@unpublished{19940, abstract = {{Two smooth map germs are right-equivalent if and only if they generate two Lagrangian submanifolds in a cotangent bundle which have the same contact with the zero-section. In this paper we provide a reverse direction to this classical result of Golubitsky and Guillemin. Two Lagrangian submanifolds of a symplectic manifold have the same contact with a third Lagrangian submanifold if and only if the intersection problems correspond to stably right equivalent map germs. We, therefore, obtain a correspondence between local Lagrangian intersection problems and catastrophe theory while the classical version only captures tangential intersections. The correspondence is defined independently of any Lagrangian fibration of the ambient symplectic manifold, in contrast to other classical results. Moreover, we provide an extension of the correspondence to families of local Lagrangian intersection problems. This gives rise to a framework which allows a natural transportation of the notions of catastrophe theory such as stability, unfolding and (uni-)versality to the geometric setting such that we obtain a classification of families of local Lagrangian intersection problems. An application is the classification of Lagrangian boundary value problems for symplectic maps.}}, author = {{Offen, Christian}}, booktitle = {{arXiv:1811.10165}}, title = {{{Local intersections of Lagrangian manifolds correspond to catastrophe theory}}}, year = {{2018}}, } @article{19943, abstract = {{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. }}, author = {{McLachlan, Robert I and Offen, Christian}}, journal = {{New Zealand Journal of Mathematics}}, keywords = {{Hamiltonian boundary value problems, singularities, conformal symplectic geometry, catastrophe theory, conjugate loci}}, pages = {{83--99}}, title = {{{Hamiltonian boundary value problems, conformal symplectic symmetries, and conjugate loci}}}, doi = {{10.53733/34 }}, volume = {{48}}, year = {{2018}}, } @inproceedings{5914, abstract = {{During the last years, alternative drive technologies, for example electrically powered vehicles (EV), have gained more and more attention, mainly caused by an increasing awareness of the impact of CO2 emissions on climate change and by the limitation of fossil fuels. However, these technologies currently come with new challenges due to limited lithium ion battery storage density and high battery costs which lead to a considerably reduced range in comparison to conventional internal combustion engine powered vehicles. For this reason, it is desirable to increase the vehicle range without enlarging the battery. When the route and the road slope are known in advance, it is possible to vary the vehicles velocity within certain limits in order to reduce the overall drivetrain energy consumption. This may either result in an increased range or, alternatively, in larger energy reserves for comfort functions such as air conditioning. In this presentation, we formulate the challenge of range extension as a multiobjective optimal control problem. We then apply different numerical methods to calculate the so-called Pareto set of optimal compromises for the drivetrain power profile with respect to the two concurrent objectives battery state of charge and mean velocity. In order to numerically solve the optimal control problem by means of a direct method, a time discretization of the drivetrain power profile is necessary. In combination with a vehicle dynamics simulation model, the optimal control problem is transformed into a high dimensional nonlinear optimization problem. For the approximation of the Pareto set, two different optimization algorithms implemented in the software package GAIO are used. The first one yields a global optimal solution by applying a set-oriented subdivision technique to parameter space. By construction, this technique is limited to coarse discretizations of the drivetrain power profile. In contrast, the