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Margellos, in: n.d., pp. 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} }"},"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"}],"date_created":"2021-04-03T03:00:35Z","external_id":{"arxiv":["2103.08813"]},"department":[{"_id":"636"}],"type":"conference","author":[{"id":"87056","last_name":"Vertovec","first_name":"Nikolaus","full_name":"Vertovec, Nikolaus"},{"id":"16494","first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina"},{"full_name":"Margellos, Kostas","last_name":"Margellos","first_name":"Kostas"}],"conference":{"end_date":"2021-07-02","location":"Rotterdam, the Netherlands","name":"2021 European Control Conference (ECC)","start_date":"2021-06-29"},"status":"public","title":"Multi-objective minimum time optimal control for low-thrust trajectory design","year":"2021","publication_status":"accepted","date_updated":"2023-11-29T10:26:49Z","language":[{"iso":"eng"}],"_id":"21592","page":"1975-1980","user_id":"15694"},{"publication":"Nichtlineare Sci 31","citation":{"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>.","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."},"type":"conference","department":[{"_id":"636"}],"date_created":"2022-02-17T07:28:47Z","date_updated":"2023-11-29T10:23:46Z","intvolume":"        46","title":"Fractional Damping Through Restricted Calculus of Variations","status":"public","year":"2021","author":[{"last_name":"Jiménez","first_name":"F.","full_name":"Jiménez, F."},{"full_name":"Ober-Blöbaum, Sina","first_name":"Sina","last_name":"Ober-Blöbaum","id":"16494"}],"user_id":"15694","volume":46,"language":[{"iso":"eng"}],"_id":"29868","series_title":"J Nonlinear Sci "},{"intvolume":"        20","article_type":"original","date_updated":"2022-01-06T06:54:14Z","publication_status":"published","author":[{"full_name":"McLachlan, Robert I","last_name":"McLachlan","first_name":"Robert I"},{"id":"85279","full_name":"Offen, Christian","orcid":"https://orcid.org/0000-0002-5940-8057","last_name":"Offen","first_name":"Christian"}],"title":"Preservation of Bifurcations of Hamiltonian Boundary Value Problems Under Discretisation","year":"2020","doi":"10.1007/s10208-020-09454-z","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://rdcu.be/b79aB"}],"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. 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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.","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>.","short":"R.I. McLachlan, C. Offen, Foundations of Computational Mathematics 20 (2020) 1363–1400.","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} }"}},{"oa":"1","citation":{"short":"L.M. Kreusser, R.I. McLachlan, C. 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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>","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>."},"user_id":"85279","volume":33,"page":"2335-2363","_id":"19939","status":"public","type":"journal_article","department":[{"_id":"636"}],"date_created":"2020-10-06T16:32:04Z","extern":"1","issue":"5","publication":"Nonlinearity","doi":"10.1088/1361-6544/ab7293","main_file_link":[{"url":"https://doi.org/10.1088/1361-6544/ab7293","open_access":"1"}],"language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2022-01-06T06:54:14Z","article_type":"original","intvolume":"        33","year":"2020","title":"Detection of high codimensional bifurcations in variational PDEs","author":[{"full_name":"Kreusser, Lisa Maria","first_name":"Lisa Maria","last_name":"Kreusser"},{"full_name":"McLachlan, Robert I","last_name":"McLachlan","first_name":"Robert I"},{"full_name":"Offen, Christian","first_name":"Christian","last_name":"Offen","orcid":"https://orcid.org/0000-0002-5940-8057","id":"85279"}],"publication_identifier":{"issn":["0951-7715","1361-6544"]}},{"type":"journal_article","department":[{"_id":"636"}],"date_created":"2022-01-18T11:17:25Z","publication":"IEEE Transactions on Automatic Control","citation":{"ama":"Limebeer DJN, Ober-Blöbaum S, Farshi FH. 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Ober-Blöbaum, “Modelling of the convection-diffusion equation through fractional restricted calculus of variations,” 2020."