Learning of discrete models of variational PDEs from data - Offen, Christian; Ober-Blöbaum, Sina (Chaos)
We show how to learn discrete field theories from observational data of fields on a space-time lattice. For this, we train a neural network model of a discrete Lagrangian density such that the discrete Euler--Lagrange equations are consistent with the given training data. We, thus, obtain a structure-preserving machine learning architecture. Lagrangian densities are not uniquely defined by the solutions of a field theory. We introduce a technique to derive regularisers for the training process which optimise numerical regularity of the discrete field theory. Minimisation of the regularisers guarantees that close to the training data the discrete field theory behaves robust and efficient when used in numerical simulations. Further, we show how to identify structurally simple solutions of the underlying continuous field theory such as travelling waves. This is possible even when travelling waves are not present in the training data. This is compared to data-driven model order reduction based approaches, which struggle to identify suitable latent spaces containing structurally simple solutions when these are not present in the training data. Ideas are demonstrated on examples based on the wave equation and the Schrödinger equation.

A new Lagrangian approach to control affine systems with a quadratic Lagrange term - Leyendecker, Sigrid; Maslovskaya, Sofya; Ober-Blöbaum, Sina; Almagro, Rodrigo T. Sato Martín de; Szemenyei, Flóra Orsolya (Journal of Computational Dynamics)
In this work, we consider optimal control problems for mechanical systems with fixed initial and free final state and a quadratic Lagrange term. Specifically, the dynamics is described by a second order ODE containing an affine control term. Classically, Pontryagin's maximum principle gives necessary optimality conditions for the optimal control problem. For smooth problems, alternatively, a variational approach based on an augmented objective can be followed. Here, we propose a new Lagrangian approach leading to equivalent necessary optimality conditions in the form of Euler-Lagrange equations. Thus, the differential geometric structure (similar to classical Lagrangian dynamics) can be exploited in the framework of optimal control problems. In particular, the formulation enables the symplectic discretisation of the optimal control problem via variational integrators in a straightforward way.
Keywords: Optimal control problem; Lagrangian system; Hamiltonian system; Variations; Pontryagin's maximum principle.

Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves - Offen, Christian; Ober-Blöbaum, Sina (Geometric Science of Information)
The article shows how to learn models of dynamical systems from data which are governed by an unknown variational PDE. Rather than employing reduction techniques, we learn a discrete field theory governed by a discrete Lagrangian density $L_d$ that is modelled as a neural network. Careful regularisation of the loss function for training $L_d$ is necessary to obtain a field theory that is suitable for numerical computations: we derive a regularisation term which optimises the solvability of the discrete Euler--Lagrange equations. Secondly, we develop a method to find solutions to machine learned discrete field theories which constitute travelling waves of the underlying continuous PDE.
Keywords: System identification; discrete Lagrangians; travelling waves

Variational Learning of Euler–Lagrange Dynamics from Data - Ober-Blöbaum, Sina; Offen, Christian (Journal of Computational and Applied Mathematics)
The principle of least action is one of the most fundamental physical principle. It says that among all possible motions connecting two points in a phase space, the system will exhibit those motions which extremise an action functional. Many qualitative features of dynamical systems, such as the presence of conservation laws and energy balance equations, are related to the existence of an action functional. Incorporating variational structure into learning algorithms for dynamical systems is, therefore, crucial in order to make sure that the learned model shares important features with the exact physical system. In this paper we show how to incorporate variational principles into trajectory predictions of learned dynamical systems. The novelty of this work is that (1) our technique relies only on discrete position data of observed trajectories. Velocities or conjugate momenta do not need to be observed or approximated and no prior knowledge about the form of the variational principle is assumed. Instead, they are recovered using backward error analysis. (2) Moreover, our technique compensates discretisation errors when trajectories are computed from the learned system. This is important when moderate to large step-sizes are used and high accuracy is required. For this, we introduce and rigorously analyse the concept of inverse modified Lagrangians by developing an inverse version of variational backward error analysis. (3) Finally, we introduce a method to perform system identification from position observations only, based on variational backward error analysis.
Keywords: Lagrangian learning; variational backward error analysis; modified Lagrangian; variational integrators; physics informed learning

