ECC)","start_date":"2021-06-29","end_date":"2021-07-02","location":"Rotterdam, the Netherlands"}},{"_id":"29868","user_id":"15694","series_title":"J Nonlinear Sci ","department":[{"_id":"636"}],"language":[{"iso":"eng"}],"type":"conference","publication":"Nichtlineare Sci 31","status":"public","date_updated":"2023-11-29T10:23:46Z","author":[{"last_name":"Jiménez","full_name":"Jiménez, F.","first_name":"F."},{"first_name":"Sina","id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum"}],"date_created":"2022-02-17T07:28:47Z","volume":46,"title":"Fractional Damping Through Restricted Calculus of Variations","year":"2021","citation":{"mla":"Jiménez, F., and Sina Ober-Blöbaum. “Fractional Damping Through Restricted Calculus of Variations.” <i>Nichtlineare Sci 31</i>, vol. 46, 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 } }","short":"F. Jiménez, S. Ober-Blöbaum, in: Nichtlineare Sci 31, 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.","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.","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."},"intvolume":"        46"},{"language":[{"iso":"eng"}],"user_id":"15694","_id":"47146","status":"public","type":"conference","title":"A multirate variational approach to Nonlinear MPC","date_created":"2023-09-21T07:14:57Z","author":[{"first_name":"Y.","last_name":"Lishkova","full_name":"Lishkova, Y."},{"first_name":"M.","full_name":"Cannon, M.","last_name":"Cannon"},{"first_name":"Sina","last_name":"Ober-Blöbaum","id":"16494","full_name":"Ober-Blöbaum, Sina"}],"publisher":"European Control Conference (ECC), IEEE","date_updated":"2023-09-21T07:27:30Z","citation":{"short":"Y. Lishkova, M. Cannon, S. Ober-Blöbaum, 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.","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} }","apa":"Lishkova, Y., Cannon, M., &#38; Ober-Blöbaum, S. (2021). <i>A multirate variational approach to Nonlinear MPC</i>.","ama":"Lishkova Y, Cannon M, Ober-Blöbaum S. A multirate variational approach to Nonlinear MPC. In: 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.","ieee":"Y. Lishkova, M. Cannon, and S. Ober-Blöbaum, “A multirate variational approach to Nonlinear MPC,” 2021."},"year":"2021"},{"page":"1381-1396","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.","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.","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.","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.","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} }","short":"D.J.N. Limebeer, S. Ober-Blöbaum, F.H. Farshi, IEEE Transactions on Automatic Control 65(4) (2020) 1381–1396."},"year":"2020","title":"Variational integrators for dissipative systems","volume":"65(4)","date_created":"2022-01-18T11:17:25Z","author":[{"full_name":"Limebeer, D. J. N.","last_name":"Limebeer","first_name":"D. J. N."},{"full_name":"Ober-Blöbaum, Sina","id":"16494","last_name":"Ober-Blöbaum","first_name":"Sina"},{"first_name":"F. H.","last_name":"Farshi","full_name":"Farshi, F. H."}],"date_updated":"2022-01-21T08:26:46Z","status":"public","publication":"IEEE Transactions on Automatic Control","type":"journal_article","language":[{"iso":"eng"}],"department":[{"_id":"636"}],"user_id":"15694","_id":"29399"},{"user_id":"15694","department":[{"_id":"101"}],"_id":"16297","language":[{"iso":"eng"}],"type":"journal_article","publication":"International Journal of Robust and Nonlinear Control","status":"public","abstract":[{"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.","lang":"eng"}],"date_created":"2020-03-13T12:45:56Z","author":[{"first_name":"Carlos Ignacio","full_name":"Hernández Castellanos, Carlos Ignacio","last_name":"Hernández Castellanos"},{"id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"},{"first_name":"Sebastian","full_name":"Peitz, Sebastian","id":"47427","last_name":"Peitz","orcid":"https://orcid.org/0000-0002-3389-793X"}],"volume":"30(17)","date_updated":"2022-01-21T09:55:39Z","doi":"10.1002/rnc.5197","title":"Explicit Multi-objective