TY - JOUR AB - 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. AU - Offen, Christian AU - Ober-Blöbaum, Sina ID - 46469 IS - 1 JF - Chaos SN - 1054-1500 TI - Learning of discrete models of variational PDEs from data VL - 34 ER - TY - JOUR AB - 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. AU - Leyendecker, Sigrid AU - Maslovskaya, Sofya AU - Ober-Blöbaum, Sina AU - Almagro, Rodrigo T. Sato Martín de AU - Szemenyei, Flóra Orsolya ID - 53101 JF - Journal of Computational Dynamics KW - Optimal control problem KW - Lagrangian system KW - Hamiltonian system KW - Variations KW - Pontryagin's maximum principle. SN - 2158-2491 TI - A new Lagrangian approach to control affine systems with a quadratic Lagrange term ER - TY - CONF AB - 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. AU - Offen, Christian AU - Ober-Blöbaum, Sina ED - Nielsen, F ED - Barbaresco, F ID - 42163 KW - System identification KW - discrete Lagrangians KW - travelling waves T2 - Geometric Science of Information TI - Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves VL - 14071 ER - TY - JOUR AB - 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. AU - Ober-Blöbaum, Sina AU - Offen, Christian ID - 29240 JF - Journal of Computational and Applied Mathematics KW - Lagrangian learning KW - variational backward error analysis KW - modified Lagrangian KW - variational integrators KW - physics informed learning SN - 0377-0427 TI - Variational Learning of Euler–Lagrange Dynamics from Data VL - 421 ER - TY - JOUR AB - 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. AU - Dierkes, Eva AU - Offen, Christian AU - Ober-Blöbaum, Sina AU - Flaßkamp, Kathrin ID - 37654 IS - 6 JF - Chaos SN - 1054-1500 TI - Hamiltonian Neural Networks with Automatic Symmetry Detection VL - 33 ER - TY - JOUR AB - 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. AU - Dellnitz, Michael AU - Hüllermeier, Eyke AU - Lücke, Marvin AU - Ober-Blöbaum, Sina AU - Offen, Christian AU - Peitz, Sebastian AU - Pfannschmidt, Karlson ID - 21600 IS - 2 JF - SIAM Journal on Scientific Computing TI - Efficient time stepping for numerical integration using reinforcement learning VL - 45 ER - TY - GEN AU - Lishkova, Yana AU - Ober-Blöbaum, Sina AU - Leyendecker, Sigrid ID - 47147 TI - Multirate Discrete Mechanics and Optimal Control for a Flexible Satelite Model ER - TY - CONF AU - Lishkova, Y. AU - Bando, M. AU - Ober-Blöbaum, Sina ID - 47148 TI - Variational approach for modelling and optimal control of electrodynamic tether motion ER - TY - CONF AB - 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. AU - Lishkova, Yana AU - Scherer, Paul AU - Ridderbusch, Steffen AU - Jamnik, Mateja AU - Liò, Pietro AU - Ober-Blöbaum, Sina AU - Offen, Christian ID - 34135 IS - 2 T2 - IFAC-PapersOnLine TI - Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery VL - 56 ER - TY - JOUR AU - Cresson, Jacky AU - Jiménez, Fernando AU - Ober-Blöbaum, Sina ID - 30490 JF - AIMS TI - Continuous and discrete Noether's fractional conserved quantities for restricted calculus of variations VL - 14(1) ER - TY - JOUR AU - Faulwasser, Timm AU - Flaßkamp, Kathrin AU - Ober-Blöbaum, Sina AU - Schaller, Manuel AU - Worthmann, Karl ID - 44624 JF - Mathematics of Control, Signals, and Systems TI - Manifold turnpikes, trims, and symmetries VL - 34 ER - TY - JOUR AB - 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. AU - Offen, Christian AU - Ober-Blöbaum, Sina ID - 23382 JF - Chaos: An Interdisciplinary Journal of Nonlinear Science TI - Symplectic integration of learned Hamiltonian systems VL - 32(1) ER - TY - CONF AB - 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. AU - Vertovec, Nikolaus AU - Ober-Blöbaum, Sina AU - Margellos, Kostas ID - 30733 TI - Verification of safety critical control policies using kernel methods ER - TY - CONF AU - Ober-Blöbaum, Sina AU - Vermeeren, M. ID - 29421 T2 - 7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC TI - Superconvergence of galerkin variational integrators VL - 54(19) ER - TY - JOUR AB - 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. AU - Ober-Blöbaum, Sina AU - Peitz, Sebastian ID - 16294 JF - International Journal of Robust and Nonlinear Control TI - Explicit multiobjective model predictive control for nonlinear systems with symmetries VL - 31(2) ER - TY - CONF AU - Lishkova, Y. AU - Cannon, M. AU - Ober-Blöbaum, Sina ID - 47146 TI - A multirate variational approach to Nonlinear MPC ER - TY - CONF AB - 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. AU - Offen, Christian AU - Ober-Blöbaum, Sina ID - 22894 KW - optimal control KW - catastrophe theory KW - bifurcations KW - variational methods KW - symplectic integrators SN - 2405-8963 TI - Bifurcation preserving discretisations of optimal control problems VL - 54(19) ER - TY - CONF AU - Ridderbusch, Steffen AU - Offen, Christian AU - Ober-Blöbaum, Sina AU - Goulart, Paul ID - 21572 T2 - 2021 60th IEEE Conference on Decision and Control (CDC) TI - Learning ODE Models with Qualitative Structure Using Gaussian Processes ER - TY - CONF AB - 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. AU - Vertovec, Nikolaus AU - Ober-Blöbaum, Sina AU - Margellos, Kostas ID - 21592 TI - Multi-objective minimum time optimal control for low-thrust trajectory design ER - TY - CONF AU - Jiménez, F. AU - Ober-Blöbaum, Sina ID - 29868 T2 - Nichtlineare Sci 31 TI - Fractional Damping Through Restricted Calculus of Variations VL - 46 ER - TY - JOUR AU - Limebeer, D. J. N. AU - Ober-Blöbaum, Sina AU - Farshi, F. H. ID - 29399 JF - IEEE Transactions on Automatic Control TI - Variational integrators for dissipative systems VL - 65(4) ER - TY - JOUR AB - 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. AU - Hernández Castellanos, Carlos Ignacio AU - Ober-Blöbaum, Sina AU - Peitz, Sebastian ID - 16297 JF - International Journal of Robust and Nonlinear Control TI - Explicit Multi-objective Model Predictive Control for Nonlinear Systems Under Uncertainty VL - 30(17) ER - TY - JOUR AU - Hernández Castellanos, C. I. O. AU - Schütze, G. AU - Sun, J.-Q. AU - Ober-Blöbaum, Sina AU - Morales-Luna, G. ID - 29398 JF - Mathematics TI - Numerical computation of lightly multi-objective robust optimal solutions by means of generalized cell mapping VL - 8(11):1959 ER - TY - CONF AU - Lishkova, Y. AU - Ober-Blöbaum, Sina AU - Cannon, M. AU - Leyendecker, S. ID - 29422 T2 - Accepted for publication in Proceedings of 2020 AAS/AIAA Astrodynamics Specialist Conference - Lake Tahoe TI - A multirate variational approach to simulation and optimal control for flexible spacecraft ER - TY - CONF AU - Faulwasser, T. AU - Flaßkamp, K. AU - Ober-Blöbaum, Sina AU - Worthmann, K. ID - 29423 T2 - 24th International Symposium on Mathematical Theory of Networks and Systems TI - A dissipativity characterization of velocity turnpikes in optimal control problems for mechanical systems ER - TY - CONF