[{"publication_identifier":{"isbn":["9783030512637","9783030512644"],"issn":["2198-4182","2198-4190"]},"publication_status":"published","place":"Cham","year":"2020","citation":{"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, Cham, 2020.","bibtex":"@inbook{Flaßkamp_Ober-Blöbaum_Peitz_2020, place={Cham}, title={Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach}, DOI={<a href=\"https://doi.org/10.1007/978-3-030-51264-4_9\">10.1007/978-3-030-51264-4_9</a>}, booktitle={Advances in Dynamics, Optimization and Computation}, publisher={Springer}, author={Flaßkamp, Kathrin and Ober-Blöbaum, Sina and Peitz, Sebastian}, editor={Junge, Oliver and Schütze, Oliver and Froyland, Gary and Ober-Blöbaum, Sina and Padberg-Gehle, KathrinEditors}, year={2020} }","mla":"Flaßkamp, Kathrin, 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, 2020, doi:<a href=\"https://doi.org/10.1007/978-3-030-51264-4_9\">10.1007/978-3-030-51264-4_9</a>.","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>. Cham: Springer. <a href=\"https://doi.org/10.1007/978-3-030-51264-4_9\">https://doi.org/10.1007/978-3-030-51264-4_9</a>","chicago":"Flaßkamp, Kathrin, Sina Ober-Blöbaum, and Sebastian 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. Cham: Springer, 2020. <a href=\"https://doi.org/10.1007/978-3-030-51264-4_9\">https://doi.org/10.1007/978-3-030-51264-4_9</a>.","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, 2020.","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>. Cham: Springer; 2020. doi:<a href=\"https://doi.org/10.1007/978-3-030-51264-4_9\">10.1007/978-3-030-51264-4_9</a>"},"publisher":"Springer","date_updated":"2022-01-06T06:53:11Z","author":[{"first_name":"Kathrin","full_name":"Flaßkamp, Kathrin","last_name":"Flaßkamp"},{"full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"},{"first_name":"Sebastian","full_name":"Peitz, Sebastian","id":"47427","last_name":"Peitz","orcid":"0000-0002-3389-793X"}],"date_created":"2020-07-27T09:50:19Z","title":"Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach","doi":"10.1007/978-3-030-51264-4_9","publication":"Advances in Dynamics, Optimization and Computation","type":"book_chapter","editor":[{"first_name":"Oliver","full_name":"Junge, Oliver","last_name":"Junge"},{"first_name":"Oliver","last_name":"Schütze","full_name":"Schütze, Oliver"},{"last_name":"Froyland","full_name":"Froyland, Gary","first_name":"Gary"},{"full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"},{"full_name":"Padberg-Gehle, Kathrin","last_name":"Padberg-Gehle","first_name":"Kathrin"}],"abstract":[{"text":"Many dynamical systems possess symmetries, e.g. rotational and translational invariances of mechanical systems. These can be beneficially exploited in the design of numerical optimal control methods. We present a model predictive control scheme which is based on a library of precomputed motion primitives. The primitives are equivalence classes w.r.t. the symmetry of the optimal control problems. Trim primitives as relative equilibria w.r.t. this symmetry, play a crucial role in the algorithm. The approach is illustrated using an academic mobile robot example.","lang":"eng"}],"status":"public","_id":"17411","department":[{"_id":"101"}],"user_id":"47427","language":[{"iso":"eng"}]},{"abstract":[{"lang":"eng","text":"In this work we review the novel framework for the computation of finite dimensional invariant sets of infinite dimensional dynamical systems developed in [6] and [36]. By utilizing results on embedding techniques for infinite dimensional systems we extend a classical subdivision scheme [8] as well as a continuation algorithm [7] for the computation of attractors and invariant manifolds of finite dimensional systems to the infinite dimensional case. We show how to implement this approach for the analysis of delay differential equations and partial differential equations and illustrate the feasibility of our implementation by computing the attractor of the Mackey-Glass equation and the unstable manifold of the one-dimensional Kuramoto-Sivashinsky equation."