Hamiltonian Neural Networks with Automatic Symmetry Detection - Dierkes, Eva; Offen, Christian; Ober-Blöbaum, Sina; Flaßkamp, Kathrin (Chaos)
Recently, Hamiltonian neural networks (HNN) have been introduced to incorporate prior physical knowledge when learning the dynamical equations of Hamiltonian systems. Hereby, the symplectic system structure is preserved despite the data-driven modeling approach. However, preserving symmetries requires additional attention. In this research, we enhance the HNN with a Lie algebra framework to detect and embed symmetries in the neural network. This approach allows to simultaneously learn the symmetry group action and the total energy of the system. As illustrating examples, a pendulum on a cart and a two-body problem from astrodynamics are considered.

Efficient time stepping for numerical integration using reinforcement learning - Dellnitz, Michael; Hüllermeier, Eyke; Lücke, Marvin; Ober-Blöbaum, Sina; Offen, Christian; Peitz, Sebastian; Pfannschmidt, Karlson (SIAM Journal on Scientific Computing)
Many problems in science and engineering require an efficient numerical approximation of integrals or solutions to differential equations. For systems with rapidly changing dynamics, an equidistant discretization is often inadvisable as it results in prohibitively large errors or computational effort. To this end, adaptive schemes, such as solvers based on Runge–Kutta pairs, have been developed which adapt the step size based on local error estimations at each step. While the classical schemes apply very generally and are highly efficient on regular systems, they can behave suboptimally when an inefficient step rejection mechanism is triggered by structurally complex systems such as chaotic systems. To overcome these issues, we propose a method to tailor numerical schemes to the problem class at hand. This is achieved by combining simple, classical quadrature rules or ODE solvers with data-driven time-stepping controllers. Compared with learning solution operators to ODEs directly, it generalizes better to unseen initial data as our approach employs classical numerical schemes as base methods. At the same time it can make use of identified structures of a problem class and, therefore, outperforms state-of-the-art adaptive schemes. Several examples demonstrate superior efficiency. Source code is available at https://github.com/lueckem/quadrature-ML.

Multirate Discrete Mechanics and Optimal Control for a Flexible Satelite Model - Lishkova, Yana; Ober-Blöbaum, Sina; Leyendecker, Sigrid

Variational approach for modelling and optimal control of electrodynamic tether motion - Lishkova, Y.; Bando, M.; Ober-Blöbaum, Sina

Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery - Lishkova, Yana; Scherer, Paul; Ridderbusch, Steffen; Jamnik, Mateja; Liò, Pietro; Ober-Blöbaum, Sina; Offen, Christian (IFAC-PapersOnLine)
By one of the most fundamental principles in physics, a dynamical system will exhibit those motions which extremise an action functional. This leads to the formation of the Euler-Lagrange equations, which serve as a model of how the system will behave in time. If the dynamics exhibit additional symmetries, then the motion fulfils additional conservation laws, such as conservation of energy (time invariance), momentum (translation invariance), or angular momentum (rotational invariance). To learn a system representation, one could learn the discrete Euler-Lagrange equations, or alternatively, learn the discrete Lagrangian function Ld which defines them. Based on ideas from Lie group theory, in this work we introduce a framework to learn a discrete Lagrangian along with its symmetry group from discrete observations of motions and, therefore, identify conserved quantities. The learning process does not restrict the form of the Lagrangian, does not require velocity or momentum observations or predictions and incorporates a cost term which safeguards against unwanted solutions and against potential numerical issues in forward simulations. The learnt discrete quantities are related to their continuous analogues using variational backward error analysis and numerical results demonstrate the improvement such models can have both qualitatively and quantitatively even in the presence of noise.

