[{"type":"journal_article","department":[{"_id":"101"}],"oa":"1","date_created":"2020-03-13T12:44:36Z","abstract":[{"lang":"eng","text":"Model predictive control is a prominent approach to construct a feedback\r\ncontrol loop for dynamical systems. Due to real-time constraints, the major\r\nchallenge in MPC is to solve model-based optimal control problems in a very\r\nshort amount of time. For linear-quadratic problems, Bemporad et al. have\r\nproposed an explicit formulation where the underlying optimization problems are\r\nsolved a priori in an offline phase. In this article, we present an extension\r\nof this concept in two significant ways. We consider nonlinear problems and -\r\nmore importantly - problems with multiple conflicting objective functions. In\r\nthe offline phase, we build a library of Pareto optimal solutions from which we\r\nthen obtain a valid compromise solution in the online phase according to a\r\ndecision maker's preference. Since the standard multi-parametric programming\r\napproach is no longer valid in this situation, we instead use interpolation\r\nbetween different entries of the library. To reduce the number of problems that\r\nhave to be solved in the offline phase, we exploit symmetries in the dynamical\r\nsystem and the corresponding multiobjective optimal control problem. The\r\nresults are verified using two different examples from autonomous driving."}],"project":[{"_id":"52","name":"Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"publication":"International Journal of Robust and Nonlinear Control","citation":{"ama":"Ober-Blöbaum S, Peitz S. Explicit multiobjective model predictive control for nonlinear systems  with symmetries. <i>International Journal of Robust and Nonlinear Control</i>. 2021;31(2):380-403. doi:<a href=\"https://doi.org/10.1002/rnc.5281\">10.1002/rnc.5281</a>","bibtex":"@article{Ober-Blöbaum_Peitz_2021, title={Explicit multiobjective model predictive control for nonlinear systems  with symmetries}, volume={31(2)}, DOI={<a href=\"https://doi.org/10.1002/rnc.5281\">10.1002/rnc.5281</a>}, journal={International Journal of Robust and Nonlinear Control}, author={Ober-Blöbaum, Sina and Peitz, Sebastian}, year={2021}, pages={380–403} }","mla":"Ober-Blöbaum, Sina, and Sebastian Peitz. “Explicit Multiobjective Model Predictive Control for Nonlinear Systems  with Symmetries.” <i>International Journal of Robust and Nonlinear Control</i>, vol. 31(2), 2021, pp. 380–403, doi:<a href=\"https://doi.org/10.1002/rnc.5281\">10.1002/rnc.5281</a>.","chicago":"Ober-Blöbaum, Sina, and Sebastian Peitz. “Explicit Multiobjective Model Predictive Control for Nonlinear Systems  with Symmetries.” <i>International Journal of Robust and Nonlinear Control</i> 31(2) (2021): 380–403. <a href=\"https://doi.org/10.1002/rnc.5281\">https://doi.org/10.1002/rnc.5281</a>.","short":"S. Ober-Blöbaum, S. Peitz, International Journal of Robust and Nonlinear Control 31(2) (2021) 380–403.","apa":"Ober-Blöbaum, S., &#38; Peitz, S. (2021). Explicit multiobjective model predictive control for nonlinear systems  with symmetries. <i>International Journal of Robust and Nonlinear Control</i>, <i>31(2)</i>, 380–403. <a href=\"https://doi.org/10.1002/rnc.5281\">https://doi.org/10.1002/rnc.5281</a>","ieee":"S. Ober-Blöbaum and S. Peitz, “Explicit multiobjective model predictive control for nonlinear systems  with symmetries,” <i>International Journal of Robust and Nonlinear Control</i>, vol. 31(2), pp. 380–403, 2021, doi: <a href=\"https://doi.org/10.1002/rnc.5281\">10.1002/rnc.5281</a>."},"user_id":"15694","doi":"10.1002/rnc.5281","volume":"31(2)","page":"380-403","main_file_link":[{"open_access":"1","url":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/rnc.5281"}],"_id":"16294","language":[{"iso":"eng"}],"date_updated":"2022-01-24T13:27:50Z","title":"Explicit multiobjective model predictive control for nonlinear systems  with symmetries","year":"2021","status":"public","author":[{"id":"16494","full_name":"Ober-Blöbaum, Sina","first_name":"Sina","last_name":"Ober-Blöbaum"},{"orcid":"https://orcid.org/0000-0002-3389-793X","last_name":"Peitz","first_name":"Sebastian","full_name":"Peitz, Sebastian","id":"47427"}]},{"abstract":[{"text":"In real-world problems, uncertainties (e.g., errors in the measurement,\r\nprecision errors) often