Model Predictive Control for Nonlinear Systems  Under Uncertainty","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>","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>.","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>.","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} }","short":"C.I. Hernández Castellanos, S. Ober-Blöbaum, S. Peitz, International Journal of Robust and Nonlinear Control 30(17) (2020) 7593–7618.","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>"},"page":"7593-7618","year":"2020"},{"date_updated":"2022-01-21T09:57:35Z","author":[{"last_name":"Hernández Castellanos","full_name":"Hernández Castellanos, C. I. O.","first_name":"C. I. O."},{"first_name":"G.","full_name":"Schütze, G.","last_name":"Schütze"},{"full_name":"Sun, J.-Q.","last_name":"Sun","first_name":"J.-Q."},{"first_name":"Sina","last_name":"Ober-Blöbaum","id":"16494","full_name":"Ober-Blöbaum, Sina"},{"full_name":"Morales-Luna, G.","last_name":"Morales-Luna","first_name":"G."}],"date_created":"2022-01-18T11:08:28Z","volume":"8(11):1959","title":"Numerical computation of lightly multi-objective robust optimal solutions by means of generalized cell mapping","year":"2020","citation":{"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).","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.","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.","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.","short":"C.I.O. Hernández Castellanos, G. Schütze, J.-Q. Sun, S. Ober-Blöbaum, G. Morales-Luna, Mathematics 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>."},"_id":"29398","user_id":"15694","department":[{"_id":"636"}],"language":[{"iso":"eng"}],"type":"journal_article","publication":"Mathematics","status":"public"},{"date_updated":"2022-01-21T13:45:40Z","author":[{"full_name":"Lishkova, Y.","last_name":"Lishkova","first_name":"Y."},{"last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","id":"16494","first_name":"Sina"},{"last_name":"Cannon","full_name":"Cannon, M.","first_name":"M."},{"full_name":"Leyendecker, S.","last_name":"Leyendecker","first_name":"S."}],"date_created":"2022-01-18T14:37:53Z","title":"A multirate variational approach to simulation and optimal control for flexible spacecraft","year":"2020","citation":{"ieee":"Y. Lishkova, S. Ober-Blöbaum, M. Cannon, and S. Leyendecker, “A multirate variational approach to simulation and optimal control for flexible spacecraft,” 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.","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.","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>.","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.","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.","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} }"},"_id":"29422","user_id":"15694","department":[{"_id":"636"}],"language":[{"iso":"eng"}],"type":"conference","publication":"Accepted for publication in Proceedings of 2020 AAS/AIAA Astrodynamics Specialist Conference - Lake Tahoe","status":"public"},{"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."},{"first_name":"K.","last_name":"Flaßkamp","full_name":"Flaßkamp, K."},{"first_name":"Sina","id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum"},{"last_name":"Worthmann","full_name":"Worthmann, K. ","first_name":"K. "}],"year":"2020","citation":{"short":"T. Faulwasser, K. Flaßkamp, S. Ober-Blöbaum, K. Worthmann, in: 24th International Symposium on Mathematical Theory of Networks and Systems, 2020.","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} }","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.","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>.","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."}},{"author":[{"full_name":"Cresson, J. ","last_name":"Cresson","first_name":"J. "},{"first_name":"F.","last_name":"Jiménez","full_name":"Jiménez, F."