},"type":"conference","department":[{"_id":"636"}],"date_created":"2022-01-18T14:45:22Z"},{"citation":{"ieee":"F. Jean, S. Maslovskaya, and I. Zelenko, “On Weyl’s type theorems and genericity of projective rigidity in sub-Riemannian geometry,” <i>Geometriae Dedicata</i>, vol. 213, no. 1, pp. 295–314, 2020, doi: <a href=\"https://doi.org/10.1007/s10711-020-00581-z\">10.1007/s10711-020-00581-z</a>.","apa":"Jean, F., Maslovskaya, S., &#38; Zelenko, I. (2020). On Weyl’s type theorems and genericity of projective rigidity in sub-Riemannian geometry. <i>Geometriae Dedicata</i>, <i>213</i>(1), 295–314. <a href=\"https://doi.org/10.1007/s10711-020-00581-z\">https://doi.org/10.1007/s10711-020-00581-z</a>","short":"F. Jean, S. Maslovskaya, I. Zelenko, Geometriae Dedicata 213 (2020) 295–314.","chicago":"Jean, Frédéric, Sofya Maslovskaya, and Igor Zelenko. “On Weyl’s Type Theorems and Genericity of Projective Rigidity in Sub-Riemannian Geometry.” <i>Geometriae Dedicata</i> 213, no. 1 (2020): 295–314. <a href=\"https://doi.org/10.1007/s10711-020-00581-z\">https://doi.org/10.1007/s10711-020-00581-z</a>.","mla":"Jean, Frédéric, et al. “On Weyl’s Type Theorems and Genericity of Projective Rigidity in Sub-Riemannian Geometry.” <i>Geometriae Dedicata</i>, vol. 213, no. 1, Springer Science and Business Media LLC, 2020, pp. 295–314, doi:<a href=\"https://doi.org/10.1007/s10711-020-00581-z\">10.1007/s10711-020-00581-z</a>.","bibtex":"@article{Jean_Maslovskaya_Zelenko_2020, title={On Weyl’s type theorems and genericity of projective rigidity in sub-Riemannian geometry}, volume={213}, DOI={<a href=\"https://doi.org/10.1007/s10711-020-00581-z\">10.1007/s10711-020-00581-z</a>}, number={1}, journal={Geometriae Dedicata}, publisher={Springer Science and Business Media LLC}, author={Jean, Frédéric and Maslovskaya, Sofya and Zelenko, Igor}, year={2020}, pages={295–314} }","ama":"Jean F, Maslovskaya S, Zelenko I. On Weyl’s type theorems and genericity of projective rigidity in sub-Riemannian geometry. <i>Geometriae Dedicata</i>. 2020;213(1):295-314. doi:<a href=\"https://doi.org/10.1007/s10711-020-00581-z\">10.1007/s10711-020-00581-z</a>"},"volume":213,"user_id":"87909","_id":"29545","publisher":"Springer Science and Business Media LLC","page":"295-314","status":"public","department":[{"_id":"636"}],"keyword":["Geometry and Topology"],"type":"journal_article","date_created":"2022-01-26T13:19:18Z","issue":"1","publication":"Geometriae Dedicata","doi":"10.1007/s10711-020-00581-z","language":[{"iso":"eng"}],"intvolume":"       213","date_updated":"2022-01-26T13:19:39Z","publication_status":"published","author":[{"full_name":"Jean, Frédéric","first_name":"Frédéric","last_name":"Jean"},{"first_name":"Sofya","last_name":"Maslovskaya","full_name":"Maslovskaya, Sofya","id":"87909"},{"full_name":"Zelenko, Igor","first_name":"Igor","last_name":"Zelenko"}],"publication_identifier":{"issn":["0046-5755","1572-9168"]},"year":"2020","title":"On Weyl’s type theorems and genericity of projective rigidity in sub-Riemannian geometry"},{"type":"conference_abstract","oa":"1","department":[{"_id":"636"}],"date_created":"2022-01-26T13:26:36Z","quality_controlled":"1","extern":"1","citation":{"chicago":"Maslovskaya, Sofya, Jean-Baptiste Caillau, Walid Djema, Laetitia Giraldi, Jean-Luc Jean-Luc, and Jean-Baptiste Pomet. “The Turnpike Property in Maximization of Microbial Metabolite Production,” 2020.","ama":"Maslovskaya S, Caillau J-B, Djema W, Giraldi L, Jean-Luc J-L, Pomet J-B. The turnpike property in maximization of microbial metabolite production. In: ; 2020.","short":"S. Maslovskaya, J.-B. Caillau, W. Djema, L. Giraldi, J.-L. Jean-Luc, J.-B. Pomet, in: 2020.","bibtex":"@inproceedings{Maslovskaya_Caillau_Djema_Giraldi_Jean-Luc_Pomet_2020, title={The turnpike property in maximization of microbial metabolite production}, author={Maslovskaya, Sofya and Caillau, Jean-Baptiste and Djema, Walid and Giraldi, Laetitia and Jean-Luc, Jean-Luc and Pomet, Jean-Baptiste}, year={2020} }","apa":"Maslovskaya, S., Caillau, J.-B., Djema, W., Giraldi, L., Jean-Luc, J.-L., &#38; Pomet, J.-B. (2020). <i>The turnpike property in maximization of microbial metabolite production</i>. IFAC 2020 - 21rst IFAC World Congress.","mla":"Maslovskaya, Sofya, et al. <i>The Turnpike Property in Maximization of Microbial Metabolite Production</i>. 2020.","ieee":"S. Maslovskaya, J.-B. Caillau, W. Djema, L. Giraldi, J.-L. Jean-Luc, and J.-B. Pomet, “The turnpike property in maximization of microbial metabolite production,” presented at the IFAC 2020 - 21rst IFAC World Congress, 2020."