@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 = {IFAC-PapersOnLine},
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},
}
@article{16657,
author = {Peitz, Sebastian and Schäfer, Kai and Ober-Blöbaum, Sina and Eckstein, Julian and Köhler, Ulrich and Dellnitz, Michael},
issn = {2405-8963},
journal = {IFAC-PapersOnLine},
pages = {8674--8679},
title = {{A Multiobjective MPC Approach for Autonomously Driven Electric Vehicles * *This research was funded by the German Federal Ministry of Education and Research (BMBF) within the Leading-Edge Cluster Intelligent Technical Systems OstWestfalenLippe (it’s OWL).}},
doi = {10.1016/j.ifacol.2017.08.1526},
year = {2017},
}
@inproceedings{8752,
abstract = {In this article we develop a gradient-based algorithm for the solution of multiobjective optimization problems with uncertainties. To this end, an additional condition is derived for the descent direction in order to account for inaccuracies in the gradients and then incorporated into a subdivision algorithm for the computation of global solutions to multiobjective optimization problems. Convergence to a superset of the Pareto set is proved and an upper bound for the maximal distance to the set of substationary points is given. Besides the applicability to problems with uncertainties, the algorithm is developed with the intention to use it in combination with model order reduction techniques in order to efficiently solve PDE-constrained multiobjective optimization problems.},
author = {Peitz, Sebastian and Dellnitz, Michael},
booktitle = {NEO 2016},
isbn = {9783319640624},
issn = {1860-949X},
pages = {159--182},
title = {{Gradient-Based Multiobjective Optimization with Uncertainties}},
doi = {10.1007/978-3-319-64063-1_7},
year = {2017},
}
@inproceedings{7767,
author = {Schumacher, Jan},
booktitle = {Beiträge zum Mathematikunterricht 2017},
editor = {Kortenkamp, Ulrich and Kuzle, Ana},
publisher = {WTM-Verlag},
title = {{Sinnkonstruktion beim Erkunden von Mustern und Strukturen}},
year = {2017},
}
@inbook{8570,
author = {Liebendörfer, Michael and Hochmuth, Reinhard and Biehler, Rolf and Schaper, Niclas and Kuklinski, Christiane and Khellaf, Sarah and Colberg, Christoph and Schürmann, Mirko and Rothe, Lukas},
booktitle = {Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME10, February 1 – 5, 2017)},
editor = {Dooley, T. and Gueudet, Ghislaine},
keyword = {Ziele der Lehre},
pages = {2177--2184},
publisher = {DCU Institute of Education & ERME},
title = {{A framework for goal dimensions of mathematics learning support in universities}},
year = {2017},
}
@article{16540,
author = {Dellnitz, Michael and Klus, Stefan},
issn = {1468-9367},
journal = {Dynamical Systems},
pages = {61--79},
title = {{Sensing and control in symmetric networks}},
doi = {10.1080/14689367.2016.1215410},
year = {2017},
}
@article{8564,
author = {Liebendörfer, Michael and Schukajlow, Stanislaw},
issn = {1863-9690, 1863-9704},
journal = {ZDM},
number = {3},
pages = {355--366},
title = {{Interest development during the first year at university: do mathematical beliefs predict interest in mathematics?}},
doi = {10.1007/s11858-016-0827-3},
volume = {49},
year = {2017},
}
@phdthesis{10594,
abstract = {Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute
the set of optimal compromises (the Pareto set) between the conflicting objectives.
Since – in contrast to the solution of a single objective optimization problem – the
Pareto set generally consists of an infinite number of solutions, the computational
effort can quickly become challenging. This is even more the case when many problems have to be solved, when the number of objectives is high, or when the objectives
are costly to evaluate. Consequently, this thesis is devoted to the identification and
exploitation of structure both in the Pareto set and the dynamics of the underlying
model as well as to the development of efficient algorithms for solving problems with
additional parameters, with a high number of objectives or with PDE-constraints.
