[{"type":"journal_article","department":[{"_id":"636"}],"date_created":"2022-03-24T12:26:10Z","publication":"AIMS","citation":{"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.","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.","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} }","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.","short":"J. Cresson, F. Jiménez, S. Ober-Blöbaum, AIMS 14(1) (2022) 57–89.","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."},"user_id":"15694","volume":"14(1)","page":"57-89","_id":"30490","language":[{"iso":"eng"}],"date_updated":"2022-03-24T12:26:32Z","year":"2022","status":"public","title":"Continuous and discrete Noether's fractional conserved quantities for restricted calculus of variations","author":[{"full_name":"Cresson, Jacky","first_name":"Jacky","last_name":"Cresson"},{"last_name":"Jiménez","first_name":"Fernando","full_name":"Jiménez, Fernando"},{"last_name":"Ober-Blöbaum","first_name":"Sina","full_name":"Ober-Blöbaum, Sina","id":"16494"}]},{"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":[{"lang":"eng","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>"}],"publication":"Journal of Optimization Theory and Applications","citation":{"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>.","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>","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>.","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>.","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} }","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>"},"user_id":"87909","doi":"10.1007/s10957-022-02023-0","_id":"30861","publisher":"Springer Science and Business Media LLC","language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2022-04-08T18:23:02Z","status":"public","title":"Turnpike Property in Optimal Microbial Metabolite Production","year":"2022","publication_identifier":{"issn":["0022-3239","1573-2878"]},"author":[{"full_name":"Caillau, Jean-Baptiste","first_name":"Jean-Baptiste","last_name":"Caillau"},{"full_name":"Djema, Walid","last_name":"Djema","first_name":"Walid"},{"last_name":"Gouzé","first_name":"Jean-Luc","full_name":"Gouzé, Jean-Luc"},{"id":"87909","last_name":"Maslovskaya","first_name":"Sofya","full_name":"Maslovskaya, Sofya"},{"full_name":"Pomet, Jean-Baptiste","last_name":"Pomet","first_name":"Jean-Baptiste"}]},{"citation":{"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} }","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.","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.","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."},"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."}],"date_created":"2022-03-31T11:14:13Z","type":"conference","department":[{"_id":"636"}],"year":"2022","status":"public","title":"Verification of safety critical control policies using kernel methods","conference":{"end_date":"2022-07-15","name":"2022 European Control Conference (ECC)","start_date":"2022-07-12","location":"London"},"author":[{"last_name":"Vertovec","first_name":"Nikolaus","full_name":"Vertovec, Nikolaus","id":"93930"},{"full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina","id":"16494"},{"last_name":"Margellos","first_name":"Kostas","full_name":"Margellos, Kostas"}],"date_updated":"2023-11-29T10:00:18Z","has_accepted_license":"1","page":"1870-1875","_id":"30733","language":[{"iso":"eng"}],"ddc":["510"],"user_id":"15694"},{"date_created":"2023-05-08T09:04:06Z","department":[{"_id":"636"}],"type":"journal_article","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.","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.","short":"T. Faulwasser, K. Flaßkamp, S. Ober-Blöbaum, M. Schaller, K. Worthmann, Mathematics of Control, Signals, and Systems 34 (2022) 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.","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.","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} }"},"publication":"Mathematics of Control, Signals, and Systems","language":[{"iso":"eng"}],"_id":"44624","publisher":"Springer","page":"759-788","volume":34,"user_id":"15694","author":[{"full_name":"Faulwasser, Timm","first_name":"Timm","last_name":"Faulwasser"},{"first_name":"Kathrin","last_name":"Flaßkamp","full_name":"Flaßkamp, Kathrin"},{"id":"16494","first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina"},{"last_name":"Schaller","first_name":"Manuel","full_name":"Schaller, Manuel"},{"last_name":"Worthmann","first_name":"Karl","full_name":"Worthmann, Karl"}],"year":"2022","status":"public","title":"Manifold