second technique, which is based on an image space continuation method, is more suitable when the number of parameters is large while the number of objectives is less than five. We compare the solutions of the two algorithms and study the influence of different discretizations on the quality of the solutions. A MATLAB/Simulink model is used to describe the dynamics of an EV. It is based on a drivetrain efficiency map and considers vehicle properties such as rolling friction and air drag, as well as environmental conditions like slope and ambient temperature. The vehicle model takes into account the traction battery too, enabling an exact prediction of the batterys response to power requests of drivetrain and auxiliary loads, including state of charge.}}, author = {{Dellnitz, Michael and Eckstein, Julian and Flaßkamp, Kathrin and Friedel, Patrick and Horenkamp, Christian and Köhler, Ulrich and Ober-Blöbaum, Sina and Peitz, Sebastian and Tiemeyer, Sebastian}}, booktitle = {{Progress in Industrial Mathematics at ECMI 2014 }}, isbn = {{9783319234120}}, issn = {{1612-3956}}, pages = {{633--641}}, publisher = {{Springer International Publishing}}, title = {{{Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control}}}, doi = {{10.1007/978-3-319-23413-7_87}}, year = {{2017}}, } @article{20061, author = {{Mergel, J.C. and Sauer, R.A. and Ober-Blöbaum, Sina}}, issn = {{1521-4001}}, journal = {{ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik}}, pages = {{433--457}}, title = {{{C1-continuous space-time discretization based on Hamilton's law of varying action}}}, doi = {{10.1002/zamm.201600062}}, volume = {{97(4)}}, year = {{2017}}, } @article{20091, author = {{Wenger, T. and Ober-Blöbaum, Sina and Leyendecker, S.}}, journal = {{Advances in Computational Mathematics}}, pages = {{1163--1195}}, title = {{{Construction and analysis of higher order variational integrators for dynamical systems with holonomic constraints}}}, doi = {{10.1007/s10444-017-9520-5}}, volume = {{43(5)}}, year = {{2017}}, } @article{20059, author = {{Ober-Blöbaum, Sina}}, journal = {{IMA Journal of Numerical Analysis}}, pages = {{375--406}}, title = {{{Galerkin variational integrators and modified symplectic Runge-Kutta methods}}}, doi = {{10.1093/imanum/drv062}}, volume = {{37(1)}}, year = {{2017}}, } @article{20093, author = {{Stellato, B, and Ober-Blöbaum, Sina and Goulart, P.J.}}, journal = {{IEEE Transactions on Automatic Control}}, pages = {{5407--5414}}, title = {{{Second-order switching time optimization for switched dynamical systems}}}, volume = {{62(10)}}, year = {{2017}}, } @article{8756, abstract = {{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.}}, author = {{Peitz, Sebastian and Schäfer, Kai and Ober-Blöbaum, Sina and Eckstein, Julian and Köhler, Ulrich and Dellnitz, Michael}}, issn = {{2405-8963}}, journal = {{Proceedings of the 20th World Congress of the International Federation of Automatic Control (IFAC)}}, number = {{1}}, pages = {{8674--8679}}, title = {{{A multiobjective MPC approach for autonomously driven electric vehicles}}}, doi = {{10.1016/j.ifacol.2017.08.1526}}, volume = {{50}}, year = {{2017}}, } @inproceedings{29430, author = {{Gail, T. and Ober-Blöbaum, Sina and Leyendecker, S. }}, booktitle = {{ECCOMAS Thematic Conference on Multibody Dynamics}}, title = {{{Variational multirate integration in discrete mechanics and optimal control}}}, year = {{2017}}, } @article{20106, author = {{Wenger, T. and Ober-Blöbaum, Sina and Leyendecker, S.}}, journal = {{PAMM}}, number = {{1}}, publisher = {{WILEY-VCH Verlag}}, title = {{{Variational integrators of mixed order for constrained and unconstrained systems acting on multiple time scales}}}, doi = {{10.1002/pamm.201710057}}, volume = {{17}}, year = {{2017}}, } @article{20060, author = {{Ringkamp, M. and Ober-Blöbaum, Sina and Leyendecker, S.