Continuous and discrete Noether's fractional conserved quantities for restricted calculus of variations - Cresson, Jacky; Jiménez, Fernando; Ober-Blöbaum, Sina (AIMS)

Manifold turnpikes, trims, and symmetries - Faulwasser, Timm; Flaßkamp, Kathrin; Ober-Blöbaum, Sina; Schaller, Manuel; Worthmann, Karl (Mathematics of Control, Signals, and Systems)

Symplectic integration of learned Hamiltonian systems - Offen, Christian; Ober-Blöbaum, Sina (Chaos: An Interdisciplinary Journal of Nonlinear Science)
Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation laws. To predict Hamiltonian dynamics based on discrete trajectory observations, incorporation of prior knowledge about Hamiltonian structure greatly improves predictions. This is typically done by learning the system's Hamiltonian and then integrating the Hamiltonian vector field with a symplectic integrator. For this, however, Hamiltonian data needs to be approximated based on the trajectory observations. Moreover, the numerical integrator introduces an additional discretisation error. In this paper, we show that an inverse modified Hamiltonian structure adapted to the geometric integrator can be learned directly from observations. A separate approximation step for the Hamiltonian data avoided. The inverse modified data compensates for the discretisation error such that the discretisation error is eliminated. The technique is developed for Gaussian Processes.

Verification of safety critical control policies using kernel methods - Vertovec, Nikolaus; Ober-Blöbaum, Sina; Margellos, Kostas
Hamilton-Jacobi reachability methods for safety-critical control have been well studied, but the safety guarantees derived rely on the accuracy of the numerical computation. Thus, it is crucial to understand and account for any inaccuracies that occur due to uncertainty in the underlying dynamics and environment as well as the induced numerical errors. To this end, we propose a framework for modeling the error of the value function inherent in Hamilton-Jacobi reachability using a Gaussian process. The derived safety controller can be used in conjuncture with arbitrary controllers to provide a safe hybrid control law. The marginal likelihood of the Gaussian process then provides a confidence metric used to determine switches between a least restrictive controller and a safety controller. We test both the prediction as well as the correction capabilities of the presented method in a classical pursuit-evasion example.

Superconvergence of galerkin variational integrators - Ober-Blöbaum, Sina; Vermeeren, M. (7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC)

Explicit multiobjective model predictive control for nonlinear systems with symmetries - Ober-Blöbaum, Sina; Peitz, Sebastian (International Journal of Robust and Nonlinear Control)
Model predictive control is a prominent approach to construct a feedback control loop for dynamical systems. Due to real-time constraints, the major challenge in MPC is to solve model-based optimal control problems in a very short amount of time. For linear-quadratic problems, Bemporad et al. have proposed an explicit formulation where the underlying optimization problems are solved a priori in an offline phase. In this article, we present an extension of this concept in two significant ways. We consider nonlinear problems and - more importantly - problems with multiple conflicting objective functions. In the offline phase, we build a library of Pareto optimal solutions from which we then obtain a valid compromise solution in the online phase according to a decision maker's preference. Since the standard multi-parametric programming approach is no longer valid in this situation, we instead use interpolation between different entries of the library. To reduce the number of problems that have to be solved in the offline phase, we exploit symmetries in the dynamical system and the corresponding multiobjective optimal control problem. The results are verified using two different examples from autonomous driving.

A multirate variational approach to Nonlinear MPC - Lishkova, Y.; Cannon, M.; Ober-Blöbaum, Sina

Bifurcation preserving discretisations of optimal control problems - Offen, Christian; Ober-Blöbaum, Sina
The first order optimality conditions of optimal control problems (OCPs) can be regarded as boundary value problems for Hamiltonian systems. Variational or symplectic discretisation methods are classically known for their excellent long term behaviour. As boundary value problems are posed on intervals of fixed, moderate length, it is not immediately clear whether methods can profit from structure preservation in this context. When parameters are present, solutions can undergo bifurcations, for instance, two solutions can merge and annihilate one another as parameters are varied. We will show that generic bifurcations of an OCP are preserved under discretisation when the OCP is either directly discretised to a discrete OCP (direct method) or translated into a Hamiltonian boundary value problem using first order necessary conditions of optimality which is then solved using a symplectic integrator (indirect method). Moreover, certain bifurcations break when a non-symplectic scheme is used. The general phenomenon is illustrated on the example of a cut locus of an ellipsoid.
Keywords: optimal control; catastrophe theory; bifurcations; variational methods; symplectic integrators