These three challenges are addressed in three respective parts.
In the first part, predictor-corrector methods are extended to entire Pareto sets.
When certain smoothness assumptions are satisfied, then the set of parameter dependent Pareto sets possesses additional structure, i.e. it is a manifold. The tangent
space can be approximated numerically which yields a direction for the predictor
step. In the corrector step, the predicted set converges to the Pareto set at a new
parameter value. The resulting algorithm is applied to an example from autonomous
driving.
In the second part, the hierarchical structure of Pareto sets is investigated. When
considering a subset of the objectives, the resulting solution is a subset of the Pareto
set of the original problem. Under additional smoothness assumptions, the respective subsets are located on the boundary of the Pareto set of the full problem. This
way, the “skeleton” of a Pareto set can be computed and due to the exponential
increase in computing time with the number of objectives, the computations of
these subsets are significantly faster which is demonstrated using an example from
industrial laundries.
In the third part, PDE-constrained multiobjective optimal control problems are
addressed by reduced order modeling methods. Reduced order models exploit the
structure in the system dynamics, for example by describing the dynamics of only the
most energetic modes. The model reduction introduces an error in both the function values and their gradients, which has to be taken into account in the development of
algorithms. Both scalarization and set-oriented approaches are coupled with reduced
order modeling. Convergence results are presented and the numerical benefit is
investigated. The algorithms are applied to semi-linear heat flow problems as well
as to the Navier-Stokes equations.
},
author = {Peitz, Sebastian},
title = {{ Exploiting structure in multiobjective optimization and optimal control}},
year = {2017},
}
@inproceedings{7765,
author = {Schumacher, Jan},
booktitle = {Beiträge zum Mathematikunterricht 2016},
publisher = {WTM-Verlag},
title = {{Erkunden mathematischer Strukturen anstatt Interpretation in Modellen – Ein innermathematischer Zugang zu negativen Zahlen}},
year = {2016},
}
@inproceedings{8566,
author = {Göller, Robin and Liebendörfer, Michael},
booktitle = {Beiträge zum Mathematikunterricht 2016},
editor = {für Didaktik der Mathematik, Gesellschaft},
keyword = {\_tablet, Abschreiben},
pages = {321--324},
publisher = {WTM-Verlag für wissenschaftliche Texte und Medien},
title = {{Eine alternative Einstiegsvorlesung in die Fachmathematik – Konzept und Auswirkungen}},
doi = {http://dx.doi.org/10.17877/DE290R-17398},
year = {2016},
}
@inbook{16579,
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 = {Mathematics in Industry},
isbn = {9783319234120},
issn = {1612-3956},
title = {{Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control}},
doi = {10.1007/978-3-319-23413-7_87},
year = {2016},
}
@inbook{8555,
author = {Kolter, Jana and Liebendörfer, Michael and Schukajlow, Stanislaw},
booktitle = {Lehren und Lernen von Mathematik in der Studieneingangsphase},
editor = {Hoppenbrock, Axel and Biehler, Rolf and Hochmuth, Reinhard and Rück, Hans-Georg},
isbn = {978-3-658-10260-9 978-3-658-10261-6},
pages = {567--583},
publisher = {Springer Fachmedien Wiesbaden},
title = {{Mathe – nein danke? Interesse, Beliefs und Lernstrategien im Mathematikstudium bei Grundschullehramtsstudierenden mit Pflichtfach}},
year = {2016},
}
@inproceedings{8562,
author = {Colberg, Christoph and Biehler, Rolf and Hochmuth, Reinhard and Schaper, Niclas and Liebendörfer, Michael and Schürmann, Mirko},
booktitle = {Beiträge zum Mathematikunterricht 2016},
pages = {213--216},
publisher = {WTM-Verlag für wissenschaftliche Texte und Medien},
title = {{Wirkung und Gelingensbedingungen von Unterstützungsmaßnahmen für mathematikbezogenes Lernen in der Studieneingangsphase}},
doi = {http://dx.doi.org/10.17877/DE290R-17376},
year = {2016},
}
@article{8567,
author = {Liebendörfer, Michael and Göller, Robin},
journal = {Mitteilungen der Deutschen Mathematiker-Vereinigung},
