@article{29399, author = {{Limebeer, D. J. N. and Ober-Blöbaum, Sina and Farshi, F. H.}}, journal = {{IEEE Transactions on Automatic Control}}, pages = {{1381--1396}}, title = {{{Variational integrators for dissipative systems}}}, volume = {{65(4)}}, year = {{2020}}, } @article{16297, abstract = {{In real-world problems, uncertainties (e.g., errors in the measurement, precision errors) often lead to poor performance of numerical algorithms when not explicitly taken into account. This is also the case for control problems, where optimal solutions can degrade in quality or even become infeasible. Thus, there is the need to design methods that can handle uncertainty. In this work, we consider nonlinear multi-objective optimal control problems with uncertainty on the initial conditions, and in particular their incorporation into a feedback loop via model predictive control (MPC). In multi-objective optimal control, an optimal compromise between multiple conflicting criteria has to be found. For such problems, not much has been reported in terms of uncertainties. To address this problem class, we design an offline/online framework to compute an approximation of efficient control strategies. This approach is closely related to explicit MPC for nonlinear systems, where the potentially expensive optimization problem is solved in an offline phase in order to enable fast solutions in the online phase. In order to reduce the numerical cost of the offline phase, we exploit symmetries in the control problems. Furthermore, in order to ensure optimality of the solutions, we include an additional online optimization step, which is considerably cheaper than the original multi-objective optimization problem. We test our framework on a car maneuvering problem where safety and speed are the objectives. The multi-objective framework allows for online adaptations of the desired objective. Alternatively, an automatic scalarizing procedure yields very efficient feedback controls. Our results show that the method is capable of designing driving strategies that deal better with uncertainties in the initial conditions, which translates into potentially safer and faster driving strategies.}}, author = {{Hernández Castellanos, Carlos Ignacio and Ober-Blöbaum, Sina and Peitz, Sebastian}}, journal = {{International Journal of Robust and Nonlinear Control}}, pages = {{7593--7618}}, title = {{{Explicit Multi-objective Model Predictive Control for Nonlinear Systems Under Uncertainty}}}, doi = {{10.1002/rnc.5197}}, volume = {{30(17)}}, year = {{2020}}, } @article{29398, author = {{Hernández Castellanos, C. I. O. and Schütze, G. and Sun, J.-Q. and Ober-Blöbaum, Sina and Morales-Luna, G.}}, journal = {{Mathematics}}, title = {{{Numerical computation of lightly multi-objective robust optimal solutions by means of generalized cell mapping}}}, volume = {{8(11):1959}}, year = {{2020}}, } @inproceedings{29422, author = {{Lishkova, Y. and Ober-Blöbaum, Sina and Cannon, M. and Leyendecker, S.}}, booktitle = {{Accepted for publication in Proceedings of 2020 AAS/AIAA Astrodynamics Specialist Conference - Lake Tahoe}}, title = {{{A multirate variational approach to simulation and optimal control for flexible spacecraft}}}, year = {{2020}}, } @inproceedings{29423, author = {{Faulwasser, T. and Flaßkamp, K. and Ober-Blöbaum, Sina and Worthmann, K. }}, booktitle = {{24th International Symposium on Mathematical Theory of Networks and Systems}}, title = {{{A dissipativity characterization of velocity turnpikes in optimal control problems for mechanical systems}}}, year = {{2020}}, } @inproceedings{29424, author = {{Cresson, J. and Jiménez, F. and Ober-Blöbaum, Sina}}, booktitle = {{24th International Symposium on Mathematical Theory of Networks and Systems}}, title = {{{Modelling of the convection-diffusion equation through fractional restricted calculus of variations}}}, year = {{2020}}, } @article{29526, author = {{van der Meer, R. and Renema, J. J. and Brecht, Benjamin and Silberhorn, Christine and Pinkse, P. W. H.}}, issn = {{2469-9926}}, journal = {{Physical Review A}}, number = {{6}}, publisher = {{American Physical Society (APS)}}, title = {{{Optimizing spontaneous parametric down-conversion sources for boson sampling}}}, doi = {{10.1103/physreva.101.063821}}, volume = {{101}}, year = {{2020}}, } @article{29545, author = {{Jean, Frédéric and Maslovskaya, Sofya and Zelenko, Igor}}, issn = {{0046-5755}}, journal = {{Geometriae Dedicata}}, keywords = {{Geometry and Topology}}, number = {{1}}, pages = {{295--314}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{On Weyl’s type theorems and genericity of projective rigidity in sub-Riemannian geometry}}}, doi = {{10.1007/s10711-020-00581-z}}, volume = {{213}}, year = {{2020}}, } @inproceedings{29546, author = {{Maslovskaya, Sofya and Caillau, Jean-Baptiste and Djema, Walid and Giraldi, Laetitia and Jean-Luc, Jean-Luc and Pomet, Jean-Baptiste}}, title = {{{The turnpike property in maximization of microbial metabolite production}}}, year = {{2020}}, } @inproceedings{20813, author = {{Caillau, Jean-Baptiste and Maslovskaya, Sofya and Mensch, Thomas and Moulinier, Timothee and Pomet, Jean-Baptiste}}, booktitle = {{2019 IEEE 58th Conference on Decision and Control (CDC)}}, isbn = {{9781728113982}}, title = {{{Zermelo-Markov-Dubins problem and extensions in marine navigation}}}, doi = {{10.1109/cdc40024.2019.9029293}}, year = {{2020}}, }