},"user_id":"87909","main_file_link":[{"open_access":"1","url":"https://hal.archives-ouvertes.fr/hal-02916081/document"}],"language":[{"iso":"eng"}],"_id":"29546","date_updated":"2022-01-26T13:39:01Z","year":"2020","title":"The turnpike property in maximization of microbial metabolite production","status":"public","conference":{"name":"IFAC 2020 - 21rst IFAC World Congress"},"author":[{"id":"87909","full_name":"Maslovskaya, Sofya","first_name":"Sofya","last_name":"Maslovskaya"},{"last_name":"Caillau","first_name":"Jean-Baptiste","full_name":"Caillau, Jean-Baptiste"},{"last_name":"Djema","first_name":"Walid","full_name":"Djema, Walid"},{"last_name":"Giraldi","first_name":"Laetitia","full_name":"Giraldi, Laetitia"},{"first_name":"Jean-Luc","last_name":"Jean-Luc","full_name":"Jean-Luc, Jean-Luc"},{"full_name":"Pomet, Jean-Baptiste","last_name":"Pomet","first_name":"Jean-Baptiste"}]},{"publisher":"Springer International Publishing","_id":"29413","language":[{"iso":"eng"}],"page":"209-237","editor":[{"full_name":"Junge, Oliver","first_name":"Oliver","last_name":"Junge"},{"last_name":"Schütze","first_name":"Oliver","full_name":"Schütze, Oliver"},{"full_name":"Froyland, Gary","last_name":"Froyland","first_name":"Gary"},{"first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina"},{"first_name":"Kathrin","last_name":"Padberg-Gehle","full_name":"Padberg-Gehle, Kathrin"}],"user_id":"15694","author":[{"first_name":"K.","last_name":"Flaßkamp","full_name":"Flaßkamp, K."},{"full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina","id":"16494"},{"full_name":"Peitz, S. ","last_name":"Peitz","first_name":"S. "}],"year":"2020","title":"Symmetry in optimal control: A multiobjective model predictive control approach","status":"public","date_updated":"2023-11-08T08:15:14Z","date_created":"2022-01-18T12:58:18Z","place":"Cham","department":[{"_id":"636"}],"type":"book_chapter","citation":{"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.","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.","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.","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.","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} }","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.","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."},"publication":"Advances in Dynamics, Optimization and Computation"},{"status":"public","page":"111-130","_id":"19945","publisher":"American Institute of Mathematical Sciences (AIMS)","user_id":"85279","volume":6,"citation":{"chicago":"McLachlan, Robert I, Christian Offen, and Benjamin K Tapley. “Symplectic Integration of PDEs Using Clebsch Variables.” <i>Journal of Computational Dynamics</i> 6, no. 1 (2019): 111–30. <a href=\"https://doi.org/10.3934/jcd.2019005\">https://doi.org/10.3934/jcd.2019005</a>.","short":"R.I. McLachlan, C. Offen, B.K. Tapley, Journal of Computational Dynamics 6 (2019) 111–130.","ieee":"R. I. McLachlan, C. Offen, and B. K. Tapley, “Symplectic integration of PDEs using Clebsch variables,” <i>Journal of Computational Dynamics</i>, vol. 6, no. 1, pp. 111–130, 2019.","apa":"McLachlan, R. I., Offen, C., &#38; Tapley, B. K. (2019). Symplectic integration of PDEs using Clebsch variables. <i>Journal of Computational Dynamics</i>, <i>6</i>(1), 111–130. <a href=\"https://doi.org/10.3934/jcd.2019005\">https://doi.org/10.3934/jcd.2019005</a>","bibtex":"@article{McLachlan_Offen_Tapley_2019, title={Symplectic integration of PDEs using Clebsch variables}, volume={6}, DOI={<a href=\"https://doi.org/10.3934/jcd.2019005\">10.3934/jcd.2019005</a>}, number={1}, journal={Journal of Computational Dynamics}, publisher={American Institute of Mathematical Sciences (AIMS)}, author={McLachlan, Robert I and Offen, Christian and Tapley, Benjamin K}, year={2019}, pages={111–130} }","ama":"McLachlan RI, Offen C, Tapley BK. Symplectic integration of PDEs using Clebsch variables. <i>Journal of Computational Dynamics</i>. 2019;6(1):111-130. doi:<a href=\"https://doi.org/10.3934/jcd.2019005\">10.3934/jcd.2019005</a>","mla":"McLachlan, Robert I., et al. “Symplectic Integration of PDEs Using Clebsch Variables.” <i>Journal of Computational Dynamics</i>, vol. 6, no. 1, American Institute of Mathematical Sciences (AIMS), 2019, pp. 111–30, doi:<a href=\"https://doi.org/10.3934/jcd.2019005\">10.3934/jcd.2019005</a>."},"oa":"1","title":"Symplectic integration of PDEs using Clebsch variables","year":"2019","author":[{"first_name":"Robert I","last_name":"McLachlan","full_name":"McLachlan, Robert I"},{"full_name":"Offen, Christian","last_name":"Offen","orcid":"https://orcid.org/0000-0002-5940-8057","first_name":"Christian","id":"85279"},{"first_name":"Benjamin K","last_name":"Tapley","full_name":"Tapley, Benjamin K"}],"publication_identifier":{"issn":["2158-2505"]},"date_updated":"2022-01-06T06:54:15Z","intvolume":"         6","article_type":"original","main_file_link":[{"url":"http://www.aimsciences.org/article/doi/10.3934/jcd.2019005","open_access":"1"}],"language":[{"iso":"eng"}],"doi":"10.3934/jcd.2019005","issue":"1","publication":"Journal of Computational