lead to poor performance of numerical algorithms when\r\nnot explicitly taken into account. This is also the case for control problems,\r\nwhere optimal solutions can degrade in quality or even become infeasible. Thus,\r\nthere is the need to design methods that can handle uncertainty. In this work,\r\nwe consider nonlinear multi-objective optimal control problems with uncertainty\r\non the initial conditions, and in particular their incorporation into a\r\nfeedback loop via model predictive control (MPC). In multi-objective optimal\r\ncontrol, an optimal compromise between multiple conflicting criteria has to be\r\nfound. For such problems, not much has been reported in terms of uncertainties.\r\nTo address this problem class, we design an offline/online framework to compute\r\nan approximation of efficient control strategies. This approach is closely\r\nrelated to explicit MPC for nonlinear systems, where the potentially expensive\r\noptimization problem is solved in an offline phase in order to enable fast\r\nsolutions in the online phase. In order to reduce the numerical cost of the\r\noffline phase, we exploit symmetries in the control problems. Furthermore, in\r\norder to ensure optimality of the solutions, we include an additional online\r\noptimization step, which is considerably cheaper than the original\r\nmulti-objective optimization problem. We test our framework on a car\r\nmaneuvering problem where safety and speed are the objectives. The\r\nmulti-objective framework allows for online adaptations of the desired\r\nobjective. Alternatively, an automatic scalarizing procedure yields very\r\nefficient feedback controls. Our results show that the method is capable of\r\ndesigning driving strategies that deal better with uncertainties in the initial\r\nconditions, which translates into potentially safer and faster driving\r\nstrategies.","lang":"eng"}],"citation":{"chicago":"Hernández Castellanos, Carlos Ignacio, Sina Ober-Blöbaum, and Sebastian Peitz. “Explicit Multi-Objective Model Predictive Control for Nonlinear Systems  Under Uncertainty.” <i>International Journal of Robust and Nonlinear Control</i> 30(17) (2020): 7593–7618. <a href=\"https://doi.org/10.1002/rnc.5197\">https://doi.org/10.1002/rnc.5197</a>.","short":"C.I. Hernández Castellanos, S. Ober-Blöbaum, S. Peitz, International Journal of Robust and Nonlinear Control 30(17) (2020) 7593–7618.","ieee":"C. I. Hernández Castellanos, S. Ober-Blöbaum, and S. Peitz, “Explicit Multi-objective Model Predictive Control for Nonlinear Systems  Under Uncertainty,” <i>International Journal of Robust and Nonlinear Control</i>, vol. 30(17), pp. 7593–7618, 2020, doi: <a href=\"https://doi.org/10.1002/rnc.5197\">10.1002/rnc.5197</a>.","apa":"Hernández Castellanos, C. I., Ober-Blöbaum, S., &#38; Peitz, S. (2020). Explicit Multi-objective Model Predictive Control for Nonlinear Systems  Under Uncertainty. <i>International Journal of Robust and Nonlinear Control</i>, <i>30(17)</i>, 7593–7618. <a href=\"https://doi.org/10.1002/rnc.5197\">https://doi.org/10.1002/rnc.5197</a>","bibtex":"@article{Hernández Castellanos_Ober-Blöbaum_Peitz_2020, title={Explicit Multi-objective Model Predictive Control for Nonlinear Systems  Under Uncertainty}, volume={30(17)}, DOI={<a href=\"https://doi.org/10.1002/rnc.5197\">10.1002/rnc.5197</a>}, journal={International Journal of Robust and Nonlinear Control}, author={Hernández Castellanos, Carlos Ignacio and Ober-Blöbaum, Sina and Peitz, Sebastian}, year={2020}, pages={7593–7618} }","ama":"Hernández Castellanos CI, Ober-Blöbaum S, Peitz S. Explicit Multi-objective Model Predictive Control for Nonlinear Systems  Under Uncertainty. <i>International Journal of Robust and Nonlinear Control</i>. 2020;30(17):7593-7618. doi:<a href=\"https://doi.org/10.1002/rnc.5197\">10.1002/rnc.5197</a>","mla":"Hernández Castellanos, Carlos Ignacio, et al. “Explicit Multi-Objective Model Predictive Control for Nonlinear Systems  Under Uncertainty.” <i>International Journal of Robust and Nonlinear Control</i>, vol. 30(17), 2020, pp. 7593–618, doi:<a href=\"https://doi.org/10.1002/rnc.5197\">10.1002/rnc.5197</a>."