turnpikes, trims, and symmetries","intvolume":"        34","date_updated":"2023-05-08T09:04:26Z"},{"doi":"10.3934/jgm.2022014","language":[{"iso":"eng"}],"intvolume":"        14","article_type":"original","date_updated":"2023-08-10T08:44:55Z","publication_status":"published","author":[{"first_name":"Robert I","last_name":"McLachlan","full_name":"McLachlan, Robert I"},{"id":"85279","orcid":"https://orcid.org/0000-0002-5940-8057","last_name":"Offen","first_name":"Christian","full_name":"Offen, Christian"}],"year":"2022","title":"Backward error analysis for variational discretisations of partial  differential equations","department":[{"_id":"636"}],"type":"journal_article","date_created":"2020-10-06T16:33:19Z","file":[{"title":"Backward error analysis for variational discretisations of PDEs","file_id":"31859","content_type":"application/pdf","relation":"main_file","date_updated":"2022-06-13T09:11:38Z","file_name":"2_BlendedBEASymmPDE.pdf","access_level":"open_access","file_size":1507248,"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.","date_created":"2022-06-13T09:11:38Z","creator":"coffen"}],"abstract":[{"lang":"eng","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."}],"related_material":{"link":[{"url":"https://github.com/Christian-Offen/multisymplectic","relation":"software"}]},"issue":"3","publication":"Journal of Geometric Mechanics","volume":14,"ddc":["510"],"user_id":"85279","publisher":"AIMS","_id":"19941","page":"447 - 471","has_accepted_license":"1","status":"public","oa":"1","external_id":{"arxiv":["2006.14172"]},"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>."},"file_date_updated":"2022-06-13T09:11:38Z"},{"has_accepted_license":"1","status":"public","volume":"32(1)","ddc":["510"],"user_id":"85279","_id":"23382","publisher":"AIP","quality_controlled":"1","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>.","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>","short":"C. Offen, S. Ober-Blöbaum, Chaos: An Interdisciplinary Journal of Nonlinear Science 32(1) (2022).","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} }"},"file_date_updated":"2021-12-13T14:56:15Z","oa":"1","external_id":{"arxiv":["2108.02492"]},"article_type":"original","date_updated":"2023-08-10T08:48:14Z","publication_status":"published","author":[{"id":"85279","full_name":"Offen, Christian","orcid":"0000-0002-5940-8057","first_name":"Christian","last_name":"Offen"},{"full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina","id":"16494"}],"title":"Symplectic integration of learned Hamiltonian systems","year":"2022","doi":"10.1063/5.0065913","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://aip.scitation.org/doi/abs/10.1063/5.0065913"}],"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."}],"related_material":{"link":[{"description":"GitHub","url":"https://github.com/Christian-Offen/symplectic-shadow-integration","relation":"software"}]},"publication":"Chaos: An Interdisciplinary Journal of Nonlinear Science","department":[{"_id":"636"}],"type":"journal_article","date_created":"2021-08-11T08:24:02Z","file":[{"date_created":"2021-12-13T14:56:15Z","creator":"coffen","file_id":"28734","content_type":"application/pdf","relation":"main_file","date_updated":"2021-12-13T14:56:15Z","file_name":"SymplecticShadowIntegration_AIP.pdf","file_size":2285059,"access_level":"open_access"}]},{"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","_id":"29421","language":[{"iso":"eng"}],"page":"327-333","volume":"54(19)","user_id":"15694","author":[{"first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","id":"16494"},{"last_name":"Vermeeren","first_name":"M.","full_name":"Vermeeren, M."}],"corporate_editor":["IFAC-PapersOnLine"],"year":"2021","status":"public","title":"Superconvergence of galerkin variational integrators","date_updated":"2022-01-21T13:36:53Z"},{"doi":"10.1016/j.automatica.2021.109804","article_number":"109804","language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2022-01-26T13:15:33Z","intvolume":"       132","title":"Turnpike features in optimal selection of species represented by quota models","year":"2021","publication_identifier":{"issn":["0005-1098"]},"author":[{"full_name":"Djema, Walid","first_name":"Walid","last_name":"Djema"},{"last_name":"Giraldi","first_name":"Laetitia","full_name":"Giraldi, Laetitia"},{"full_name":"Maslovskaya, Sofya","first_name":"Sofya","last_name":"Maslovskaya","id":"87909"},{"last_name":"Bernard","first_name":"Olivier","full_name":"Bernard, Olivier"}],"type":"journal_article","keyword":["Electrical