Learning ODE Models with Qualitative Structure Using Gaussian Processes - Ridderbusch, Steffen; Offen, Christian; Ober-Blöbaum, Sina; Goulart, Paul (2021 60th IEEE Conference on Decision and Control (CDC))

Multi-objective minimum time optimal control for low-thrust trajectory design - Vertovec, Nikolaus; Ober-Blöbaum, Sina; Margellos, Kostas
We propose a reachability approach for infinite and finite horizon multi-objective optimization problems for low-thrust spacecraft trajectory design. The main advantage of the proposed method is that the Pareto front can be efficiently constructed from the zero level set of the solution to a Hamilton-Jacobi-Bellman equation. We demonstrate the proposed method by applying it to a low-thrust spacecraft trajectory design problem. By deriving the analytic expression for the Hamiltonian and the optimal control policy, we are able to efficiently compute the backward reachable set and reconstruct the optimal trajectories. Furthermore, we show that any reconstructed trajectory will be guaranteed to be weakly Pareto optimal. The proposed method can be used as a benchmark for future research of applying reachability analysis to low-thrust spacecraft trajectory design.

Fractional Damping Through Restricted Calculus of Variations - Jiménez, F.; Ober-Blöbaum, Sina (Nichtlineare Sci 31)

Variational integrators for dissipative systems - Limebeer, D. J. N.; Ober-Blöbaum, Sina; Farshi, F. H. (IEEE Transactions on Automatic Control)

Explicit Multi-objective Model Predictive Control for Nonlinear Systems Under Uncertainty - Hernández Castellanos, Carlos Ignacio; Ober-Blöbaum, Sina; Peitz, Sebastian (International Journal of Robust and Nonlinear Control)
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.

Numerical computation of lightly multi-objective robust optimal solutions by means of generalized cell mapping - Hernández Castellanos, C. I. O.; Schütze, G.; Sun, J.-Q.; Ober-Blöbaum, Sina; Morales-Luna, G. (Mathematics)

A multirate variational approach to simulation and optimal control for flexible spacecraft - Lishkova, Y.; Ober-Blöbaum, Sina; Cannon, M.; Leyendecker, S. (Accepted for publication in Proceedings of 2020 AAS/AIAA Astrodynamics Specialist Conference - Lake Tahoe)

A dissipativity characterization of velocity turnpikes in optimal control problems for mechanical systems - Faulwasser, T.; Flaßkamp, K.; Ober-Blöbaum, Sina; Worthmann, K. (24th International Symposium on Mathematical Theory of Networks and Systems)

Modelling of the convection-diffusion equation through fractional restricted calculus of variations - Cresson, J.; Jiménez, F.; Ober-Blöbaum, Sina (24th International Symposium on Mathematical Theory of Networks and Systems)

Symmetry in optimal control: A multiobjective model predictive control approach - Flaßkamp, K.; Ober-Blöbaum, Sina; Peitz, S. (Advances in Dynamics, Optimization and Computation)

Symmetry and motion primitives in model predictive control - Flaßkamp, Kathrin; Ober-Blöbaum, Sina; Worthmann, Karl (MCSS)

Towards velocity turnpikes in optimal control of mechanical systems - Faulwasser, Tim; Flaßkamp, K.; Ober-Blöbaum, Sina; Worthmann, Karl

Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling - Peitz, Sebastian; Ober-Blöbaum, Sina; Dellnitz, Michael (Acta Applicandae Mathematicae)
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.

