TY - JOUR
AU - Peitz, Sebastian
AU - Schäfer, Kai
AU - Ober-Blöbaum, Sina
AU - Eckstein, Julian
AU - Köhler, Ulrich
AU - Dellnitz, Michael
ID - 16657
JF - IFAC-PapersOnLine
SN - 2405-8963
TI - 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).
ER -
TY - JOUR
AU - Bittracher, Andreas
AU - Koltai, Péter
AU - Klus, Stefan
AU - Banisch, Ralf
AU - Dellnitz, Michael
AU - Schütte, Christof
ID - 16715
JF - Journal of Nonlinear Science
SN - 0938-8974
TI - Transition Manifolds of Complex Metastable Systems
ER -
TY - CONF
AB - 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.
AU - Peitz, Sebastian
AU - Dellnitz, Michael
ID - 8752
SN - 1860-949X
T2 - NEO 2016
TI - Gradient-Based Multiobjective Optimization with Uncertainties
ER -
TY - CONF
AU - Schumacher, Jan
ED - Kortenkamp, Ulrich
ED - Kuzle, Ana
ID - 7767
T2 - Beiträge zum Mathematikunterricht 2017
TI - Sinnkonstruktion beim Erkunden von Mustern und Strukturen
ER -
TY - CHAP
AU - Liebendörfer, Michael
AU - Hochmuth, Reinhard
AU - Biehler, Rolf
AU - Schaper, Niclas
AU - Kuklinski, Christiane
AU - Khellaf, Sarah
AU - Colberg, Christoph
AU - Schürmann, Mirko
AU - Rothe, Lukas
ED - Dooley, T.
ED - Gueudet, Ghislaine
ID - 8570
KW - Ziele der Lehre
T2 - Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME10, February 1 – 5, 2017)
TI - A framework for goal dimensions of mathematics learning support in universities
ER -
TY - JOUR
AU - Dellnitz, Michael
AU - Klus, Stefan
ID - 16540
JF - Dynamical Systems
SN - 1468-9367
TI - Sensing and control in symmetric networks
ER -
TY - JOUR
AU - Liebendörfer, Michael
AU - Schukajlow, Stanislaw
ID - 8564
IS - 3
JF - ZDM
SN - 1863-9690, 1863-9704
TI - Interest development during the first year at university: do mathematical beliefs predict interest in mathematics?
VL - 49
ER -
TY - THES
AB - 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.
AU - Peitz, Sebastian
ID - 10594
TI - Exploiting structure in multiobjective optimization and optimal control
ER -
TY - CONF
AU - Schumacher, Jan
ID - 7765
T2 - Beiträge zum Mathematikunterricht 2016
TI - Erkunden mathematischer Strukturen anstatt Interpretation in Modellen – Ein innermathematischer Zugang zu negativen Zahlen
ER -
TY - CONF
AU - Göller, Robin
AU - Liebendörfer, Michael
ED - für Didaktik der Mathematik, Gesellschaft
ID - 8566
KW - \_tablet
KW - Abschreiben
T2 - Beiträge zum Mathematikunterricht 2016
TI - Eine alternative Einstiegsvorlesung in die Fachmathematik – Konzept und Auswirkungen
ER -
TY - CHAP
AU - Dellnitz, Michael
AU - Eckstein, Julian
AU - Flaßkamp, Kathrin
AU - Friedel, Patrick
AU - Horenkamp, Christian
AU - Köhler, Ulrich
AU - Ober-Blöbaum, Sina
AU - Peitz, Sebastian
AU - Tiemeyer, Sebastian
ID - 16579
SN - 1612-3956
T2 - Mathematics in Industry
TI - Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control
ER -
TY - CHAP
AU - Kolter, Jana
AU - Liebendörfer, Michael
AU - Schukajlow, Stanislaw
ED - Hoppenbrock, Axel
ED - Biehler, Rolf
ED - Hochmuth, Reinhard
ED - Rück, Hans-Georg
ID - 8555
SN - 978-3-658-10260-9 978-3-658-10261-6
T2 - Lehren und Lernen von Mathematik in der Studieneingangsphase
TI - Mathe – nein danke? Interesse, Beliefs und Lernstrategien im Mathematikstudium bei Grundschullehramtsstudierenden mit Pflichtfach
ER -
TY - CONF
AU - Colberg, Christoph
AU - Biehler, Rolf
AU - Hochmuth, Reinhard
AU - Schaper, Niclas
AU - Liebendörfer, Michael
AU - Schürmann, Mirko
ID - 8562
T2 - Beiträge zum Mathematikunterricht 2016
TI - Wirkung und Gelingensbedingungen von Unterstützungsmaßnahmen für mathematikbezogenes Lernen in der Studieneingangsphase
ER -
TY - JOUR
AU - Liebendörfer, Michael
AU - Göller, Robin
ID - 8567
IS - 4
JF - Mitteilungen der Deutschen Mathematiker-Vereinigung
KW - \_tablet
KW - Abschreiben
TI - Abschreiben von Übungsaufgaben in traditionellen und innovativen Mathematikvorlesungen
VL - 24
ER -
TY - CONF
AB - 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.
AU - Eckstein, Julian
AU - Peitz, Sebastian
AU - Schäfer, Kai
AU - Friedel, Patrick
AU - Köhler, Ulrich
AU - Molo, Mirko Hessel-von
AU - Ober-Blöbaum, Sina
AU - Dellnitz, Michael
ID - 8758
SN - 2212-0173
T2 - Procedia Technology
TI - A Comparison of two Predictive Approaches to Control the Longitudinal Dynamics of Electric Vehicles
ER -
TY - THES
AB - 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.
AU - Steinle, Tobias
ID - 33
TI - Modeling and simulation of metallic, particle-damped spheres for lightweight materials
ER -
TY - CONF
AU - Jurgelucks, Benjamin
AU - Claes, Leander
ID - 6570
T2 - AD2016 The 7th International Conference on Algorithmic Differentiation
TI - Optimisation of triple-ring-electrodes on piezoceramic transducers using algorithmic differentiation
ER -
TY - CONF
AB - 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.
AU - Peitz, Sebastian
AU - Gräler, Manuel
AU - Henke, Christian
AU - Molo, Mirko Hessel-von
AU - Dellnitz, Michael
AU - Trächtler, Ansgar
ID - 8759
SN - 2212-0173
T2 - Procedia Technology
TI - Multiobjective Model Predictive Control of an Industrial Laundry
ER -
TY - JOUR
AU - Ziessler, Adrian
AU - Molo, Mirko Hessel-Von
AU - Dellnitz, Michael
ID - 16580
JF - Journal of Computational Dynamics
SN - 2158-2491
TI - On the computation of attractors for delay differential equations
ER -
TY - CONF
AU - Dellnitz, Michael
AU - Eckstein, Julian
AU - Flaßkamp, Kathrin
AU - Friedel, Patrick
AU - Horenkamp, Christian
AU - Köhler, Ulrich
AU - Ober-Blöbaum, Sina
AU - Peitz, Sebastian
AU - Tiemeyer, Sebastian
ID - 34
SN - 2212-0173
T2 - Progress in Industrial Mathematics at ECMI
TI - Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control
VL - 22
ER -