and Electronic Engineering","Control and Systems Engineering"],"department":[{"_id":"636"}],"date_created":"2022-01-26T13:13:06Z","publication":"Automatica","user_id":"87909","volume":132,"_id":"29543","publisher":"Elsevier BV","status":"public","citation":{"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>.","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} }"}},{"date_created":"2021-07-29T09:38:32Z","file":[{"content_type":"application/pdf","file_id":"22895","date_updated":"2021-07-29T09:37:49Z","relation":"main_file","file_size":3125220,"access_level":"open_access","file_name":"ifacconf.pdf","date_created":"2021-07-29T09:37:49Z","creator":"coffen"}],"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","url":"https://doi.org/10.5281/zenodo.4562664","relation":"software"}]},"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","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","last_name":"Ober-Blöbaum","first_name":"Sina"}],"publication_identifier":{"issn":["2405-8963"]},"year":"2021","title":"Bifurcation preserving discretisations of optimal control problems","date_updated":"2023-11-29T10:19:41Z","publication_status":"published","external_id":{"arxiv":["2107.13853"]},"oa":"1","citation":{"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>.","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>","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>","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>.","short":"C. Offen, S. Ober-Blöbaum, 54(19) (2021) 334–339."},"file_date_updated":"2021-07-29T09:37:49Z","quality_controlled":"1","_id":"22894","page":"334-339","volume":"54(19)","ddc":["510"],"user_id":"15694","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"},{"publisher":"IEEE","_id":"21572","page":"2896","user_id":"15694","conference":{"name":"60th IEEE Conference on Decision and Control (CDC)","start_date":"2021-12-14","location":"Austin, TX, USA","end_date":"2021-12-17"},"status":"public","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","author":[{"full_name":"Ridderbusch, Steffen","first_name":"Steffen","last_name":"Ridderbusch"},{"last_name":"Offen","orcid":"0000-0002-5940-8057","first_name":"Christian","full_name":"Offen, Christian","id":"85279"},{"id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"},{"full_name":"Goulart, Paul","last_name":"Goulart","first_name":"Paul"}],"publication_identifier":{"eisbn":["978-1-6654-3659-5"]},"year":"2021","title":"Learning ODE Models with Qualitative Structure Using Gaussian Processes ","date_updated":"2023-11-29T10:24:55Z","publication_status":"published","date_created":"2021-03-30T10:27:44Z","department":[{"_id":"636"}],"type":"conference","publication":"2021 60th IEEE Conference on Decision and Control (CDC)","related_material":{"link":[{"relation":"software","url":"https://github.com/Crown421/StructureGPs-paper","description":"GitHub"}]}},{"user_id":"15694","page":"1975-1980","language":[{"iso":"eng"}],"_id":"21592","publication_status":"accepted","date_updated":"2023-11-29T10:26:49Z","status":"public","title":"Multi-objective minimum time optimal control for low-thrust trajectory design","year":"2021","author":[{"id":"87056","full_name":"Vertovec, Nikolaus","first_name":"Nikolaus","last_name":"Vertovec"},{"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":{"end_date":"2021-07-02","start_date":"2021-06-29","name":"2021 European Control Conference (ECC)","location":"Rotterdam, the Netherlands"},"type":"conference","department":[{"_id":"636"}],"external_id":{"arxiv":["2103.08813"]},"date_created":"2021-04-03T03:00:35Z","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."}],"citation":{"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.","mla":"Vertovec, Nikolaus, et al. <i>Multi-Objective Minimum Time Optimal Control for Low-Thrust Trajectory Design</i>. pp. 1975–80.","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.","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} }","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."}},{"user_id":"15694","volume":46,"_id":"29868","language":[{"iso":"eng"}],"series_title":"J Nonlinear Sci ","date_updated":"2023-11-29T10:23:46Z","intvolume":"        46","status":"public","title":"Fractional Damping Through Restricted Calculus of Variations","year":"2021","author":[{"first_name":"F.","last_name":"Jiménez","full_name":"Jiménez, F."