},{"last_name":"Ober-Blöbaum","id":"16494","full_name":"Ober-Blöbaum, Sina","first_name":"Sina"}],"date_created":"2022-01-18T14:45:22Z","date_updated":"2022-01-21T13:47:49Z","title":"Modelling of the convection-diffusion equation through fractional restricted calculus of variations","citation":{"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.","ieee":"J. Cresson, F. Jiménez, and S. Ober-Blöbaum, “Modelling of the convection-diffusion equation through fractional restricted calculus of variations,” 2020.","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.","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.","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} }","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>."},"year":"2020","department":[{"_id":"636"}],"user_id":"15694","_id":"29424","language":[{"iso":"eng"}],"publication":"24th International Symposium on Mathematical Theory of Networks and Systems","type":"conference","status":"public"},{"page":"209-237","citation":{"ama":"Flaßkamp K, Ober-Blöbaum S, Peitz S. Symmetry in optimal control: A multiobjective model predictive control approach. In: Junge O, Schütze O, Froyland G, Ober-Blöbaum S, Padberg-Gehle K, eds. <i>Advances in Dynamics, Optimization and Computation</i>. Springer International Publishing; 2020:209-237.","ieee":"K. Flaßkamp, S. Ober-Blöbaum, and S. Peitz, “Symmetry in optimal control: A multiobjective model predictive control approach,” in <i>Advances in Dynamics, Optimization and Computation</i>, O. Junge, O. Schütze, G. Froyland, S. Ober-Blöbaum, and K. Padberg-Gehle, Eds. Cham: Springer International Publishing, 2020, pp. 209–237.","chicago":"Flaßkamp, K., Sina Ober-Blöbaum, and S.  Peitz. “Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach.” In <i>Advances in Dynamics, Optimization and Computation</i>, edited by Oliver Junge, Oliver Schütze, Gary Froyland, Sina Ober-Blöbaum, and Kathrin Padberg-Gehle, 209–37. Cham: Springer International Publishing, 2020.","apa":"Flaßkamp, K., Ober-Blöbaum, S., &#38; Peitz, S. (2020). Symmetry in optimal control: A multiobjective model predictive control approach. In O. Junge, O. Schütze, G. Froyland, S. Ober-Blöbaum, &#38; K. Padberg-Gehle (Eds.), <i>Advances in Dynamics, Optimization and Computation</i> (pp. 209–237). Springer International Publishing.","short":"K. Flaßkamp, S. Ober-Blöbaum, S. Peitz, in: O. Junge, O. Schütze, G. Froyland, S. Ober-Blöbaum, K. Padberg-Gehle (Eds.), Advances in Dynamics, Optimization and Computation, Springer International Publishing, Cham, 2020, pp. 209–237.","bibtex":"@inbook{Flaßkamp_Ober-Blöbaum_Peitz_2020, place={Cham}, title={Symmetry in optimal control: A multiobjective model predictive control approach}, booktitle={Advances in Dynamics, Optimization and Computation}, publisher={Springer International Publishing}, author={Flaßkamp, K. and Ober-Blöbaum, Sina and Peitz, S. }, editor={Junge, Oliver and Schütze, Oliver and Froyland, Gary and Ober-Blöbaum, Sina and Padberg-Gehle, Kathrin}, year={2020}, pages={209–237} }","mla":"Flaßkamp, K., et al. “Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach.” <i>Advances in Dynamics, Optimization and Computation</i>, edited by Oliver Junge et al., Springer International Publishing, 2020, pp. 209–37."},"place":"Cham","year":"2020","date_created":"2022-01-18T12:58:18Z","author":[{"first_name":"K.","last_name":"Flaßkamp","full_name":"Flaßkamp, K."},{"first_name":"Sina","id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum"},{"last_name":"Peitz","full_name":"Peitz, S. ","first_name":"S. "}],"publisher":"Springer International Publishing","date_updated":"2023-11-08T08:15:14Z","title":"Symmetry in optimal control: A multiobjective model predictive control approach","publication":"Advances in Dynamics, Optimization and