keyword = {\_tablet, Abschreiben},
number = {4},
pages = {230--233},
title = {{Abschreiben von Übungsaufgaben in traditionellen und innovativen Mathematikvorlesungen}},
volume = {24},
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 Molo, Mirko Hessel-von and Ober-Blöbaum, Sina and Dellnitz, Michael},
booktitle = {Procedia Technology},
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},
year = {2016},
}
@phdthesis{33,
abstract = {Lightweight materials play an ever growing role in today's world. Saving on the mass of a machine will usually translate into a lower energy consumption. However, lightweight applications are prone to develop performance problems due to vibration induced by the operation of the machine. The Fraunhofer Institute for Manufacturing Technology and Advanced Materials in Dresden conducts research into the damping properties of composite materials. They are experimenting with hollow, particle filled spheres embedded in the lightweight material. Such a system is the technical motivation of this thesis. Ultimately, a numerical experiment to derive the coefficient of restitution is required. The simulation developed in this thesis is based on a discrete element method to track the individual particle and sphere trajectories. Based on a potential based approach for the particle interactions deployed in molecular dynamics, the behavior of the particles can be controlled effectively. The simulated volume is using reflecting boundaries and encloses the hollow sphere. In this work, a highly flexible memory structure was used with a linked cell approach to cope with the highly flexible mass of particles. This allows for a linear complexity of the method in regard to the particle number by reducing the computational overhead of the interaction computation. Multiple numerical experiments show the great effect the particles have on the damping behavior of the system.},
author = {Steinle, Tobias},
title = {{Modeling and simulation of metallic, particle-damped spheres for lightweight materials}},
year = {2016},
}
@inproceedings{6570,
author = {Jurgelucks, Benjamin and Claes, Leander},
booktitle = {AD2016 The 7th International Conference on Algorithmic Differentiation},
location = {Christ Church, Oxford, United Kingdom},
pages = {99--102},
title = {{Optimisation of triple-ring-electrodes on piezoceramic transducers using algorithmic differentiation}},
year = {2016},
}
@inproceedings{8759,
abstract = {In a wide range of applications, it is desirable to optimally control a 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 it is not possible to compute the entire control trajectory in advance, for instance due to uncertainties or unforeseeable events, model predictive control methods can be applied to control the system during operation in real time. In this article, we present an algorithm for the solution of multiobjective model predictive control problems. In an offline scenario, it can be used to compute the entire set of optimal compromises whereas in a real time scenario, one optimal compromise is computed according to an operator's preference. The results are illustrated using the example of an industrial laundry. A logistics model of the laundry is developed and then utilized in the optimization routine. Results are presented for an offline as well as an online scenario.},
author = {Peitz, Sebastian and Gräler, Manuel and Henke, Christian and Molo, Mirko Hessel-von and Dellnitz, Michael and Trächtler, Ansgar},
booktitle = {Procedia Technology},
issn = {2212-0173},
pages = {483--490},
title = {{Multiobjective Model Predictive Control of an Industrial Laundry}},
doi = {10.1016/j.protcy.2016.08.061},
year = {2016},
}
@article{16580,
author = {Ziessler, Adrian and Molo, Mirko Hessel-Von and Dellnitz, Michael},
issn = {2158-2491},
journal = {Journal of Computational Dynamics},
pages = {5--5},
title = {{On the computation of attractors for delay differential equations}},
doi = {10.3934/jcd.2016005},
year = {2016},
}
@inproceedings{34,
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},
issn = {2212-0173},
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},
volume = {22},
year = {2016},
}