},{"id":"16494","full_name":"Ober-Blöbaum, Sina","first_name":"Sina","last_name":"Ober-Blöbaum"}],"type":"conference","department":[{"_id":"636"}],"date_created":"2022-02-17T07:28:47Z","publication":"Nichtlineare Sci 31","citation":{"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 } }","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.","mla":"Jiménez, F., and Sina Ober-Blöbaum. “Fractional Damping Through Restricted Calculus of Variations.” <i>Nichtlineare Sci 31</i>, vol. 46, 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.","short":"F. Jiménez, S. Ober-Blöbaum, in: Nichtlineare Sci 31, 2021.","ieee":"F. Jiménez and S. Ober-Blöbaum, “Fractional Damping Through Restricted Calculus of Variations,” in <i>Nichtlineare Sci 31</i>, 2021, vol. 46.","apa":"Jiménez, F., &#38; Ober-Blöbaum, S. (2021). Fractional Damping Through Restricted Calculus of Variations. <i>Nichtlineare Sci 31</i>, <i>46</i>."}},{"doi":"10.1007/s10208-020-09454-z","main_file_link":[{"url":"https://rdcu.be/b79aB"}],"language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2022-01-06T06:54:14Z","article_type":"original","intvolume":"        20","year":"2020","title":"Preservation of Bifurcations of Hamiltonian Boundary Value Problems Under Discretisation","author":[{"first_name":"Robert I","last_name":"McLachlan","full_name":"McLachlan, Robert I"},{"orcid":"https://orcid.org/0000-0002-5940-8057","last_name":"Offen","first_name":"Christian","full_name":"Offen, Christian","id":"85279"}],"type":"journal_article","department":[{"_id":"636"}],"date_created":"2020-10-06T16:31:46Z","extern":"1","abstract":[{"lang":"eng","text":"We show that symplectic integrators preserve bifurcations of Hamiltonian boundary value problems and that nonsymplectic integrators do not. We provide a universal description of the breaking of umbilic bifurcations by nonysmplectic integrators. We discover extra structure induced from certain types of boundary value problems, including classical Dirichlet problems, that is useful to locate bifurcations. Geodesics connecting two points are an example of a Hamiltonian boundary value problem, and we introduce the jet-RATTLE method, a symplectic integrator that easily computes geodesics and their bifurcations. Finally, we study the periodic pitchfork bifurcation, a codimension-1 bifurcation arising in integrable Hamiltonian systems. It is not preserved by either symplectic on nonsymplectic integrators, but in some circumstances symplecticity greatly reduces the error. "}],"publication":"Foundations of Computational Mathematics","issue":"6","user_id":"85279","volume":20,"page":"1363-1400","_id":"19938","status":"public","citation":{"apa":"McLachlan, R. I., &#38; Offen, C. (2020). Preservation of Bifurcations of Hamiltonian Boundary Value Problems Under Discretisation. <i>Foundations of Computational Mathematics</i>, <i>20</i>(6), 1363–1400. <a href=\"https://doi.org/10.1007/s10208-020-09454-z\">https://doi.org/10.1007/s10208-020-09454-z</a>","ieee":"R. I. McLachlan and C. Offen, “Preservation of Bifurcations of Hamiltonian Boundary Value Problems Under Discretisation,” <i>Foundations of Computational Mathematics</i>, vol. 20, no. 6, pp. 1363–1400, 2020.","short":"R.I. McLachlan, C. Offen, Foundations of Computational Mathematics 20 (2020) 1363–1400.","chicago":"McLachlan, Robert I, and Christian Offen. “Preservation of Bifurcations of Hamiltonian Boundary Value Problems Under Discretisation.” <i>Foundations of Computational Mathematics</i> 20, no. 6 (2020): 1363–1400. <a href=\"https://doi.org/10.1007/s10208-020-09454-z\">https://doi.org/10.1007/s10208-020-09454-z</a>.","mla":"McLachlan, Robert I., and Christian Offen. “Preservation of Bifurcations of Hamiltonian Boundary Value Problems Under Discretisation.” <i>Foundations of Computational Mathematics</i>, vol. 20, no. 6, 2020, pp. 1363–400, doi:<a href=\"https://doi.org/10.1007/s10208-020-09454-z\">10.1007/s10208-020-09454-z</a>.","ama":"McLachlan RI, Offen C. Preservation of Bifurcations of Hamiltonian Boundary Value Problems Under Discretisation. <i>Foundations of Computational Mathematics</i>. 