}],"publication":"Advances in Dynamics, Optimization and Computation","language":[{"iso":"eng"}],"year":"2020","title":"The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems","publisher":"Springer International Publishing","date_created":"2020-08-14T15:02:22Z","editor":[{"first_name":"Oliver","full_name":"Junge, Oliver","last_name":"Junge"},{"first_name":"Oliver","full_name":"Schütze, Oliver","last_name":"Schütze"},{"first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina"},{"first_name":"Kathrin","full_name":"Padberg-Gehle, Kathrin","last_name":"Padberg-Gehle"}],"status":"public","type":"book_chapter","_id":"17994","user_id":"32655","series_title":"Studies in Systems, Decision and Control","department":[{"_id":"101"}],"place":"Cham","citation":{"bibtex":"@inbook{Gerlach_Ziessler_2020, place={Cham}, series={Studies in Systems, Decision and Control}, title={The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems}, volume={304}, DOI={<a href=\"https://doi.org/10.1007/978-3-030-51264-4_3\">10.1007/978-3-030-51264-4_3</a>}, booktitle={Advances in Dynamics, Optimization and Computation}, publisher={Springer International Publishing}, author={Gerlach, Raphael and Ziessler, Adrian}, editor={Junge, Oliver and Schütze, Oliver and Ober-Blöbaum, Sina and Padberg-Gehle, Kathrin}, year={2020}, pages={66–85}, collection={Studies in Systems, Decision and Control} }","mla":"Gerlach, Raphael, and Adrian Ziessler. “The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems.” <i>Advances in Dynamics, Optimization and Computation</i>, edited by Oliver Junge et al., vol. 304, Springer International Publishing, 2020, pp. 66–85, doi:<a href=\"https://doi.org/10.1007/978-3-030-51264-4_3\">10.1007/978-3-030-51264-4_3</a>.","short":"R. Gerlach, A. Ziessler, in: O. Junge, O. Schütze, S. Ober-Blöbaum, K. Padberg-Gehle (Eds.), Advances in Dynamics, Optimization and Computation, Springer International Publishing, Cham, 2020, pp. 66–85.","apa":"Gerlach, R., &#38; Ziessler, A. (2020). The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems. In O. Junge, O. Schütze, S. Ober-Blöbaum, &#38; K. Padberg-Gehle (Eds.), <i>Advances in Dynamics, Optimization and Computation</i> (Vol. 304, pp. 66–85). Springer International Publishing. <a href=\"https://doi.org/10.1007/978-3-030-51264-4_3\">https://doi.org/10.1007/978-3-030-51264-4_3</a>","ama":"Gerlach R, Ziessler A. The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems. In: Junge O, Schütze O, Ober-Blöbaum S, Padberg-Gehle K, eds. <i>Advances in Dynamics, Optimization and Computation</i>. Vol 304. Studies in Systems, Decision and Control. Springer International Publishing; 2020:66-85. doi:<a href=\"https://doi.org/10.1007/978-3-030-51264-4_3\">10.1007/978-3-030-51264-4_3</a>","ieee":"R. Gerlach and A. Ziessler, “The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems,” in <i>Advances in Dynamics, Optimization and Computation</i>, vol. 304, O. Junge, O. Schütze, S. Ober-Blöbaum, and K. Padberg-Gehle, Eds. Cham: Springer International Publishing, 2020, pp. 66–85.","chicago":"Gerlach, Raphael, and Adrian Ziessler. “The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems.” In <i>Advances in Dynamics, Optimization and Computation</i>, edited by Oliver Junge, Oliver Schütze, Sina Ober-Blöbaum, and Kathrin Padberg-Gehle, 304:66–85. Studies in Systems, Decision and Control. Cham: Springer International Publishing, 2020. <a href=\"https://doi.org/10.1007/978-3-030-51264-4_3\">https://doi.org/10.1007/978-3-030-51264-4_3</a>."},"page":"66-85","intvolume":"       304","publication_status":"published","publication_identifier":{"isbn":["9783030512637","9783030512644"],"issn":["2198-4182","2198-4190"]},"main_file_link":[{"url":"https://link.springer.com/chapter/10.1007/978-3-030-51264-4_3"}],"doi":"10.1007/978-3-030-51264-4_3","date_updated":"2023-11-17T13:13:25Z","author":[{"last_name":"Gerlach","id":"32655","full_name":"Gerlach, Raphael","first_name":"Raphael"},{"last_name":"Ziessler","full_name":"Ziessler, Adrian","first_name":"Adrian"}],"volume":304}]