Improving optimal control of grid-connected lithium-ion batteries through more accurate battery and degradation modelling - Reniers, J.M.; Mulder, G.; Ober-Blöbaum, Sina; Howe, D.A. (Journal of Power Sources)

Necessary optimality conditions for optimally controlled dissipative mechanical systems modelled through fractional derivatives - Jiménez, F.; Ober-Blöbaum, Sina (6th European Conference on Computational Mechanics)

A fractional variational approach for modelling dissipative mechanical systems continuous and discrete settings - Jiménez, F.; Ober-Blöbaum, Sina (6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2018)

Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control - Dellnitz, Michael; Eckstein, Julian; Flaßkamp, Kathrin; Friedel, Patrick; Horenkamp, Christian; Köhler, Ulrich; Ober-Blöbaum, Sina; Peitz, Sebastian; Tiemeyer, Sebastian (Progress in Industrial Mathematics at ECMI 2014)
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.

C1-continuous space-time discretization based on Hamilton's law of varying action - Mergel, J.C.; Sauer, R.A.; Ober-Blöbaum, Sina (ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik)

Construction and analysis of higher order variational integrators for dynamical systems with holonomic constraints - Wenger, T.; Ober-Blöbaum, Sina; Leyendecker, S. (Advances in Computational Mathematics)

Galerkin variational integrators and modified symplectic Runge-Kutta methods - Ober-Blöbaum, Sina (IMA Journal of Numerical Analysis)

Second-order switching time optimization for switched dynamical systems - Stellato, B,; Ober-Blöbaum, Sina; Goulart, P.J. (IEEE Transactions on Automatic Control)

A multiobjective MPC approach for autonomously driven electric vehicles - Peitz, Sebastian; Schäfer, Kai; Ober-Blöbaum, Sina; Eckstein, Julian; Köhler, Ulrich; Dellnitz, Michael (Proceedings of the 20th World Congress of the International Federation of Automatic Control (IFAC))
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.

Variational multirate integration in discrete mechanics and optimal control - Gail, T.; Ober-Blöbaum, Sina; Leyendecker, S. (ECCOMAS Thematic Conference on Multibody Dynamics)

Variational integrators of mixed order for constrained and unconstrained systems acting on multiple time scales - Wenger, T.; Ober-Blöbaum, Sina; Leyendecker, S. (PAMM)

On the time transformation of mixed integer optimal control problems using a consistent fixed integer control function - Ringkamp, M.; Ober-Blöbaum, Sina; Leyendecker, S. (Mathematical Programming)

A comparison of two predictive approaches to control the longitudinal dynamics of electric vehicles - Eckstein, Julian; Peitz, Sebastian; Schäfer, Kai; Friedel, Patrick; Köhler, Ulrich; Hessel von Molo, Mirko; Ober-Blöbaum, Sina; Dellnitz, Michael (Procedia Technology, 3rd International Conference on System-Integrated Intelligence: New Challenges for Product and Production Engineering)
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.

Variational integrators of mixed order for dynamical systems with multiple time scales and split potentials - Wenger, T.; Ober-Blöbaum, Sina; Leyendecker, S. (ECCOMAS Congress 2016 - Proceedings of the 7th European Congress on Computational Methods in Applied Sciences and Engineering)

Constrained Galerkin variational integrators and modified constrained symplectic Runge-Kutta methods - Wenger, T.; Ober-Blöbaum, Sina; Leyendecker, S. (International Conference of Numerical Analysis and Applied Mathematics (ICNAAM))

Reduced order model based multiobjective optimal control of fluids - Peitz, Sebastian; Ober-Blöbaum, Sina; Dellnitz, M. (Proceedings of International Congress of Theoretical and Applied Mechanics)

Optimal control of switching times in switched linear systems - Stellato, B.; Ober-Blöbaum, Sina; Goulart, P.J. (2016 IEEE 55th Conference on Decision and Control (CDC))

Variational integrators of higher order for constrained dynamical systems - Wenger, T.; Ober-Blöbaum, Sina; Leyendecker, S. (PAMM)

C1-continuous time integration based on cubic Hermite interpolation - Mergel, J.C.; Sauer, R.A.; Ober-Blöbaum, Sina (PAMM)

Time transformed mixed integer optimal control problems with impacts - Ringkamp, M.; Ober-Blöbaum, Sina; Leyendecker, S. (PAMM)

Higher order variational integrators in optimal control theory - Ober-Blöbaum, Sina (PAMM)