Dynamics","abstract":[{"text":"Many PDEs (Burgers' equation, KdV, Camassa-Holm, Euler's fluid equations, …) can be formulated as infinite-dimensional Lie-Poisson systems. These are Hamiltonian systems on manifolds equipped with Poisson brackets. The Poisson structure is connected to conservation properties and other geometric features of solutions to the PDE and, therefore, of great interest for numerical integration. For the example of Burgers' equations and related PDEs we use Clebsch variables to lift the original system to a collective Hamiltonian system on a symplectic manifold whose structure is related to the original Lie-Poisson structure. On the collective Hamiltonian system a symplectic integrator can be applied. Our numerical examples show excellent conservation properties and indicate that the disadvantage of an increased phase-space dimension can be outweighed by the advantage of symplectic integration.","lang":"eng"}],"extern":"1","date_created":"2020-10-06T16:44:07Z","type":"journal_article","department":[{"_id":"636"}]},{"page":"490-495","_id":"29867","language":[{"iso":"eng"}],"user_id":"15694","volume":"52(16)","year":"2019","title":"Towards velocity turnpikes in optimal control of mechanical systems","status":"public","author":[{"full_name":"Faulwasser, Tim","first_name":"Tim","last_name":"Faulwasser"},{"last_name":"Flaßkamp","first_name":"K.","full_name":"Flaßkamp, K."},{"id":"16494","first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina"},{"full_name":"Worthmann, Karl","last_name":"Worthmann","first_name":"Karl"}],"corporate_editor":["IFAC-PapersOnLine"],"date_updated":"2023-11-08T08:09:01Z","date_created":"2022-02-17T07:23:52Z","type":"conference","department":[{"_id":"636"}],"citation":{"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} }","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.","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.","short":"T. Faulwasser, K. Flaßkamp, S. Ober-Blöbaum, K. Worthmann, in: IFAC-PapersOnLine (Ed.), 2019, 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.","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.","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)."}},{"page":"2895-2927","_id":"19935","user_id":"85279","status":"public","citation":{"ieee":"R. I. McLachlan and C. Offen, “Bifurcation of solutions to Hamiltonian boundary value problems,” <i>Nonlinearity</i>, pp. 2895–2927, 2018.","mla":"McLachlan, Robert I., and Christian Offen. “Bifurcation of Solutions to Hamiltonian Boundary Value Problems.” <i>Nonlinearity</i>, 2018, pp. 2895–927, doi:<a href=\"https://doi.org/10.1088/1361-6544/aab630\">10.1088/1361-6544/aab630</a>.","apa":"McLachlan, R. I., &#38; Offen, C. (2018). Bifurcation of solutions to Hamiltonian boundary value problems. <i>Nonlinearity</i>, 2895–2927. <a href=\"https://doi.org/10.1088/1361-6544/aab630\">https://doi.org/10.1088/1361-6544/aab630</a>","bibtex":"@article{McLachlan_Offen_2018, title={Bifurcation of solutions to Hamiltonian boundary value problems}, DOI={<a href=\"https://doi.org/10.1088/1361-6544/aab630\">10.1088/1361-6544/aab630</a>}, journal={Nonlinearity}, author={McLachlan, Robert I and Offen, Christian}, year={2018}, pages={2895–2927} }","chicago":"McLachlan, Robert I, and Christian Offen. “Bifurcation of Solutions to Hamiltonian Boundary Value Problems.” <i>Nonlinearity</i>, 2018, 2895–2927. <a href=\"https://doi.org/10.1088/1361-6544/aab630\">https://doi.org/10.1088/1361-6544/aab630</a>.","short":"R.I. McLachlan, C. Offen, Nonlinearity (2018) 2895–2927.","ama":"McLachlan RI, Offen C. Bifurcation of solutions to Hamiltonian boundary value problems. <i>Nonlinearity</i>. 2018:2895-2927. doi:<a href=\"https://doi.org/10.1088/1361-6544/aab630\">10.1088/1361-6544/aab630</a>"},"main_file_link":[{"url":"https://doi.org/10.1088/1361-6544/aab630"}],"language":[{"iso":"eng"}],"doi":"10.1088/1361-6544/aab630","year":"2018","title":"Bifurcation of solutions to Hamiltonian boundary value problems","author":[{"full_name":"McLachlan, Robert I","first_name":"Robert I","last_name":"McLachlan"},{"orcid":"https://orcid.org/0000-0002-5940-8057","first_name":"Christian","last_name":"Offen","full_name":"Offen, Christian","id":"85279"}],"publication_identifier":{"issn":["0951-7715","1361-6544"]},"publication_status":"published","date_updated":"2022-01-06T06:54:14Z","article_type":"original","date_created":"2020-10-06T16:28:36Z","type":"journal_article","department":[{"_id":"636"}],"publication":"Nonlinearity","extern":"1","abstract":[{"lang":"eng","text":"A bifurcation is a qualitative change in a family of solutions to an equation produced by varying parameters. In