AU - Cresson, J. AU - Jiménez, F. AU - Ober-Blöbaum, Sina ID - 29424 T2 - 24th International Symposium on Mathematical Theory of Networks and Systems TI - Modelling of the convection-diffusion equation through fractional restricted calculus of variations ER - TY - CHAP AU - Flaßkamp, K. AU - Ober-Blöbaum, Sina AU - Peitz, S. ED - Junge, Oliver ED - Schütze, Oliver ED - Froyland, Gary ED - Ober-Blöbaum, Sina ED - Padberg-Gehle, Kathrin ID - 29413 T2 - Advances in Dynamics, Optimization and Computation TI - Symmetry in optimal control: A multiobjective model predictive control approach ER - TY - JOUR AU - Flaßkamp, Kathrin AU - Ober-Blöbaum, Sina AU - Worthmann, Karl ID - 19993 JF - MCSS TI - Symmetry and motion primitives in model predictive control VL - 31 ER - TY - CONF AU - Faulwasser, Tim AU - Flaßkamp, K. AU - Ober-Blöbaum, Sina AU - Worthmann, Karl ID - 29867 TI - Towards velocity turnpikes in optimal control of mechanical systems VL - 52(16) ER - TY - JOUR AB - 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. AU - Peitz, Sebastian AU - Ober-Blöbaum, Sina AU - Dellnitz, Michael ID - 8753 IS - 1 JF - Acta Applicandae Mathematicae SN - 0167-8019 TI - Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling VL - 161 ER - TY - JOUR AU - Reniers, J.M. AU - Mulder, G. AU - Ober-Blöbaum, Sina AU - Howe, D.A. ID - 20112 JF - Journal of Power Sources SN - 0378-7753 TI - Improving optimal control of grid-connected lithium-ion batteries through more accurate battery and degradation modelling VL - 379 ER - TY - CONF AU - Jiménez, F. AU - Ober-Blöbaum, Sina ID - 29425 T2 - 6th European Conference on Computational Mechanics TI - Necessary optimality conditions for optimally controlled dissipative mechanical systems modelled through fractional derivatives ER - TY - CONF AU - Jiménez, F. AU - Ober-Blöbaum, Sina ID - 29427 T2 - 6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2018 TI - A fractional variational approach for modelling dissipative mechanical systems continuous and discrete settings VL - 51(3) ER - TY - CONF AB - 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. 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 - 5914 SN - 1612-3956 T2 - Progress in Industrial Mathematics at ECMI 2014 TI - Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control ER - TY - JOUR AU - Mergel, J.C. AU - Sauer, R.A. AU - Ober-Blöbaum, Sina ID - 20061 JF - ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik SN - 1521-4001 TI - C1-continuous space-time discretization based on Hamilton's law of varying action VL - 97(4) ER - TY - JOUR AU - Wenger, T. AU - Ober-Blöbaum, Sina AU - Leyendecker, S. ID - 20091 JF - Advances in Computational Mathematics TI - Construction and analysis of higher order variational integrators for dynamical systems with holonomic constraints VL - 43(5) ER - TY - JOUR AU - Ober-Blöbaum, Sina ID - 20059 JF - IMA Journal of Numerical Analysis TI - Galerkin variational integrators and modified symplectic Runge-Kutta methods VL - 37(1) ER - TY - JOUR AU - Stellato, B, AU - Ober-Blöbaum, Sina AU - Goulart, P.J. ID - 20093 JF - IEEE Transactions on Automatic Control TI - Second-order switching time optimization for switched dynamical systems VL - 62(10) ER - TY - JOUR AB - 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. AU - Peitz, Sebastian AU - Schäfer, Kai AU - Ober-Blöbaum, Sina AU - Eckstein, Julian AU - Köhler, Ulrich AU - Dellnitz, Michael ID - 8756 IS - 1 JF - Proceedings of the 20th World Congress of the International Federation of Automatic Control (IFAC) SN - 2405-8963 TI - A multiobjective MPC approach for autonomously driven electric vehicles VL - 50 ER - TY - CONF AU - Gail, T. AU - Ober-Blöbaum, Sina AU - Leyendecker, S. ID - 29430 T2 - ECCOMAS Thematic Conference on Multibody Dynamics TI - Variational multirate integration in discrete mechanics and optimal control ER - TY - JOUR AU - Wenger, T. AU - Ober-Blöbaum, Sina AU - Leyendecker, S. ID - 20106 IS - 1 JF - PAMM TI - Variational integrators of mixed order for constrained and unconstrained systems acting on multiple time scales VL - 17 ER - TY - JOUR AU - Ringkamp, M. AU - Ober-Blöbaum, Sina AU - Leyendecker, S. ID - 20060 JF - Mathematical Programming TI - On the time transformation of mixed integer optimal control problems using a consistent fixed integer control function 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 - Hessel von Molo, Mirko AU - Ober-Blöbaum, Sina AU - Dellnitz, Michael ID - 8758 SN - 2212-0173 T2 - Procedia Technology, 3rd International Conference on System-Integrated Intelligence: New Challenges for Product and Production Engineering TI - A comparison of two predictive approaches to control the longitudinal dynamics of electric vehicles VL - 26 ER - TY - CONF AU - Wenger, T. AU - Ober-Blöbaum, Sina AU - Leyendecker, S. ID - 29435 T2 - ECCOMAS Congress 2016 - Proceedings of the 7th European Congress on Computational Methods in Applied Sciences and Engineering TI - Variational integrators of mixed order for dynamical systems with multiple time scales and split potentials ER - TY - CONF AU - Wenger, T. AU - Ober-Blöbaum, Sina AU - Leyendecker, S. ID - 29432 T2 - International Conference of Numerical Analysis and Applied Mathematics (ICNAAM) TI - Constrained Galerkin variational integrators and modified constrained symplectic Runge-Kutta methods ER - TY - CONF AU - Peitz, Sebastian AU - Ober-Blöbaum, Sina AU - Dellnitz, M. ID - 29433 T2 - Proceedings of International Congress of Theoretical and Applied Mechanics TI - Reduced order model based multiobjective optimal control of fluids ER - TY - CONF AU - Stellato, B. AU - Ober-Blöbaum, Sina AU - Goulart, P.J. ID - 29436 T2 - 2016 IEEE 55th Conference on Decision and Control (CDC) TI - Optimal control of switching times in switched linear systems ER - TY - JOUR AU - Wenger, T. AU - Ober-Blöbaum, Sina AU - Leyendecker, S. ID - 20101 JF - PAMM SN - 1617-7061 TI - Variational integrators of higher order for constrained dynamical systems VL - 16(1) ER - TY - JOUR AU - Mergel, J.C. AU - Sauer, R.A. AU - Ober-Blöbaum, Sina ID - 20105 JF - PAMM SN - 1617-7061 TI - C1-continuous time integration based on cubic Hermite interpolation VL - 16(1) ER - TY - JOUR AU - Ringkamp, M. AU - Ober-Blöbaum, Sina AU - Leyendecker, S. ID - 20103 JF - PAMM SN - 1617-7061 TI - Time transformed mixed integer optimal control problems with impacts VL - 16(1) ER - TY - JOUR AU - Ober-Blöbaum, Sina ID - 20104 JF - PAMM SN - 1617-7061 TI - Higher order variational integrators in optimal control theory VL - 16(1) ER - TY - CONF AU - Ober-Blöbaum, Sina ID - 20097 T2 - International Conference of Numerical Analysis and Applied Mathematics (ICNAAM) TI - On higher order variational integrators and their relation to Runge-Kutta methods ER - TY - JOUR AU - Flaßkamp, K. AU - Hage-Packhäuser, S. AU - Ober-Blöbaum, Sina ID - 29402 JF - Journal of Computational Dynamics