On higher order variational integrators and their relation to Runge-Kutta methods - Ober-Blöbaum, Sina (International Conference of Numerical Analysis and Applied Mathematics (ICNAAM))

Symmetry exploiting control of hybrid mechanical systems - Flaßkamp, K.; Hage-Packhäuser, S.; Ober-Blöbaum, Sina (Journal of Computational Dynamics)

Discrete variational Lie group formulation of geometrically exact beam dynamics - Demoures, F.; Gay-Balmaz, F.; Leyendecker, S.; Ober-Blöbaum, Sina; Ratiu, T.S.; Weinand, Y. (Numerische Mathematik)
Keywords: 53D05; 65P10; 74B20; 74H15

High order variational integrators in the optimal control of mechanical systems - Campos, C. M.; Ober-Blöbaum, Sina; Trélat, E. (Discrete and Continuous Dynamical Systems)

Relaxing mixed integer optimal control problems using a time transformation - Ringkamp, M.; Ober-Blöbaum, Sina; Leyendecker, S. (Proceedings of Applied Mathematics and Mechanics)

Multiobjective optimal control of fluid mixing - Ober-Blöbaum, Sina; Padberg-Gehle, K. (PAMM)

Self-optimizing Mechatronic Systems - Dellnitz, Michael; Flaßkamp, Kathrin; Hartmann, Philip; Krüger, Martin; Meyer, Tobias; Priesterjahn, Claudia; Ober-Blöbaum, Sina; Rasche, Christoph; Sextro, Walter; Stahl, Katharina; Trächtler, Ansgar (Dependability of Self-optimizing Mechatronic Systems, Kapitel: 1.1)

Development of the RailCab Vehicle - Flaßkamp, Kathrin; Grösbrink, Stefan; Hartmann, Philip; Heinzemann, Christian; Kleinjohann, Bernd; Kleinjohann, Lisa; Krüger, Martin; Ober-Blöbaum, Sina; Priesterjahn, Claudia; Rasche, Christoph; Schäfer, Wilhelm; Steenken, Dominik; et al. (Dependability of Self-Optimizing Mechatronic Systems)

Verification for Interacting Mechatronic Systems with Motion Profiles - Flaßkamp, Kathrin; Heinzemann, Christian; Krüger, Martin; Ober-Blöbaum, Sina; Schäfer, Wilhelm; Steenken, Dominik; Trächtler, Ansgar; Wehrheim, Heike (Dependability of Self-optimizing Mechatronic Systems)

Control strategies on stable manifolds for energyefficient swing-ups of double pendula - Flaßkamp, Kathrin; Timmermann, Julia; Ober-Blöbaum, Sina; Trächtler, Ansgar (International Journal of Control)

Variational formulation and structure-preserving discretization of nonlinear electric circuits - Ober-Blöbaum, Sina; Lindhorst, H. (21st International Symposium on Mathematical Theory of Networks and Systems)

On the role of quadrature rules and system dimensions in variational multirate integrators - Gail, T.; Leyendecker, S.; Ober-Blöbaum, Sina (3rd Joint Interntaional Conference on Multibody System Dynamics)

Control strategies on stable manifolds for energy-efficient swing-ups of double pendula - Flaßkamp, K.; Timmermann, J.; Ober-Blöbaum, Sina; Trächtler, A. (International Journal of Control)

Construction and analysis of higher order Galerkin variational integrators - Ober-Blöbaum, Sina; Saake, N. (Advances in Computational Mathematics)

Methods for the Design and Development - Anacker, H.; Dellnitz, M.; Flaßkamp, K.; Grocsbrink, S.; Hartmann, P.; Heinzemann, C.; Horenkamp, C.; Kleinjohann, B.; Korf, S.; Krüger, M.; Müller, W.; Ober-Blöbaum, Sina; et al. (Jürgen Gausemeier, Franz Josef Rammig, and Wilhelm Schäfer, editors, Design Methodology for Intelligent Technical Systems)