contrast to the local bifurcations of dynamical systems that are often related to a change in the number or stability of equilibria, bifurcations of boundary value problems are global in nature and may not be related to any obvious change in dynamical behaviour. Catastrophe theory is a well-developed framework which studies the bifurcations of critical points of functions. In this paper we study the bifurcations of solutions of boundary-value problems for symplectic maps, using the language of (finite-dimensional) singularity theory. We associate certain such problems with a geometric picture involving the intersection of Lagrangian submanifolds, and hence with the critical points of a suitable generating function. Within this framework, we then study the effect of three special cases: (i) some common boundary conditions, such as Dirichlet boundary conditions for second-order systems, restrict the possible types of bifurcations (for example, in generic planar systems only the A-series beginning with folds and cusps can occur); (ii) integrable systems, such as planar Hamiltonian systems, can exhibit a novel periodic pitchfork bifurcation; and (iii) systems with Hamiltonian symmetries or reversing symmetries can exhibit restricted bifurcations associated with the symmetry. This approach offers an alternative to the analysis of critical points in function spaces, typically used in the study of bifurcation of variational problems, and opens the way to the detection of more exotic bifurcations than the simple folds and cusps that are often found in examples. "}]},{"citation":{"ama":"McLachlan RI, Offen C. Symplectic integration of boundary value problems. <i>Numerical Algorithms</i>. 2018:1219-1233. doi:<a href=\"https://doi.org/10.1007/s11075-018-0599-7\">10.1007/s11075-018-0599-7</a>","bibtex":"@article{McLachlan_Offen_2018, title={Symplectic integration of boundary value problems}, DOI={<a href=\"https://doi.org/10.1007/s11075-018-0599-7\">10.1007/s11075-018-0599-7</a>}, journal={Numerical Algorithms}, author={McLachlan, Robert I and Offen, Christian}, year={2018}, pages={1219–1233} }","mla":"McLachlan, Robert I., and Christian Offen. “Symplectic Integration of Boundary Value Problems.” <i>Numerical Algorithms</i>, 2018, pp. 1219–33, doi:<a href=\"https://doi.org/10.1007/s11075-018-0599-7\">10.1007/s11075-018-0599-7</a>.","chicago":"McLachlan, Robert I, and Christian Offen. “Symplectic Integration of Boundary Value Problems.” <i>Numerical Algorithms</i>, 2018, 1219–33. <a href=\"https://doi.org/10.1007/s11075-018-0599-7\">https://doi.org/10.1007/s11075-018-0599-7</a>.","short":"R.I. McLachlan, C. Offen, Numerical Algorithms (2018) 1219–1233.","apa":"McLachlan, R. I., &#38; Offen, C. (2018). Symplectic integration of boundary value problems. <i>Numerical Algorithms</i>, 1219–1233. <a href=\"https://doi.org/10.1007/s11075-018-0599-7\">https://doi.org/10.1007/s11075-018-0599-7</a>","ieee":"R. I. McLachlan and C. Offen, “Symplectic integration of boundary value problems,” <i>Numerical Algorithms</i>, pp. 1219–1233, 2018."},"status":"public","user_id":"85279","page":"1219-1233","_id":"19937","extern":"1","abstract":[{"text":"Symplectic integrators can be excellent for Hamiltonian initial value problems. Reasons for this include their preservation of invariant sets like tori, good energy behaviour, nonexistence of attractors, and good behaviour of statistical properties. These all refer to {\\em long-time} behaviour. They are directly connected to the dynamical behaviour of symplectic maps φ:M→M' on the phase space under iteration. Boundary value problems, in contrast, are posed for fixed (and often quite short) times. Symplecticity manifests as a symplectic map φ:M→M' which is not iterated. Is there any point, therefore, for a symplectic integrator to be used on a Hamiltonian boundary value problem? In this paper we announce results that symplectic integrators preserve bifurcations of Hamiltonian boundary value problems and that nonsymplectic integrators do not.","lang":"eng"}],"publication":"Numerical Algorithms","type":"journal_article","department":[{"_id":"636"}],"date_created":"2020-10-06T16:29:14Z","publication_status":"published","date_updated":"2022-01-06T06:54:14Z","article_type":"original","year":"2018","title":"Symplectic integration of boundary value problems","author":[{"last_name":"McLachlan","first_name":"Robert I","full_name":"McLachlan, Robert I"},{"id":"85279","first_name":"Christian","orcid":"https://orcid.org/0000-0002-5940-8057","last_name":"Offen","full_name":"Offen, Christian"}],"publication_identifier":{"issn":["1017-1398","1572-9265"]},"doi":"10.1007/s11075-018-0599-7","main_file_link":[{"url":"https://rdcu.be/b79ap"}],"language":[{"iso":"eng"}]},{"language":[{"iso":"eng"}],"_id":"29425","user_id":"15694","conference":{"end_date":"2018-06-15","start_date":"2018-06-11"},"author":[{"full_name":"Jiménez, F.","last_name":"Jiménez","first_name":"F."