[{"_id":"22894","series_title":"IFAC-PapersOnLine","user_id":"15694","department":[{"_id":"636"}],"file_date_updated":"2021-07-29T09:37:49Z","type":"conference","status":"public","date_updated":"2023-11-29T10:19:41Z","oa":"1","author":[{"full_name":"Offen, Christian","id":"85279","orcid":"0000-0002-5940-8057","last_name":"Offen","first_name":"Christian"},{"id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"}],"volume":"54(19)","main_file_link":[{"open_access":"1","url":"https://www.sciencedirect.com/science/article/pii/S2405896321021236"}],"conference":{"location":"Berlin, Germany","end_date":"2021-10-13","start_date":"2021-10-11","name":"7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, LHMNC 2021"},"doi":"https://doi.org/10.1016/j.ifacol.2021.11.099","publication_status":"published","publication_identifier":{"issn":["2405-8963"]},"has_accepted_license":"1","related_material":{"link":[{"description":"GitHub/Zenodo","relation":"software","url":"https://doi.org/10.5281/zenodo.4562664"}]},"citation":{"ieee":"C. Offen and S. Ober-Blöbaum, “Bifurcation preserving discretisations of optimal control problems,” vol. 54(19). pp. 334–339, 2021, doi: <a href=\"https://doi.org/10.1016/j.ifacol.2021.11.099\">https://doi.org/10.1016/j.ifacol.2021.11.099</a>.","chicago":"Offen, Christian, and Sina Ober-Blöbaum. “Bifurcation Preserving Discretisations of Optimal Control Problems.” IFAC-PapersOnLine, 2021. <a href=\"https://doi.org/10.1016/j.ifacol.2021.11.099\">https://doi.org/10.1016/j.ifacol.2021.11.099</a>.","ama":"Offen C, Ober-Blöbaum S. Bifurcation preserving discretisations of optimal control problems. 2021;54(19):334-339. doi:<a href=\"https://doi.org/10.1016/j.ifacol.2021.11.099\">https://doi.org/10.1016/j.ifacol.2021.11.099</a>","mla":"Offen, Christian, and Sina Ober-Blöbaum. <i>Bifurcation Preserving Discretisations of Optimal Control Problems</i>. 2021, pp. 334–39, doi:<a href=\"https://doi.org/10.1016/j.ifacol.2021.11.099\">https://doi.org/10.1016/j.ifacol.2021.11.099</a>.","short":"C. Offen, S. Ober-Blöbaum, 54(19) (2021) 334–339.","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} }","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>"},"page":"334-339","external_id":{"arxiv":["2107.13853"]},"ddc":["510"],"keyword":["optimal control","catastrophe theory","bifurcations","variational methods","symplectic integrators"],"language":[{"iso":"eng"}],"abstract":[{"text":"The first order optimality conditions of optimal control problems (OCPs) can\r\nbe regarded as boundary value problems for Hamiltonian systems. Variational or\r\nsymplectic discretisation methods are classically known for their excellent\r\nlong term behaviour. As boundary value problems are posed on intervals of\r\nfixed, moderate length, it is not immediately clear whether methods can profit\r\nfrom structure preservation in this context. When parameters are present,\r\nsolutions can undergo bifurcations, for instance, two solutions can merge and\r\nannihilate one another as parameters are varied. We will show that generic\r\nbifurcations of an OCP are preserved under discretisation when the OCP is\r\neither directly discretised to a discrete OCP (direct method) or translated\r\ninto a Hamiltonian boundary value problem using first order necessary\r\nconditions of optimality which is then solved using a symplectic integrator\r\n(indirect method). Moreover, certain bifurcations break when a non-symplectic\r\nscheme is used. The general phenomenon is illustrated on the example of a cut\r\nlocus of an ellipsoid.","lang":"eng"}],"file":[{"access_level":"open_access","file_id":"22895","file_name":"ifacconf.pdf","file_size":3125220,"creator":"coffen","date_created":"2021-07-29T09:37:49Z","date_updated":"2021-07-29T09:37:49Z","relation":"main_file","content_type":"application/pdf"}],"date_created":"2021-07-29T09:38:32Z","title":"Bifurcation preserving discretisations of optimal control problems","quality_controlled":"1","year":"2021"},{"language":[{"iso":"eng"}],"keyword":["Hamiltonian boundary value problems","singularities","conformal symplectic geometry","catastrophe theory","conjugate loci"],"ddc":["510"],"external_id":{"arxiv":["1804.07479"]},"file":[{"access_level":"open_access","file_name":"Hamiltonian_Boundary_Value_Problems,_Conformal_Symplectic_Symmetries,_and_Conjugate_Loci.pdf","file_id":"19946","file_size":3126111,"title":"Hamiltonian Boundary Value Problems, Conformal Symplectic Symmetries, and Conjugate Loci","date_created":"2020-10-06T16:49:29Z","creator":"coffen","date_updated":"2020-10-07T14:04:01Z","relation":"main_file","content_type":"application/pdf"}],"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"}],"publication":"New Zealand Journal of Mathematics","title":"Hamiltonian boundary value problems, conformal symplectic symmetries, and conjugate loci","date_created":"2020-10-06T16:39:08Z","year":"2018","quality_controlled":"1","extern":"1","file_date_updated":"2020-10-07T14:04:01Z","article_type":"original","department":[{"_id":"636"}],"user_id":"85279","_id":"19943","status":"public","type":"journal_article","doi":"10.53733/34 ","main_file_link":[{"url":"https://nzjmath.org/index.php/NZJMATH/article/view/34","open_access":"1"}],"volume":48,"author":[{"full_name":"McLachlan, Robert I","last_name":"McLachlan","first_name":"Robert I"},{"orcid":"https://orcid.org/0000-0002-5940-8057","last_name":"Offen","full_name":"Offen, Christian","id":"85279","first_name":"Christian"}],"oa":"1","date_updated":"2023-09-21T07:29:24Z","intvolume":"        48","page":"83-99","citation":{"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} }","short":"R.I. McLachlan, C. Offen, New Zealand Journal of Mathematics 48 (2018) 83–99.","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>.","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>.","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>.","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>"},"has_accepted_license":"1","publication_status":"published"}]