Computation","type":"book_chapter","status":"public","editor":[{"first_name":"Oliver","full_name":"Junge, Oliver","last_name":"Junge"},{"last_name":"Schütze","full_name":"Schütze, Oliver","first_name":"Oliver"},{"first_name":"Gary","full_name":"Froyland, Gary","last_name":"Froyland"},{"first_name":"Sina","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum"},{"full_name":"Padberg-Gehle, Kathrin","last_name":"Padberg-Gehle","first_name":"Kathrin"}],"department":[{"_id":"636"}],"user_id":"15694","_id":"29413","language":[{"iso":"eng"}]},{"user_id":"15694","_id":"19993","language":[{"iso":"eng"}],"type":"journal_article","publication":"MCSS","status":"public","author":[{"last_name":"Flaßkamp","full_name":"Flaßkamp, Kathrin","first_name":"Kathrin"},{"id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"},{"first_name":"Karl","last_name":"Worthmann","full_name":"Worthmann, Karl"}],"date_created":"2020-10-13T18:37:24Z","volume":31,"date_updated":"2022-01-21T10:14:19Z","title":"Symmetry and motion primitives in model predictive control","citation":{"apa":"Flaßkamp, K., Ober-Blöbaum, S., &#38; Worthmann, K. (2019). Symmetry and motion primitives in model predictive control. <i>MCSS</i>, <i>31</i>, 455–485.","short":"K. Flaßkamp, S. Ober-Blöbaum, K. Worthmann, MCSS 31 (2019) 455–485.","bibtex":"@article{Flaßkamp_Ober-Blöbaum_Worthmann_2019, title={Symmetry and motion primitives in model predictive control}, volume={31}, journal={MCSS}, author={Flaßkamp, Kathrin and Ober-Blöbaum, Sina and Worthmann, Karl}, year={2019}, pages={455–485} }","mla":"Flaßkamp, Kathrin, et al. “Symmetry and Motion Primitives in Model Predictive Control.” <i>MCSS</i>, vol. 31, 2019, pp. 455–85.","ama":"Flaßkamp K, Ober-Blöbaum S, Worthmann K. Symmetry and motion primitives in model predictive control. <i>MCSS</i>. 2019;31:455-485.","ieee":"K. Flaßkamp, S. Ober-Blöbaum, and K. Worthmann, “Symmetry and motion primitives in model predictive control,” <i>MCSS</i>, vol. 31, pp. 455–485, 2019.","chicago":"Flaßkamp, Kathrin, Sina Ober-Blöbaum, and Karl Worthmann. “Symmetry and Motion Primitives in Model Predictive Control.” <i>MCSS</i> 31 (2019): 455–85."},"page":"455-485","intvolume":"        31","year":"2019"},{"year":"2019","page":"490-495","corporate_editor":["IFAC-PapersOnLine"],"citation":{"ieee":"T. Faulwasser, K. Flaßkamp, S. Ober-Blöbaum, and K. Worthmann, “Towards velocity turnpikes in optimal control of mechanical systems,” 2019, vol. 52(16), pp. 490–495.","chicago":"Faulwasser, Tim, K. Flaßkamp, Sina Ober-Blöbaum, and Karl Worthmann. “Towards Velocity Turnpikes in Optimal Control of Mechanical Systems.” edited by IFAC-PapersOnLine, 52(16):490–95, 2019.","ama":"Faulwasser T, Flaßkamp K, Ober-Blöbaum S, Worthmann K. Towards velocity turnpikes in optimal control of mechanical systems. In: IFAC-PapersOnLine, ed. Vol 52(16). ; 2019:490-495.","apa":"Faulwasser, T., Flaßkamp, K., Ober-Blöbaum, S., &#38; Worthmann, K. (2019). <i>Towards velocity turnpikes in optimal control of mechanical systems: Vol. 52(16)</i> (IFAC-PapersOnLine, Ed.; pp. 490–495).","bibtex":"@inproceedings{Faulwasser_Flaßkamp_Ober-Blöbaum_Worthmann_2019, title={Towards velocity turnpikes in optimal control of mechanical systems}, volume={52(16)}, author={Faulwasser, Tim and Flaßkamp, K. and Ober-Blöbaum, Sina and Worthmann, Karl}, editor={IFAC-PapersOnLine}, year={2019}, pages={490–495} }","short":"T. Faulwasser, K. Flaßkamp, S. Ober-Blöbaum, K. Worthmann, in: IFAC-PapersOnLine (Ed.), 2019, pp. 490–495.","mla":"Faulwasser, Tim, et al. <i>Towards Velocity Turnpikes in Optimal Control of Mechanical Systems</i>. Edited by IFAC-PapersOnLine, vol. 52(16), 2019, pp. 490–95."},"date_updated":"2023-11-08T08:09:01Z","volume":"52(16)","date_created":"2022-02-17T07:23:52Z","author":[{"first_name":"Tim","full_name":"Faulwasser, Tim","last_name":"Faulwasser"},{"first_name":"K.","full_name":"Flaßkamp, K.","last_name":"Flaßkamp"},{"first_name":"Sina","last_name":"Ober-Blöbaum","id":"16494","full_name":"Ober-Blöbaum, Sina"},{"last_name":"Worthmann","full_name":"Worthmann, Karl","first_name":"Karl"}],"title":"Towards velocity turnpikes in optimal control of mechanical systems","type":"conference","status":"public","_id":"29867","department":[{"_id":"636"}],"user_id":"15694","language":[{"iso":"eng"}]},{"language":[{"iso":"eng"}],"user_id":"15694","department":[{"_id":"101"}],"project":[{"_id":"52","name":"Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"_id":"8753","status":"public","abstract":[{"text":"In