},{"first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","id":"16494"}],"title":"Necessary optimality conditions for optimally controlled dissipative mechanical systems modelled through fractional derivatives","status":"public","year":"2018","date_updated":"2022-01-21T13:51:41Z","date_created":"2022-01-18T14:49:40Z","department":[{"_id":"636"}],"type":"conference","citation":{"ieee":"F. Jiménez and S. Ober-Blöbaum, “Necessary optimality conditions for optimally controlled dissipative mechanical systems modelled through fractional derivatives,” 2018.","apa":"Jiménez, F., &#38; Ober-Blöbaum, S. (2018). Necessary optimality conditions for optimally controlled dissipative mechanical systems modelled through fractional derivatives. <i>6th European Conference on Computational Mechanics</i>.","chicago":"Jiménez, F., and Sina Ober-Blöbaum. “Necessary Optimality Conditions for Optimally Controlled Dissipative Mechanical Systems Modelled through Fractional Derivatives.” In <i>6th European Conference on Computational Mechanics</i>, 2018.","short":"F. Jiménez, S. Ober-Blöbaum, in: 6th European Conference on Computational Mechanics, 2018.","mla":"Jiménez, F., and Sina Ober-Blöbaum. “Necessary Optimality Conditions for Optimally Controlled Dissipative Mechanical Systems Modelled through Fractional Derivatives.” <i>6th European Conference on Computational Mechanics</i>, 2018.","bibtex":"@inproceedings{Jiménez_Ober-Blöbaum_2018, title={Necessary optimality conditions for optimally controlled dissipative mechanical systems modelled through fractional derivatives}, booktitle={6th European Conference on Computational Mechanics}, author={Jiménez, F. and Ober-Blöbaum, Sina}, year={2018} }","ama":"Jiménez F, Ober-Blöbaum S. Necessary optimality conditions for optimally controlled dissipative mechanical systems modelled through fractional derivatives. In: <i>6th European Conference on Computational Mechanics</i>. ; 2018."},"publication":"6th European Conference on Computational Mechanics"},{"date_updated":"2022-01-21T13:53:24Z","year":"2018","status":"public","title":"A fractional variational approach for modelling dissipative mechanical systems continuous and discrete settings","corporate_editor":["IFAC-PapersOnLine"],"author":[{"first_name":"F.","last_name":"Jiménez","full_name":"Jiménez, F."},{"id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"}],"user_id":"15694","volume":"51(3)","page":"50-55","_id":"29427","language":[{"iso":"eng"}],"publication":"6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2018","citation":{"ieee":"F. Jiménez and S. Ober-Blöbaum, “A fractional variational approach for modelling dissipative mechanical systems continuous and discrete settings,” in <i>6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2018</i>, 2018, vol. 51(3), pp. 50–55.","apa":"Jiménez, F., &#38; Ober-Blöbaum, S. (2018). A fractional variational approach for modelling dissipative mechanical systems continuous and discrete settings. In IFAC-PapersOnLine (Ed.), <i>6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2018: Vol. 51(3)</i> (pp. 50–55).","chicago":"Jiménez, F., and Sina Ober-Blöbaum. “A Fractional Variational Approach for Modelling Dissipative Mechanical Systems Continuous and Discrete Settings.” In <i>6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2018</i>, edited by IFAC-PapersOnLine, 51(3):50–55, 2018.","short":"F. Jiménez, S. Ober-Blöbaum, in: IFAC-PapersOnLine (Ed.), 6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2018, 2018, pp. 50–55.","mla":"Jiménez, F., and Sina Ober-Blöbaum. “A Fractional Variational Approach for Modelling Dissipative Mechanical Systems Continuous and Discrete Settings.” <i>6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2018</i>, edited by IFAC-PapersOnLine, vol. 51(3), 2018, pp. 50–55.","bibtex":"@inproceedings{Jiménez_Ober-Blöbaum_2018, title={A fractional variational approach for modelling dissipative mechanical systems continuous and discrete settings}, volume={51(3)}, booktitle={6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2018}, author={Jiménez, F. and Ober-Blöbaum, Sina}, editor={IFAC-PapersOnLine}, year={2018}, pages={50–55} }","ama":"Jiménez F, Ober-Blöbaum S. A fractional variational approach for modelling dissipative mechanical systems continuous and discrete settings. In: IFAC-PapersOnLine, ed. <i>6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2018</i>. Vol 51(3). ; 2018:50-55."