Dependability of Self-optimizing Mechatronic Systems - Dangelmeier, W.; Dellnitz, M.; Dorociak, R.; Flaßkamp, K.; Gausemeier, J.; Groesbrink, S.; Hartmann, P.; Heinzemann, C.; Hölscher, C.; Iwanek, P.; Keßler, J.H.; Kleinjohann, B.; et al. (Lecture Notes in Mechanical Engineering)

The paradigm of self-optimization - Dellnitz, M.; Dumitrescu, R.; Flaßkamp, K.; Gausemeier, J.; Hartmann, P.; Iwanek, P.; Korf, S.; Krüger, M.; Ober-Blöbaum, Sina; Porrmann, M.; Priesterjahn, C.; Stahl, K.; et al. (Jürgen Gausemeier, Franz Josef Rammig, and Wilhelm Schäfer, editors, Design Methodology for Intelligent Technical Systems)

Variational Lie group formulation of geometrically exact beam dynamics: Synchronous and asynchronous integration - Leitz, T.; Ober-Blöbaum, Sina; Leyendecker, S. (Zdravko Terze, Multibody Dynamics)

Development of an intelligent cruise control using optimal control methods - Dellnitz, M.; Eckstein, J.; Flaßkamp, K.; Friedel, P.; Horenkamp, C.; Köhler, U.; Ober-Blöbaum, Sina; Peitz, S.; Tiemeyer, S. (SysInt 2014 Proceedings)

Variational integrators for dynamical systems with rotational degrees of freedom - Leitz, T.; Ober-Blöbaum, Sina; Leyendecker, S. (11th World Congress on Computational Mechanics)

Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control - Dellnitz, M.; Eckstein, J.; Flaßkamp, K.; Friedel, P.; Horenkamp, C.; Köhler, U.; Ober-Blöbaum, Sina; Peitz, S.; Tiemeyer, S. (ECMI 2014 Proceedings)

Methods for the Design and Development - Anacker, Harald; Dellnitz, Michael; Flaßkamp, Kathrin; Grösbrink, Stefan; Hartmann, Philip; Heinzemann, Christian; Horenkamp, Christian; Kleinjohann, Lisa; Kleinjohann, Bernd; Korf, Sebastian; Krüger, Martin; Müller, Wolfgang; et al. (Design Methodology for Intelligent Technical Systems Systems – Develop Intelligent Technical Systems of the Future)

Discrete-time model of an IPMSM based on variational integrators - Specht, Andreas; Ober-Blöbaum, Sina; Wallscheid, Oliver; Romaus, Christoph; Böcker, Joachim (Electric Machines & Drives Conference (IEMDC), 2013 IEEE International)

Computing time investigations for variational multirate integration - Gail, T.; Leyendecker, S.; Ober-Blöbaum, Sina (Proceedings of Applied Mathematics and Mechanics)

Set oriented methods for the numerical treatment of multi-objective optimization problems - Schütze, O.; Witting, K.; Ober-Blöbaum, Sina; Dellnitz, M.; Tantar, Emilia (EVOLVE - A Bridge Between Probability, Set Oriented Numerics, and Evolutionary Computation)

Variational integrators for electric circuits - Ober-Blöbaum, Sina; Tao, M.; Cheng, M.; Owhadi, H.; Marsden, J.E. (Journal of Computational Physics)

A variational approach to define robustness for parametric multiobjective optimization problems - Witting, K.; Ober-Blöbaum, Sina; Dellnitz, M. (Journal of Global Optimization)

A variational approach to multirate integration for constrained systems - Leyendecker, S.; Ober-Blöbaum, Sina (Jean-Claude Samin and Paul Fisette, editors, Multibody Dynamics)

Optimal control of a switched reluctance drive by a direct method using a discrete variational principle - Flaßkamp, K.; Ober-Blöbaum, Sina; Schneider, T.; Böcker, J. (52nd IEEE International Conference on Decision and Control)

A multiobjective optimization approach for optimal control problems of mechanical systems with uncertainties - Ober-Blöbaum, Sina; Seifried, A. (European Control Conference)