a wide range of applications it is desirable to optimally control a dynamical system with respect to concurrent, potentially competing goals. This gives rise to a multiobjective optimal control problem where, instead of computing a single optimal solution, the set of optimal compromises, the so-called Pareto set, has to be approximated. When the problem under consideration is described by a partial differential equation (PDE), as is the case for fluid flow, the computational cost rapidly increases and makes its direct treatment infeasible. Reduced order modeling is a very popular method to reduce the computational cost, in particular in a multi query context such as uncertainty quantification, parameter estimation or optimization. In this article, we show how to combine reduced order modeling and multiobjective optimal control techniques in order to efficiently solve multiobjective optimal control problems constrained by PDEs. We consider a global, derivative free optimization method as well as a local, gradient-based approach for which the optimality system is derived in two different ways. The methods are compared with regard to the solution quality as well as the computational effort and they are illustrated using the example of the flow around a cylinder and a backward-facing-step channel flow.","lang":"eng"}],"type":"journal_article","publication":"Acta Applicandae Mathematicae","doi":"10.1007/s10440-018-0209-7","title":"Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling","date_created":"2019-03-29T13:30:41Z","author":[{"first_name":"Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X","last_name":"Peitz","id":"47427","full_name":"Peitz, Sebastian"},{"id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"},{"first_name":"Michael","last_name":"Dellnitz","full_name":"Dellnitz, Michael"}],"volume":161,"date_updated":"2022-01-21T10:01:41Z","citation":{"ama":"Peitz S, Ober-Blöbaum S, Dellnitz M. Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling. <i>Acta Applicandae Mathematicae</i>. 2018;161(1):171–199. doi:<a href=\"https://doi.org/10.1007/s10440-018-0209-7\">10.1007/s10440-018-0209-7</a>","chicago":"Peitz, Sebastian, Sina Ober-Blöbaum, and Michael Dellnitz. “Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling.” <i>Acta Applicandae Mathematicae</i> 161, no. 1 (2018): 171–199. <a href=\"https://doi.org/10.1007/s10440-018-0209-7\">https://doi.org/10.1007/s10440-018-0209-7</a>.","ieee":"S. Peitz, S. Ober-Blöbaum, and M. Dellnitz, “Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling,” <i>Acta Applicandae Mathematicae</i>, vol. 161, no. 1, pp. 171–199, 2018, doi: <a href=\"https://doi.org/10.1007/s10440-018-0209-7\">10.1007/s10440-018-0209-7</a>.","short":"S. Peitz, S. Ober-Blöbaum, M. Dellnitz, Acta Applicandae Mathematicae 161 (2018) 171–199.","mla":"Peitz, Sebastian, et al. “Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling.” <i>Acta Applicandae Mathematicae</i>, vol. 161, no. 1, 2018, pp. 171–199, doi:<a href=\"https://doi.org/10.1007/s10440-018-0209-7\">10.1007/s10440-018-0209-7</a>.","bibtex":"@article{Peitz_Ober-Blöbaum_Dellnitz_2018, title={Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling}, volume={161}, DOI={<a href=\"https://doi.org/10.1007/s10440-018-0209-7\">10.1007/s10440-018-0209-7</a>}, number={1}, journal={Acta Applicandae Mathematicae}, author={Peitz, Sebastian and Ober-Blöbaum, Sina and Dellnitz, Michael}, year={2018}, pages={171–199} }","apa":"Peitz, S., Ober-Blöbaum, S., &#38; Dellnitz, M. (2018). Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling. <i>Acta Applicandae Mathematicae</i>, <i>161</i>(1), 171–199. <a href=\"https://doi.org/10.1007/s10440-018-0209-7\">https://doi.org/10.1007/s10440-018-0209-7</a>"},"page":"171–199","intvolume":"       161","year":"2018","issue":"1","publication_status":"published","publication_identifier":{"issn":["0167-8019","1572-9036"]}}]