TI - Symmetry exploiting control of hybrid mechanical systems VL - 2(1) ER - TY - JOUR AU - Demoures, F. AU - Gay-Balmaz, F. AU - Leyendecker, S. AU - Ober-Blöbaum, Sina AU - Ratiu, T.S. AU - Weinand, Y. ID - 20057 JF - Numerische Mathematik KW - 53D05 KW - 65P10 KW - 74B20 KW - 74H15 SN - 0029-599X TI - Discrete variational Lie group formulation of geometrically exact beam dynamics VL - 130(1) ER - TY - JOUR AU - Campos, C. M. AU - Ober-Blöbaum, Sina AU - Trélat, E. ID - 29403 JF - Discrete and Continuous Dynamical Systems TI - High order variational integrators in the optimal control of mechanical systems VL - 35(9) ER - TY - JOUR AU - Ringkamp, M. AU - Ober-Blöbaum, Sina AU - Leyendecker, S. ID - 20107 JF - Proceedings of Applied Mathematics and Mechanics SN - 1617-7061 TI - Relaxing mixed integer optimal control problems using a time transformation VL - 15(1) ER - TY - JOUR AU - Ober-Blöbaum, Sina AU - Padberg-Gehle, K. ID - 20111 JF - PAMM SN - 1617-7061 TI - Multiobjective optimal control of fluid mixing VL - 15(1) ER - TY - CHAP AU - Dellnitz, Michael AU - Flaßkamp, Kathrin AU - Hartmann, Philip AU - Krüger, Martin AU - Meyer, Tobias AU - Priesterjahn, Claudia AU - Ober-Blöbaum, Sina AU - Rasche, Christoph AU - Sextro, Walter AU - Stahl, Katharina AU - Trächtler, Ansgar ID - 25173 T2 - Dependability of Self-optimizing Mechatronic Systems, Kapitel: 1.1 TI - Self-optimizing Mechatronic Systems ER - TY - CHAP AU - Flaßkamp, Kathrin AU - Grösbrink, Stefan AU - Hartmann, Philip AU - Heinzemann, Christian AU - Kleinjohann, Bernd AU - Kleinjohann, Lisa AU - Krüger, Martin AU - Ober-Blöbaum, Sina AU - Priesterjahn, Claudia AU - Rasche, Christoph AU - Schäfer, Wilhelm AU - Steenken, Dominik AU - Trächtler, Ansgar AU - Wehrheim, Heike AU - Ziegert, Steffen ID - 25177 T2 - Dependability of Self-Optimizing Mechatronic Systems TI - Development of the RailCab Vehicle ER - TY - CHAP AU - Flaßkamp, Kathrin AU - Heinzemann, Christian AU - Krüger, Martin AU - Ober-Blöbaum, Sina AU - Schäfer, Wilhelm AU - Steenken, Dominik AU - Trächtler, Ansgar AU - Wehrheim, Heike ID - 23109 T2 - Dependability of Self-optimizing Mechatronic Systems TI - Verification for Interacting Mechatronic Systems with Motion Profiles ER - TY - JOUR AU - Flaßkamp, Kathrin AU - Timmermann, Julia AU - Ober-Blöbaum, Sina AU - Trächtler, Ansgar ID - 23110 JF - International Journal of Control TI - Control strategies on stable manifolds for energyefficient swing-ups of double pendula VL - DOI: 10.1080/00207179.2014.893450 ER - TY - CONF AU - Ober-Blöbaum, Sina AU - Lindhorst, H. ID - 29440 T2 - 21st International Symposium on Mathematical Theory of Networks and Systems TI - Variational formulation and structure-preserving discretization of nonlinear electric circuits ER - TY - CONF AU - Gail, T. AU - Leyendecker, S. AU - Ober-Blöbaum, Sina ID - 29438 T2 - 3rd Joint Interntaional Conference on Multibody System Dynamics TI - On the role of quadrature rules and system dimensions in variational multirate integrators ER - TY - JOUR AU - Flaßkamp, K. AU - Timmermann, J. AU - Ober-Blöbaum, Sina AU - Trächtler, A. ID - 20072 JF - International Journal of Control TI - Control strategies on stable manifolds for energy-efficient swing-ups of double pendula VL - 87(9) ER - TY - JOUR AU - Ober-Blöbaum, Sina AU - Saake, N. ID - 29404 JF - Advances in Computational Mathematics TI - Construction and analysis of higher order Galerkin variational integrators