Discretized switching time optimization problems - Flaßkamp, K.; Murphey, T.; Ober-Blöbaum, Sina (European Control Conference)

Optimale Steuerungsstrategien für selbstoptimierende mechatronische Systeme mit mehreren Zielkriterien - Flaßkamp, K.; Ober-Blöbaum, Sina (9. Paderborner Workshop Entwurf mechatronischer Systeme)

Sichere Konvoibildung mit Hilfe optimaler Bremsprofile - Heinzemann, C.; Krüger, M.; Schäfer, W.; Trächtler, A.; Flaßkamp, K.; Steenken, D.; Ober-Blöbaum, Sina; Wehrheim, H. (9. Paderborner Workshop Entwurf mechatronischer Systeme)

Discretetime model of an IPMSM based on variational integrators - Specht, A.; Ober-Blöbaum, Sina; Wallscheid, O.; Romaus, C.; Böcker, J. (IEEE International Electric Machines & Drives Conference (IEMDC))

A numerical approach to multiobjective optimal control of multibody dynamics - Ringkamp, M.; Ober-Blöbaum, Sina; Leyendecker, S. (ECCOMAS Thematic Conference on Multibody Dynamics)

Asynchronous variational Lie group integration for geometrically exact beam dynamics - Demoures, F.; Gay-Balmaz, F.; Leitz, T.; Leyendecker, S.; Ober-Blöbaum, Sina; Ratiu, T.S. (Proceedings of Applied Mathematics and Mechanics)

Multiobjective optimal control of a four-body kinematic chain - Ringkamp, M.; Leyendecker, S.; Ober-Blöbaum, Sina (Proceedings of Applied Mathematics and Mechanics)

Computing time investigations of variational multirate systems - Gail, T.; Leyendecker, S.; Ober-Blöbaum, Sina (Proceedings of Applied Mathematics and Mechanics)

Optimization for discretized switched systems - Flaßkamp, K.; Murphey, T.; Ober-Blöbaum, Sina (Proceedings of Applied Mathematics and Mechanics)

Solving multiobjective optimal control problems in space mission design using discrete mechanics and reference point techniques - Ober-Blöbaum, Sina; Ringkamp, M.; zum Felde, G. (51st IEEE International Conference on Decision and Control)

Handling high dimensional problems with multi-objective continuation methods via successive approximation of the tangent space - Ringkamp, M.; Ober-Blöbaum, Sina; Dellnitz, M.; Schütze, O. (Engineering Optimization)

Trajectory design combining invariant manifolds with discrete mechanics and optimal control - Moore, A.; Ober-Blöbaum, Sina; Marsden, J. E. (Journal of Guidance, Control, and Dynamics)

Solving optimal control problems by exploiting inherent dynamical systems structures - Flaßkamp, K.; Ober-Blöbaum, Sina; Kobilarov, M. (Journal of Nonlinear Science)

Switching time optimization in discretized hybrid dynamical systems - Flaßkamp, K.; Murphey, T.; Ober-Blöbaum, Sina (51st IEEE International Conference on Decision and Control)

Motion planning for mechanical systems with hybrid dynamics - Flaßkamp, K.; Ober-Blöbaum, Sina (Progress in Industrial Mathematics at ECMI 2012, Mathematics in Industry (To appear))

Higher order variational time discretization of optimal control problems - Campos, C.M.; Junge, O.; Ober-Blöbaum, Sina (20th International Symposium on Mathematical Theory of Networks and Systems)

Energy efficient control for mechanical systems based on inherent dynamical structures - Flaßkamp, K.; Ober-Blöbaum, Sina (American Control Conference)

Optimal Control on Stable Manifolds for a Double Pendulum - Flaßkamp, Kathrin; Timmermann, Julia; Ober-Blöbaum, Sina; Dellnitz, Michael; Trächtler, Ansgar (Proceedings in Applied Mathematics and Mechanics)

Discrete mechanics and optimal control: Structure preserving integration for the optimal control of mechanical systems - Ober-Blöbaum, Sina (Proceedings of Oberwolfach Reports ''Geometric Numerical Integration'')