},"type":"conference","department":[{"_id":"636"}],"date_created":"2022-01-18T14:55:51Z"},{"type":"preprint","department":[{"_id":"636"}],"file":[{"file_id":"29078","content_type":"application/pdf","title":"Local intersections of Lagrangian manifolds correspond to catastrophe theory","file_name":"LocalLagrangianContact.pdf","access_level":"open_access","file_size":662483,"relation":"main_file","date_updated":"2021-12-21T16:01:03Z","date_created":"2021-12-21T16:01:03Z","description":"Two smooth map germs are right-equivalent if and only if they\ngenerate two Lagrangian submanifolds in a cotangent bundle which have the\nsame contact with the zero-section. In this paper we provide a reverse direction\nto this classical result of Golubitsky and Guillemin. Two Lagrangian submanifolds of a symplectic manifold have the same contact with a third Lagrangian\nsubmanifold if and only if the intersection problems correspond to stably right\nequivalent map germs. We, therefore, obtain a correspondence between local\nLagrangian intersection problems and catastrophe theory while the classical\nversion only captures tangential intersections. The correspondence is defined\nindependently of any Lagrangian fibration of the ambient symplectic manifold, in contrast to other classical results. Moreover, we provide an extension\nof the correspondence to families of local Lagrangian intersection problems.\nThis gives rise to a framework which allows a natural transportation of the\nnotions of catastrophe theory such as stability, unfolding and (uni-)versality\nto the geometric setting such that we obtain a classification of families of lo-\ncal Lagrangian intersection problems. An application is the classification of\nLagrangian boundary value problems for symplectic maps.","creator":"coffen"}],"date_created":"2020-10-06T16:32:45Z","abstract":[{"text":"Two smooth map germs are right-equivalent if and only if they generate two\r\nLagrangian submanifolds in a cotangent bundle which have the same contact with\r\nthe zero-section. In this paper we provide a reverse direction to this\r\nclassical result of Golubitsky and Guillemin. Two Lagrangian submanifolds of a\r\nsymplectic manifold have the same contact with a third Lagrangian submanifold\r\nif and only if the intersection problems correspond to stably right equivalent\r\nmap germs. We, therefore, obtain a correspondence between local Lagrangian\r\nintersection problems and catastrophe theory while the classical version only\r\ncaptures tangential intersections. The correspondence is defined independently\r\nof any Lagrangian fibration of the ambient symplectic manifold, in contrast to\r\nother classical results. Moreover, we provide an extension of the\r\ncorrespondence to families of local Lagrangian intersection problems. This\r\ngives rise to a framework which allows a natural transportation of the notions\r\nof catastrophe theory such as stability, unfolding and (uni-)versality to the\r\ngeometric setting such that we obtain a classification of families of local\r\nLagrangian intersection problems. An application is the classification of\r\nLagrangian boundary value problems for symplectic maps.","lang":"eng"}],"publication":"arXiv:1811.10165","language":[{"iso":"eng"}],"publication_status":"submitted","date_updated":"2023-08-10T08:48:55Z","title":"Local intersections of Lagrangian manifolds correspond to catastrophe  theory","year":"2018","author":[{"full_name":"Offen, Christian","last_name":"Offen","orcid":"https://orcid.org/0000-0002-5940-8057","first_name":"Christian","id":"85279"}],"oa":"1","external_id":{"arxiv":["1811.10165"]},"file_date_updated":"2021-12-21T16:01:03Z","citation":{"chicago":"Offen, Christian. “Local Intersections of Lagrangian Manifolds Correspond to Catastrophe  Theory.” <i>ArXiv:1811.10165</i>, n.d.","ama":"Offen C. Local intersections of Lagrangian manifolds correspond to catastrophe  theory. <i>arXiv:181110165</i>.","short":"C. Offen, ArXiv:1811.10165 (n.d.).","bibtex":"@article{Offen, title={Local intersections of Lagrangian manifolds correspond to catastrophe  theory}, journal={arXiv:1811.10165}, author={Offen, Christian} }","mla":"Offen, Christian. “Local Intersections of Lagrangian Manifolds Correspond to Catastrophe  Theory.” <i>ArXiv:1811.10165</i>.","apa":"Offen, C. (n.d.). Local intersections of Lagrangian manifolds correspond to catastrophe  theory. In <i>arXiv:1811.10165</i>.","ieee":"C. Offen, “Local intersections of Lagrangian manifolds correspond to catastrophe  theory,” <i>arXiv:1811.10165</i>. ."