ER - TY - CHAP AU - Anacker, H. AU - Dellnitz, M. AU - Flaßkamp, K. AU - Grocsbrink, S. AU - Hartmann, P. AU - Heinzemann, C. AU - Horenkamp, C. AU - Kleinjohann, B. AU - Korf, S. AU - Krüger, M. AU - Müller, W. AU - Ober-Blöbaum, Sina AU - Oberthür, S. AU - Porrmann, M. AU - Priesterjahn, C. AU - Radkowski, R. AU - Rasche, C. AU - Rieke, J. AU - Ringkamp, M. AU - Stahl, K. AU - Steenken, D. AU - Stöcklein, J. AU - Timmermann, R. AU - Trächtler, A. AU - Witting, K. AU - Xie, T. AU - Ziegert, S. ID - 20080 SN - 978-3-642-45434-9 T2 - Jürgen Gausemeier, Franz Josef Rammig, and Wilhelm Schäfer, editors, Design Methodology for Intelligent Technical Systems TI - Methods for the Design and Development ER - TY - CHAP AU - Dangelmeier, W. AU - Dellnitz, M. AU - Dorociak, R. AU - Flaßkamp, K. AU - Gausemeier, J. AU - Groesbrink, S. AU - Hartmann, P. AU - Heinzemann, C. AU - Hölscher, C. AU - Iwanek, P. AU - Keßler, J.H. AU - Kleinjohann, B. AU - Kleinjohann, L. AU - Korf, S. AU - Krüger, M. AU - Meyer, T. AU - Müller, W. AU - Ober-Blöbaum, Sina AU - Porrmann, M. AU - Priesterjahn, C. AU - Rammig, F.J. AU - Rasche, C. AU - Reinold, P. AU - Schäfer, W. AU - Seifried, A. AU - Sextro, W. AU - Sondermann-Woelke, C. AU - Stahl, K. AU - Steenken, D. AU - Timmermann, R. AU - Trächtler, A. AU - Vaßholz, M. AU - Wehrheim, H. AU - Witting, K. AU - Xie, T. AU - Zhao, Y. AU - Ziegert, S. AU - Zimmer, D. ID - 29417 T2 - Lecture Notes in Mechanical Engineering TI - Dependability of Self-optimizing Mechatronic Systems ER - TY - CHAP AU - Dellnitz, M. AU - Dumitrescu, R. AU - Flaßkamp, K. AU - Gausemeier, J. AU - Hartmann, P. AU - Iwanek, P. AU - Korf, S. AU - Krüger, M. AU - Ober-Blöbaum, Sina AU - Porrmann, M. AU - Priesterjahn, C. AU - Stahl, K. AU - Trächtler, A. AU - Vaßholz, M. ID - 29416 T2 - Jürgen Gausemeier, Franz Josef Rammig, and Wilhelm Schäfer, editors, Design Methodology for Intelligent Technical Systems TI - The paradigm of self-optimization ER - TY - CHAP AU - Leitz, T. AU - Ober-Blöbaum, Sina AU - Leyendecker, S. ID - 29414 T2 - Zdravko Terze, Multibody Dynamics TI - Variational Lie group formulation of geometrically exact beam dynamics: Synchronous and asynchronous integration VL - 35 ER - TY - JOUR AU - Dellnitz, M. AU - Eckstein, J. AU - Flaßkamp, K. AU - Friedel, P. AU - Horenkamp, C. AU - Köhler, U. AU - Ober-Blöbaum, Sina AU - Peitz, S. AU - Tiemeyer, S. ID - 20071 JF - SysInt 2014 Proceedings SN - 2212-0173 TI - Development of an intelligent cruise control using optimal control methods VL - 15 ER - TY - CONF AU - Leitz, T. AU - Ober-Blöbaum, Sina AU - Leyendecker, S. ID - 20087 T2 - 11th World Congress on Computational Mechanics TI - Variational integrators for dynamical systems with rotational degrees of freedom ER - TY - CONF AU - Dellnitz, M. AU - Eckstein, J. AU - Flaßkamp, K. AU - Friedel, P. AU - Horenkamp, C. AU - Köhler, U. AU - Ober-Blöbaum, Sina AU - Peitz, S. AU - Tiemeyer, S. ID - 20070 T2 - ECMI 2014 Proceedings TI - Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control ER - TY - CHAP AU - Anacker, Harald AU - Dellnitz, Michael AU - Flaßkamp, Kathrin AU - Grösbrink, Stefan AU - Hartmann, Philip AU - Heinzemann, Christian AU - Horenkamp, Christian AU - Kleinjohann, Lisa AU - Kleinjohann, Bernd AU - Korf, Sebastian AU - Krüger, Martin AU - Müller, Wolfgang AU - Ober-Blöbaum, Sina AU - Oberthür, Simon AU - Porrmann, Mario AU - Priesterjahn, Claudia AU - Radkowski, W. AU - Rasche, Christoph