},"publication":"International Journal of Robust and Nonlinear Control","department":[{"_id":"101"}],"type":"journal_article","date_created":"2020-03-13T12:45:56Z","date_updated":"2022-01-21T09:55:39Z","author":[{"full_name":"Hernández Castellanos, Carlos Ignacio","first_name":"Carlos Ignacio","last_name":"Hernández Castellanos"},{"last_name":"Ober-Blöbaum","first_name":"Sina","full_name":"Ober-Blöbaum, Sina","id":"16494"},{"last_name":"Peitz","first_name":"Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X","full_name":"Peitz, Sebastian","id":"47427"}],"year":"2020","status":"public","title":"Explicit Multi-objective Model Predictive Control for Nonlinear Systems  Under Uncertainty","volume":"30(17)","user_id":"15694","doi":"10.1002/rnc.5197","_id":"16297","language":[{"iso":"eng"}],"page":"7593-7618"},{"date_updated":"2023-11-08T08:15:14Z","author":[{"first_name":"K.","last_name":"Flaßkamp","full_name":"Flaßkamp, K."},{"id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"},{"last_name":"Peitz","first_name":"S. ","full_name":"Peitz, S. "}],"year":"2020","title":"Symmetry in optimal control: A multiobjective model predictive control approach","status":"public","editor":[{"full_name":"Junge, Oliver","last_name":"Junge","first_name":"Oliver"},{"full_name":"Schütze, Oliver","first_name":"Oliver","last_name":"Schütze"},{"last_name":"Froyland","first_name":"Gary","full_name":"Froyland, Gary"},{"full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"},{"full_name":"Padberg-Gehle, Kathrin","first_name":"Kathrin","last_name":"Padberg-Gehle"}],"user_id":"15694","_id":"29413","language":[{"iso":"eng"}],"publisher":"Springer International Publishing","page":"209-237","citation":{"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.","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.","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.","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."},"publication":"Advances in Dynamics, Optimization and Computation","department":[{"_id":"636"}],"type":"book_chapter","date_created":"2022-01-18T12:58:18Z","place":"Cham"},{"date_created":"2020-10-13T18:37:24Z","type":"journal_article","citation":{"bibtex":"@article{Flaßkamp_Ober-Blöbaum_Worthmann_2019, title={Symmetry and motion primitives in model predictive control}, volume={31}, journal={MCSS}, author={Flaßkamp, Kathrin and Ober-Blöbaum, Sina and Worthmann, Karl}, year={2019}, pages={455–485} }","ama":"Flaßkamp K, Ober-Blöbaum S, Worthmann K. Symmetry and motion primitives in model predictive control. <i>MCSS</i>. 2019;31:455-485.","mla":"Flaßkamp, Kathrin, et al. “Symmetry and Motion Primitives in Model Predictive Control.” <i>MCSS</i>, vol. 31, 2019, pp. 455–85.","short":"K. Flaßkamp, S. Ober-Blöbaum, K. Worthmann, MCSS 31 (2019) 455–485.","chicago":"Flaßkamp, Kathrin, Sina Ober-Blöbaum, and Karl Worthmann. “Symmetry and Motion Primitives in Model Predictive Control.” <i>MCSS</i> 31 (2019): 455–85.","ieee":"K. Flaßkamp, S. Ober-Blöbaum, and K. Worthmann, “Symmetry and motion primitives in model predictive control,” <i>MCSS</i>, vol. 31, pp. 455–485, 2019.","apa":"Flaßkamp, K., Ober-Blöbaum, S., &#38; Worthmann, K. (2019). Symmetry and motion primitives in model predictive control. <i>MCSS</i>, <i>31</i>, 455–485."},"publication":"MCSS","language":[{"iso":"eng"}],"_id":"19993","page":"455-485","volume":31,"user_id":"15694","author":[{"first_name":"Kathrin","last_name":"Flaßkamp","full_name":"Flaßkamp, Kathrin"},{"id":"16494","last_name":"Ober-Blöbaum","first_name":"Sina","full_name":"Ober-Blöbaum, Sina"},{"first_name":"Karl","last_name":"Worthmann","full_name":"Worthmann, Karl"}],"title":"Symmetry and motion primitives in model predictive control","status":"public","year":"2019","intvolume":"        31","date_updated":"2022-01-21T10:14:19Z"},{"issue":"1","publication":"Proceedings of the 20th World Congress of the International Federation of Automatic Control (IFAC)","abstract":[{"lang":"eng","text":"We present a new algorithm for model predictive control of non-linear systems with respect to multiple, conflicting objectives. The idea is to provide a possibility to change the objective in real-time, e.g. as a reaction to changes in the environment or the system state itself. The algorithm utilises elements from various well-established concepts, namely multiobjective optimal control, economic as well as explicit model predictive control and motion planning with motion primitives. In order to realise real-time applicability, we split the computation into an online and an offline phase and we utilise symmetries in the open-loop optimal control problem to reduce the number of multiobjective optimal control problems that need to be solved in the offline phase. The results are illustrated using the example of an electric vehicle where the longitudinal dynamics are controlled with respect to the concurrent objectives arrival time and energy consumption."