}}, journal = {{Mathematical Programming}}, pages = {{1--31}}, title = {{{On the time transformation of mixed integer optimal control problems using a consistent fixed integer control function}}}, doi = {{10.1007/s10107-016-1023-5}}, year = {{2016}}, } @inproceedings{8758, abstract = {{In this contribution we compare two different approaches to the implementation of a Model Predictive Controller in an electric vehicle with respect to the quality of the solution and real-time applicability. The goal is to develop an intelligent cruise control in order to extend the vehicle range, i.e. to minimize energy consumption, by computing the optimal torque profile for a given track. On the one hand, a path-based linear model with strong simplifications regarding the vehicle dynamics is used. On the other hand, a nonlinear model is employed in which the dynamics of the mechanical and electrical subsystem are modeled.}}, author = {{Eckstein, Julian and Peitz, Sebastian and Schäfer, Kai and Friedel, Patrick and Köhler, Ulrich and Hessel von Molo, Mirko and Ober-Blöbaum, Sina and Dellnitz, Michael}}, booktitle = {{Procedia Technology, 3rd International Conference on System-Integrated Intelligence: New Challenges for Product and Production Engineering}}, issn = {{2212-0173}}, pages = {{465--472}}, title = {{{A comparison of two predictive approaches to control the longitudinal dynamics of electric vehicles}}}, doi = {{10.1016/j.protcy.2016.08.059}}, volume = {{26}}, year = {{2016}}, } @inproceedings{29435, author = {{Wenger, T. and Ober-Blöbaum, Sina and Leyendecker, S. }}, booktitle = {{ECCOMAS Congress 2016 - Proceedings of the 7th European Congress on Computational Methods in Applied Sciences and Engineering}}, pages = {{1818--1831}}, title = {{{Variational integrators of mixed order for dynamical systems with multiple time scales and split potentials}}}, year = {{2016}}, } @inproceedings{29432, author = {{Wenger, T. and Ober-Blöbaum, Sina and Leyendecker, S. }}, booktitle = {{International Conference of Numerical Analysis and Applied Mathematics (ICNAAM)}}, title = {{{Constrained Galerkin variational integrators and modified constrained symplectic Runge-Kutta methods}}}, year = {{2016}}, } @inproceedings{29433, author = {{Peitz, Sebastian and Ober-Blöbaum, Sina and Dellnitz, M.}}, booktitle = {{Proceedings of International Congress of Theoretical and Applied Mechanics}}, title = {{{Reduced order model based multiobjective optimal control of fluids}}}, year = {{2016}}, } @inproceedings{29436, author = {{Stellato, B. and Ober-Blöbaum, Sina and Goulart, P.J. }}, booktitle = {{2016 IEEE 55th Conference on Decision and Control (CDC)}}, pages = {{7228--7233}}, title = {{{Optimal control of switching times in switched linear systems}}}, year = {{2016}}, } @article{20101, author = {{Wenger, T. and Ober-Blöbaum, Sina and Leyendecker, S.}}, issn = {{1617-7061}}, journal = {{PAMM}}, pages = {{775--776}}, publisher = {{WILEY-VCH Verlag}}, title = {{{Variational integrators of higher order for constrained dynamical systems}}}, doi = {{10.1002/pamm.201610376}}, volume = {{16(1)}}, year = {{2016}}, } @article{20105, author = {{Mergel, J.C. and Sauer, R.A. and Ober-Blöbaum, Sina}}, issn = {{1617-7061}}, journal = {{PAMM}}, pages = {{753--754}}, publisher = {{WILEY-VCH Verlag}}, title = {{{C1-continuous time integration based on cubic Hermite interpolation}}}, doi = {{10.1002/pamm.201610365}}, volume = {{16(1)}}, year = {{2016}}, } @article{20103, author = {{Ringkamp, M. and Ober-Blöbaum, Sina and Leyendecker, S.}}, issn = {{1617-7061}}, journal = {{PAMM}}, pages = {{789--790}}, publisher = {{WILEY-VCH Verlag}}, title = {{{Time transformed mixed integer optimal control problems with impacts}}}, doi = {{10.1002/pamm.201610383}}, volume = {{16(1)}}, year = {{2016}}, } @article{20104, author = {{Ober-Blöbaum, Sina}}, issn = {{1617-7061}}, journal = {{PAMM}}, pages = {{821--822}}, publisher = {{WILEY-VCH Verlag}}, title = {{{Higher order variational integrators in optimal control theory}}}, doi = {{10.1002/pamm.201610399}}, volume = {{16(1)}}, year = {{2016}}, }