2020;20(6):1363-1400. doi:<a href=\"https://doi.org/10.1007/s10208-020-09454-z\">10.1007/s10208-020-09454-z</a>","bibtex":"@article{McLachlan_Offen_2020, title={Preservation of Bifurcations of Hamiltonian Boundary Value Problems Under Discretisation}, volume={20}, DOI={<a href=\"https://doi.org/10.1007/s10208-020-09454-z\">10.1007/s10208-020-09454-z</a>}, number={6}, journal={Foundations of Computational Mathematics}, author={McLachlan, Robert I and Offen, Christian}, year={2020}, pages={1363–1400} }"}},{"citation":{"mla":"Kreusser, Lisa Maria, et al. “Detection of High Codimensional Bifurcations in Variational PDEs.” <i>Nonlinearity</i>, vol. 33, no. 5, 2020, pp. 2335–63, doi:<a href=\"https://doi.org/10.1088/1361-6544/ab7293\">10.1088/1361-6544/ab7293</a>.","bibtex":"@article{Kreusser_McLachlan_Offen_2020, title={Detection of high codimensional bifurcations in variational PDEs}, volume={33}, DOI={<a href=\"https://doi.org/10.1088/1361-6544/ab7293\">10.1088/1361-6544/ab7293</a>}, number={5}, journal={Nonlinearity}, author={Kreusser, Lisa Maria and McLachlan, Robert I and Offen, Christian}, year={2020}, pages={2335–2363} }","ama":"Kreusser LM, McLachlan RI, Offen C. Detection of high codimensional bifurcations in variational PDEs. <i>Nonlinearity</i>. 2020;33(5):2335-2363. doi:<a href=\"https://doi.org/10.1088/1361-6544/ab7293\">10.1088/1361-6544/ab7293</a>","ieee":"L. M. Kreusser, R. I. McLachlan, and C. Offen, “Detection of high codimensional bifurcations in variational PDEs,” <i>Nonlinearity</i>, vol. 33, no. 5, pp. 2335–2363, 2020.","apa":"Kreusser, L. M., McLachlan, R. I., &#38; Offen, C. (2020). Detection of high codimensional bifurcations in variational PDEs. <i>Nonlinearity</i>, <i>33</i>(5), 2335–2363. <a href=\"https://doi.org/10.1088/1361-6544/ab7293\">https://doi.org/10.1088/1361-6544/ab7293</a>","short":"L.M. Kreusser, R.I. McLachlan, C. Offen, Nonlinearity 33 (2020) 2335–2363.","chicago":"Kreusser, Lisa Maria, Robert I McLachlan, and Christian Offen. “Detection of High Codimensional Bifurcations in Variational PDEs.” <i>Nonlinearity</i> 33, no. 5 (2020): 2335–63. <a href=\"https://doi.org/10.1088/1361-6544/ab7293\">https://doi.org/10.1088/1361-6544/ab7293</a>."},"oa":"1","status":"public","page":"2335-2363","_id":"19939","user_id":"85279","volume":33,"issue":"5","publication":"Nonlinearity","extern":"1","date_created":"2020-10-06T16:32:04Z","type":"journal_article","department":[{"_id":"636"}],"title":"Detection of high codimensional bifurcations in variational PDEs","year":"2020","author":[{"full_name":"Kreusser, Lisa Maria","last_name":"Kreusser","first_name":"Lisa Maria"},{"first_name":"Robert I","last_name":"McLachlan","full_name":"McLachlan, Robert I"},{"last_name":"Offen","first_name":"Christian","orcid":"https://orcid.org/0000-0002-5940-8057","full_name":"Offen, Christian","id":"85279"}],"publication_identifier":{"issn":["0951-7715","1361-6544"]},"date_updated":"2022-01-06T06:54:14Z","publication_status":"published","intvolume":"        33","article_type":"original","main_file_link":[{"url":"https://doi.org/10.1088/1361-6544/ab7293","open_access":"1"}],"language":[{"iso":"eng"}],"doi":"10.1088/1361-6544/ab7293"},{"date_updated":"2022-01-21T08:26:46Z","title":"Variational integrators for dissipative systems","year":"2020","status":"public","author":[{"full_name":"Limebeer, D. J. N.","first_name":"D. J. N.","last_name":"Limebeer"},{"full_name":"Ober-Blöbaum, Sina","first_name":"Sina","last_name":"Ober-Blöbaum","id":"16494"},{"first_name":"F. H.","last_name":"Farshi","full_name":"Farshi, F. H."}],"user_id":"15694","volume":"65(4)","page":"1381-1396","language":[{"iso":"eng"}],"_id":"29399","publication":"IEEE Transactions on Automatic Control","citation":{"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.","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.","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} }","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.","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.","short":"D.J.N. Limebeer, S. Ober-Blöbaum, F.H. Farshi, IEEE Transactions on Automatic Control 65(4) (2020) 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."},"type":"journal_article","department":[{"_id":"636"}],"date_created":"2022-01-18T11:17:25Z"},{"type":"journal_article","department":[{"_id":"636"}],"date_created":"2022-01-18T11:08:28Z","publication":"Mathematics","citation":{"ama":"Hernández Castellanos CIO, Schütze G, Sun J-Q, Ober-Blöbaum S, Morales-Luna G. Numerical computation of lightly multi-objective robust optimal solutions by means of generalized cell mapping. <i>Mathematics</i>. 2020;8(11):1959.","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. 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