{"file_date_updated":"2021-07-29T09:37:49Z","keyword":["optimal control","catastrophe theory","bifurcations","variational methods","symplectic integrators"],"date_created":"2021-07-29T09:38:32Z","related_material":{"link":[{"relation":"software","url":"https://doi.org/10.5281/zenodo.4562664","description":"GitHub/Zenodo"}]},"has_accepted_license":"1","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"}],"oa":"1","quality_controlled":"1","doi":"https://doi.org/10.1016/j.ifacol.2021.11.099","page":"334-339","file":[{"file_name":"ifacconf.pdf","file_id":"22895","relation":"main_file","access_level":"open_access","content_type":"application/pdf","creator":"coffen","file_size":3125220,"date_updated":"2021-07-29T09:37:49Z","date_created":"2021-07-29T09:37:49Z"}],"ddc":["510"],"publication_status":"published","volume":"54(19)","department":[{"_id":"636"}],"publication_identifier":{"issn":["2405-8963"]},"title":"Bifurcation preserving discretisations of optimal control problems","_id":"22894","citation":{"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.","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>","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>.","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>.","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>"},"external_id":{"arxiv":["2107.13853"]},"user_id":"15694","year":"2021","status":"public","author":[{"last_name":"Offen","id":"85279","full_name":"Offen, Christian","first_name":"Christian","orcid":"0000-0002-5940-8057"},{"full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","id":"16494","first_name":"Sina"}],"series_title":"IFAC-PapersOnLine","conference":{"name":"7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, LHMNC 2021","location":"Berlin, Germany","start_date":"2021-10-11","end_date":"2021-10-13"},"type":"conference","date_updated":"2023-11-29T10:19:41Z","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/S2405896321021236","open_access":"1"}],"language":[{"iso":"eng"}]}