},"user_id":"85279","ddc":["510"],"_id":"19940","has_accepted_license":"1","status":"public"},{"publication":"New Zealand Journal of Mathematics","abstract":[{"text":"In this paper we continue our study of bifurcations of solutions of boundary-value problems for symplectic maps arising as Hamiltonian diffeomorphisms. These have been shown to be connected to catastrophe theory via generating functions and ordinary and reversal phase space symmetries have been considered. Here we present a convenient, coordinate free framework to analyse separated Lagrangian boundary value problems which include classical Dirichlet, Neumann and Robin boundary value problems. The framework is then used to prove the existence of obstructions arising from conformal symplectic symmetries on the bifurcation behaviour of solutions to Hamiltonian boundary value problems. Under non-degeneracy conditions, a group action by conformal symplectic symmetries has the effect that the flow map cannot degenerate in a direction which is tangential to the action. This imposes restrictions on which singularities can occur in boundary value problems. Our results generalise classical results about conjugate loci on Riemannian manifolds to a large class of Hamiltonian boundary value problems with, for example, scaling symmetries. ","lang":"eng"}],"extern":"1","file":[{"creator":"coffen","date_created":"2020-10-06T16:49:29Z","relation":"main_file","date_updated":"2020-10-07T14:04:01Z","file_name":"Hamiltonian_Boundary_Value_Problems,_Conformal_Symplectic_Symmetries,_and_Conjugate_Loci.pdf","access_level":"open_access","file_size":3126111,"title":"Hamiltonian Boundary Value Problems, Conformal Symplectic Symmetries, and Conjugate Loci","file_id":"19946","content_type":"application/pdf"}],"date_created":"2020-10-06T16:39:08Z","type":"journal_article","keyword":["Hamiltonian boundary value problems","singularities","conformal symplectic geometry","catastrophe theory","conjugate loci"],"department":[{"_id":"636"}],"title":"Hamiltonian boundary value problems, conformal symplectic symmetries, and conjugate loci","year":"2018","author":[{"full_name":"McLachlan, Robert I","first_name":"Robert I","last_name":"McLachlan"},{"first_name":"Christian","last_name":"Offen","orcid":"https://orcid.org/0000-0002-5940-8057","full_name":"Offen, Christian","id":"85279"}],"date_updated":"2023-09-21T07:29:24Z","publication_status":"published","intvolume":"        48","article_type":"original","main_file_link":[{"url":"https://nzjmath.org/index.php/NZJMATH/article/view/34","open_access":"1"}],"language":[{"iso":"eng"}],"doi":"10.53733/34 ","file_date_updated":"2020-10-07T14:04:01Z","citation":{"ieee":"R. I. McLachlan and C. Offen, “Hamiltonian boundary value problems, conformal symplectic symmetries, and conjugate loci,” <i>New Zealand Journal of Mathematics</i>, vol. 48, pp. 83–99, 2018, doi: <a href=\"https://doi.org/10.53733/34 \">10.53733/34 </a>.","mla":"McLachlan, Robert I., and Christian Offen. “Hamiltonian Boundary Value Problems, Conformal Symplectic Symmetries, and Conjugate Loci.” <i>New Zealand Journal of Mathematics</i>, vol. 48, 2018, pp. 83–99, doi:<a href=\"https://doi.org/10.53733/34 \">10.53733/34 </a>.","apa":"McLachlan, R. I., &#38; Offen, C. (2018). Hamiltonian boundary value problems, conformal symplectic symmetries, and conjugate loci. <i>New Zealand Journal of Mathematics</i>, <i>48</i>, 83–99. <a href=\"https://doi.org/10.53733/34 \">https://doi.org/10.53733/34 </a>","bibtex":"@article{McLachlan_Offen_2018, title={Hamiltonian boundary value problems, conformal symplectic symmetries, and conjugate loci}, volume={48}, DOI={<a href=\"https://doi.org/10.53733/34 \">10.53733/34 </a>}, journal={New Zealand Journal of Mathematics}, author={McLachlan, Robert I and Offen, Christian}, year={2018}, pages={83–99} }","chicago":"McLachlan, Robert I, and Christian Offen. “Hamiltonian Boundary Value Problems, Conformal Symplectic Symmetries, and Conjugate Loci.” <i>New Zealand Journal of Mathematics</i> 48 (2018): 83–99. <a href=\"https://doi.org/10.53733/34 \">https://doi.org/10.53733/34 </a>.","short":"R.I. McLachlan, C. Offen, New Zealand Journal of Mathematics 48 (2018) 83–99.","ama":"McLachlan RI, Offen C. Hamiltonian boundary value problems, conformal symplectic symmetries, and conjugate loci. <i>New Zealand Journal of Mathematics</i>. 2018;48:83-99. doi:<a href=\"https://doi.org/10.53733/34 \">10.53733/34 </a>"},"quality_controlled":"1","external_id":{"arxiv":["1804.07479"]},"oa":"1","status":"public","has_accepted_license":"1","page":"83-99","_id":"19943","ddc":["510"],"user_id":"85279","volume":48}]