}],"date_created":"2019-03-29T13:32:46Z","department":[{"_id":"101"}],"type":"journal_article","publication_identifier":{"issn":["2405-8963"]},"author":[{"id":"47427","orcid":"https://orcid.org/0000-0002-3389-793X","first_name":"Sebastian","last_name":"Peitz","full_name":"Peitz, Sebastian"},{"last_name":"Schäfer","first_name":"Kai","full_name":"Schäfer, Kai"},{"id":"16494","last_name":"Ober-Blöbaum","first_name":"Sina","full_name":"Ober-Blöbaum, Sina"},{"last_name":"Eckstein","first_name":"Julian","full_name":"Eckstein, Julian"},{"first_name":"Ulrich","last_name":"Köhler","full_name":"Köhler, Ulrich"},{"full_name":"Dellnitz, Michael","last_name":"Dellnitz","first_name":"Michael"}],"year":"2017","title":"A multiobjective MPC approach for autonomously driven electric vehicles","intvolume":"        50","article_type":"original","date_updated":"2022-01-21T13:58:41Z","publication_status":"published","language":[{"iso":"eng"}],"doi":"10.1016/j.ifacol.2017.08.1526","citation":{"ama":"Peitz S, Schäfer K, Ober-Blöbaum S, Eckstein J, Köhler U, Dellnitz M. A multiobjective MPC approach for autonomously driven electric vehicles. <i>Proceedings of the 20th World Congress of the International Federation of Automatic Control (IFAC)</i>. 2017;50(1):8674-8679. doi:<a href=\"https://doi.org/10.1016/j.ifacol.2017.08.1526\">10.1016/j.ifacol.2017.08.1526</a>","bibtex":"@article{Peitz_Schäfer_Ober-Blöbaum_Eckstein_Köhler_Dellnitz_2017, title={A multiobjective MPC approach for autonomously driven electric vehicles}, volume={50}, DOI={<a href=\"https://doi.org/10.1016/j.ifacol.2017.08.1526\">10.1016/j.ifacol.2017.08.1526</a>}, number={1}, journal={Proceedings of the 20th World Congress of the International Federation of Automatic Control (IFAC)}, author={Peitz, Sebastian and Schäfer, Kai and Ober-Blöbaum, Sina and Eckstein, Julian and Köhler, Ulrich and Dellnitz, Michael}, year={2017}, pages={8674–8679} }","mla":"Peitz, Sebastian, et al. “A Multiobjective MPC Approach for Autonomously Driven Electric Vehicles.” <i>Proceedings of the 20th World Congress of the International Federation of Automatic Control (IFAC)</i>, vol. 50, no. 1, 2017, pp. 8674–79, doi:<a href=\"https://doi.org/10.1016/j.ifacol.2017.08.1526\">10.1016/j.ifacol.2017.08.1526</a>.","chicago":"Peitz, Sebastian, Kai Schäfer, Sina Ober-Blöbaum, Julian Eckstein, Ulrich Köhler, and Michael Dellnitz. “A Multiobjective MPC Approach for Autonomously Driven Electric Vehicles.” <i>Proceedings of the 20th World Congress of the International Federation of Automatic Control (IFAC)</i> 50, no. 1 (2017): 8674–79. <a href=\"https://doi.org/10.1016/j.ifacol.2017.08.1526\">https://doi.org/10.1016/j.ifacol.2017.08.1526</a>.","short":"S. Peitz, K. Schäfer, S. Ober-Blöbaum, J. Eckstein, U. Köhler, M. Dellnitz, Proceedings of the 20th World Congress of the International Federation of Automatic Control (IFAC) 50 (2017) 8674–8679.","apa":"Peitz, S., Schäfer, K., Ober-Blöbaum, S., Eckstein, J., Köhler, U., &#38; Dellnitz, M. (2017). A multiobjective MPC approach for autonomously driven electric vehicles. <i>Proceedings of the 20th World Congress of the International Federation of Automatic Control (IFAC)</i>, <i>50</i>(1), 8674–8679. <a href=\"https://doi.org/10.1016/j.ifacol.2017.08.1526\">https://doi.org/10.1016/j.ifacol.2017.08.1526</a>","ieee":"S. Peitz, K. Schäfer, S. Ober-Blöbaum, J. Eckstein, U. Köhler, and M. Dellnitz, “A multiobjective MPC approach for autonomously driven electric vehicles,” <i>Proceedings of the 20th World Congress of the International Federation of Automatic Control (IFAC)</i>, vol. 50, no. 1, pp. 8674–8679, 2017, doi: <a href=\"https://doi.org/10.1016/j.ifacol.2017.08.1526\">10.1016/j.ifacol.2017.08.1526</a>."},"conference":{"start_date":"2017-07-09","end_date":"2017-07-14"},"status":"public","_id":"8756","page":"8674-8679","volume":50,"user_id":"15694"}]