@inproceedings{29867,
  author       = {{Faulwasser, Tim and Flaßkamp, K. and Ober-Blöbaum, Sina and Worthmann, Karl}},
  pages        = {{490--495}},
  title        = {{{Towards velocity turnpikes in optimal control of mechanical systems}}},
  volume       = {{52(16)}},
  year         = {{2019}},
}

@article{8753,
  abstract     = {{In a wide range of applications it is desirable to optimally control a dynamical system with respect to concurrent, potentially competing goals. This gives rise to a multiobjective optimal control problem where, instead of computing a single optimal solution, the set of optimal compromises, the so-called Pareto set, has to be approximated. When the problem under consideration is described by a partial differential equation (PDE), as is the case for fluid flow, the computational cost rapidly increases and makes its direct treatment infeasible. Reduced order modeling is a very popular method to reduce the computational cost, in particular in a multi query context such as uncertainty quantification, parameter estimation or optimization. In this article, we show how to combine reduced order modeling and multiobjective optimal control techniques in order to efficiently solve multiobjective optimal control problems constrained by PDEs. We consider a global, derivative free optimization method as well as a local, gradient-based approach for which the optimality system is derived in two different ways. The methods are compared with regard to the solution quality as well as the computational effort and they are illustrated using the example of the flow around a cylinder and a backward-facing-step channel flow.}},
  author       = {{Peitz, Sebastian and Ober-Blöbaum, Sina and Dellnitz, Michael}},
  issn         = {{0167-8019}},
  journal      = {{Acta Applicandae Mathematicae}},
  number       = {{1}},
  pages        = {{171–199}},
  title        = {{{Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling}}},
  doi          = {{10.1007/s10440-018-0209-7}},
  volume       = {{161}},
  year         = {{2018}},
}

@article{20112,
  author       = {{Reniers, J.M. and Mulder, G. and Ober-Blöbaum, Sina and Howe, D.A.}},
  issn         = {{0378-7753}},
  journal      = {{Journal of Power Sources}},
  pages        = {{91 -- 102}},
  title        = {{{Improving optimal control of grid-connected lithium-ion batteries through more accurate battery and degradation modelling}}},
  doi          = {{https://doi.org/10.1016/j.jpowsour.2018.01.004}},
  volume       = {{379}},
  year         = {{2018}},
}

@inproceedings{29425,
  author       = {{Jiménez, F. and Ober-Blöbaum, Sina}},
  booktitle    = {{6th European Conference on Computational Mechanics}},
  title        = {{{Necessary optimality conditions for optimally controlled dissipative mechanical systems modelled through fractional derivatives}}},
  year         = {{2018}},
}

@inproceedings{29427,
  author       = {{Jiménez, F. and Ober-Blöbaum, Sina}},
  booktitle    = {{6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2018}},
  pages        = {{50--55}},
  title        = {{{A fractional variational approach for modelling dissipative mechanical systems continuous and discrete settings}}},
  volume       = {{51(3)}},
  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}},
}