AU - Rieke, Jan AU - Ringkamp, Maik AU - Stahl, Katharina AU - Steenken, Dominik AU - Stöcklein, Jörg AU - Timmermann, Robert AU - Trächtler, Ansgar AU - Witting, Katrin AU - Xie, Tao AU - Ziegert, Steffen ID - 25743 T2 - Design Methodology for Intelligent Technical Systems Systems – Develop Intelligent Technical Systems of the Future TI - Methods for the Design and Development ER - TY - CONF AU - Specht, Andreas AU - Ober-Blöbaum, Sina AU - Wallscheid, Oliver AU - Romaus, Christoph AU - Böcker, Joachim ID - 29603 T2 - Electric Machines & Drives Conference (IEMDC), 2013 IEEE International TI - Discrete-time model of an IPMSM based on variational integrators ER - TY - CONF AU - Gail, T. AU - Leyendecker, S. AU - Ober-Blöbaum, Sina ID - 29491 T2 - Proceedings of Applied Mathematics and Mechanics TI - Computing time investigations for variational multirate integration VL - 13(1) ER - TY - CHAP AU - Schütze, O. AU - Witting, K. AU - Ober-Blöbaum, Sina AU - Dellnitz, M. AU - Tantar, Emilia ID - 29419 T2 - EVOLVE - A Bridge Between Probability, Set Oriented Numerics, and Evolutionary Computation TI - Set oriented methods for the numerical treatment of multi-objective optimization problems ER - TY - JOUR AU - Ober-Blöbaum, Sina AU - Tao, M. AU - Cheng, M. AU - Owhadi, H. AU - Marsden, J.E. ID - 20032 JF - Journal of Computational Physics TI - Variational integrators for electric circuits VL - 242 ER - TY - JOUR AU - Witting, K. AU - Ober-Blöbaum, Sina AU - Dellnitz, M. ID - 29406 JF - Journal of Global Optimization TI - A variational approach to define robustness for parametric multiobjective optimization problems VL - 57(2) ER - TY - CHAP AU - Leyendecker, S. AU - Ober-Blöbaum, Sina ID - 29418 T2 - Jean-Claude Samin and Paul Fisette, editors, Multibody Dynamics TI - A variational approach to multirate integration for constrained systems VL - 28 ER - TY - CONF AU - Flaßkamp, K. AU - Ober-Blöbaum, Sina AU - Schneider, T. AU - Böcker, J. ID - 29441 T2 - 52nd IEEE International Conference on Decision and Control TI - Optimal control of a switched reluctance drive by a direct method using a discrete variational principle ER - TY - CONF AU - Ober-Blöbaum, Sina AU - Seifried, A. ID - 29443 T2 - European Control Conference TI - A multiobjective optimization approach for optimal control problems of mechanical systems with uncertainties ER - TY - CONF AU - Flaßkamp, K. AU - Murphey, T. AU - Ober-Blöbaum, Sina ID - 29442 T2 - European Control Conference TI - Discretized switching time optimization problems ER - TY - CONF AU - Flaßkamp, K. AU - Ober-Blöbaum, Sina ID - 20028 T2 - 9. Paderborner Workshop Entwurf mechatronischer Systeme TI - Optimale Steuerungsstrategien für selbstoptimierende mechatronische Systeme mit mehreren Zielkriterien ER - TY - CONF AU - Heinzemann, C. AU - Krüger, M. AU - Schäfer, W. AU - Trächtler, A. AU - Flaßkamp, K. AU - Steenken, D. AU - Ober-Blöbaum, Sina AU - Wehrheim, H. ID - 20029 T2 - 9. Paderborner Workshop Entwurf mechatronischer Systeme TI - Sichere Konvoibildung mit Hilfe optimaler Bremsprofile ER - TY - CONF AU - Specht, A. AU - Ober-Blöbaum, Sina AU - Wallscheid, O. AU - Romaus, C. AU - Böcker, J. ID - 29447 T2 - IEEE International Electric Machines & Drives Conference (IEMDC) TI - Discretetime model of an IPMSM based on variational integrators ER - TY - CONF AU - Ringkamp, M. AU - Ober-Blöbaum, Sina AU - Leyendecker, S. ID - 29446 T2 - ECCOMAS Thematic Conference on Multibody Dynamics TI - A numerical approach to multiobjective optimal control of multibody dynamics ER - TY - CONF AU - Demoures, F. AU - Gay-Balmaz, F. AU - Leitz, T. AU - Leyendecker, S. AU - Ober-Blöbaum, Sina AU - Ratiu, T.S. ID - 29444 T2 - Proceedings of Applied Mathematics and Mechanics TI - Asynchronous variational Lie group integration for geometrically exact beam dynamics VL - 13(1) ER - TY - CONF AU - Ringkamp, M. AU - Leyendecker, S. AU - Ober-Blöbaum, Sina ID - 29492 T2 - Proceedings of Applied Mathematics and Mechanics TI - Multiobjective optimal control of a four-body kinematic chain VL - 13(1) ER - TY - CONF AU - Gail, T. AU - Leyendecker, S. AU - Ober-Blöbaum, Sina ID - 29445 T2 - Proceedings of Applied Mathematics and Mechanics TI - Computing time investigations of variational multirate systems VL - 13(1) ER - TY - CONF AU - Flaßkamp, K. AU - Murphey, T. AU - Ober-Blöbaum, Sina ID - 29490 T2 - Proceedings of Applied Mathematics and Mechanics TI - Optimization for discretized switched systems VL - 13(1) ER - TY - CONF AU - Ober-Blöbaum, Sina AU - Ringkamp, M. AU - zum Felde, G. ID - 29452 T2 - 51st IEEE International Conference on Decision and Control TI - Solving multiobjective optimal control problems in space mission design using discrete mechanics and reference point techniques ER - TY - JOUR AU - Ringkamp, M. AU - Ober-Blöbaum, Sina AU - Dellnitz, M. AU - Schütze, O. ID - 29409 JF - Engineering Optimization TI - Handling high dimensional problems with multi-objective continuation methods via successive approximation of the tangent space VL - 44(6) ER - TY - JOUR AU - Moore, A. AU - Ober-Blöbaum, Sina AU - Marsden, J. E. ID - 29407 JF - Journal of Guidance, Control, and Dynamics TI - Trajectory design combining invariant manifolds with discrete mechanics and optimal control VL - 35(5) ER - TY - JOUR AU - Flaßkamp, K. AU - Ober-Blöbaum, Sina AU - Kobilarov, M. ID - 29408 JF - Journal of Nonlinear Science TI - Solving optimal control problems by exploiting inherent dynamical systems structures VL - 22(4) ER - TY - CONF AU - Flaßkamp, K. AU - Murphey, T. AU - Ober-Blöbaum, Sina ID - 29451 T2 - 51st IEEE International Conference on Decision and Control TI - Switching time optimization in discretized hybrid dynamical systems ER - TY - CONF AU - Flaßkamp, K. AU - Ober-Blöbaum, Sina ID - 29450 T2 - Progress in Industrial Mathematics at ECMI 2012, Mathematics in Industry (To appear) TI - Motion planning for mechanical systems with hybrid dynamics ER - TY - CONF AU - Campos, C.M. AU - Junge, O. AU - Ober-Blöbaum, Sina ID - 29453 T2 - 20th International Symposium on Mathematical Theory of Networks and Systems TI - Higher order variational time discretization of optimal control problems ER - TY - CONF AU - Flaßkamp, K. AU - Ober-Blöbaum, Sina ID - 29454 T2 - American Control Conference TI - Energy efficient control for mechanical systems based on inherent dynamical structures ER - TY - CONF AU - Flaßkamp, Kathrin AU - Timmermann, Julia AU - Ober-Blöbaum, Sina AU - Dellnitz, Michael AU - Trächtler, Ansgar ID - 23161 T2 - Proceedings in Applied Mathematics and Mechanics TI - Optimal Control on Stable Manifolds for a Double Pendulum VL - 12(1) ER - TY - CONF AU - Ober-Blöbaum, Sina ID - 29457 T2 - Proceedings of Oberwolfach Reports ''Geometric Numerical Integration'' TI - Discrete mechanics and optimal control: Structure preserving integration for the optimal control of mechanical systems ER -