Publikationen am Fachgebiet

Results: 60
Created on: Thu, 02 Dec 2021 23:14:27 +0100 in 0.0925 sec

Faulwasser, Timm; Flaßkamp, Kathrin; Ober-Blöbaum, Sina; Worthmann, Karl;
A dissipativity characterization of velocity turnpikes in optimal control problems for mechanical systems. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 54 (2021), 9, S. 624-629

Turnpikes have recently gained significant research interest in optimal control, since they allow for pivotal insights into the structure of solutions to optimal control problems. So far, mainly steady state solutions which serve as optimal operation points, are studied. This is in contrast to time-varying turnpikes, which are in the focus of this paper. More concretely, we analyze symmetry-induced velocity turnpikes, i.e. controlled relative equilibria, called trim primitives, which are optimal operation points regarding the given cost criterion. We characterize velocity turnpikes by means of dissipativity inequalities. Moreover, we study the equivalence between optimal control problems and steady-state problems via the corresponding necessary optimality conditions. An academic example is given for illustration.
Rußwurm, Franz; Esterhuizen, Willem; Worthmann, Karl; Streif, Stefan;
On MPC without terminal conditions for dynamic non-holonomic robots. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 54 (2021), 6, S. 133-138

We consider an input-constrained differential-drive robot with actuator dynamics. For this system, we establish asymptotic stability of the origin on arbitrary compact, convex sets using Model Predictive Control (MPC) without stabilizing terminal conditions despite the presence of state constraints and actuator dynamics. We note that the problem without those two additional ingredients was essentially solved beforehand, despite the fact that the linearization is not stabilizable. We propose an approach successfully solving the task at hand by combining the theory of barriers to characterize the viability kernel and an MPC framework based on so-called cost controllability. Moreover, we present a numerical case study to derive quantitative bounds on the required length of the prediction horizon. To this end, we investigate the boundary of the viability kernel and a neighbourhood of the origin, i.e. the most interesting areas.
Schaller, Manuel; Philipp, Friedrich; Faulwasser, Timm; Worthmann, Karl; Maschke, Bernhard;
Control of port-Hamiltonian systems with minimal energy supply. - In: European journal of control, ISSN 1435-5671, Bd. 62 (2021), S. 33-40

We investigate optimal control of linear port-Hamiltonian systems with control constraints, in which one aims to perform a state transition with minimal energy supply. Decomposing the state space into dissipative and non-dissipative (i.e. conservative) subspaces, we show that the set of reachable states is bounded w.r.t. the dissipative subspace. We prove that the optimal control problem exhibits the turnpike property with respect to the non-dissipative subspace, i.e., for varying initial conditions and time horizons optimal state trajectories evolve close to the conservative subspace most of the time. We analyze the corresponding steady-state optimization problem and prove that all optimal steady states lie in the non-dissipative subspace. We conclude this paper by illustrating these results by a numerical example from mechanics.
Hackenberg, Annika; Worthmann, Karl; Pätz, Torben; Keiner, Dörthe; Oertel, Joachim; Flaßkamp, Kathrin;
Neurochirurgische Planung mittels automatisierter Bilderkennung und optimaler Pfadplanung :
Neurosurgery planning based on automated image recognition and optimal path design. - In: Automatisierungstechnik, ISSN 2196-677X, Bd. 69 (2021), 8, S. 708-721

Stereotactic neurosurgery requires a careful planning of cannulae paths to spare eloquent areas of the brain that, if damaged, will result in loss of essential neurological function such as sensory processing, linguistic ability, vision, or motor function. We present an approach based on modelling, simulation, and optimization to set up a computational assistant tool. Thereby, we focus on the modeling of the brain topology, where we construct ellipsoidal approximations of voxel clouds based on processed MRI data. The outcome is integrated in a path-planning problem either via constraints or by penalization terms in the objective function. The surgical planning problem with obstacle avoidance is solved for different types of stereotactic cannulae using numerical simulations. We illustrate our method with a case study using real MRI data.
Jiang, Yuning; Sauerteig, Philipp; Houska, Boris; Worthmann, Karl;
Distributed optimization using ALADIN for MPC in smart grids. - In: IEEE transactions on control systems technology, ISSN 1558-0865, Bd. 29 (2021), 5, S. 2142-2152

This article presents a distributed optimization algorithm tailored to solve optimization problems arising in smart grids. In detail, we propose a variant of the augmented Lagrangian-based alternating direction inexact Newton (ALADIN) method, which comes along with global convergence guarantees for the considered class of linear-quadratic optimization problems. We establish local quadratic convergence of the proposed scheme and elaborate its advantages compared with the alternating direction method of multipliers (ADMM). In particular, we show that, at the cost of more communication, ALADIN requires fewer iterations to achieve the desired accuracy. Furthermore, it is numerically demonstrated that the number of iterations is independent of the number of subsystems. The effectiveness of the proposed scheme is illustrated by running both an ALADIN and an ADMM-based model predictive controller on a benchmark case study.
Grundel, Sara M.; Heyder, Stefan; Hotz, Thomas; Ritschel, Tobias K. S.; Sauerteig, Philipp; Worthmann, Karl;
How to coordinate vaccination and social distancing to mitigate SARS-CoV-2 outbreaks. - In: SIAM journal on applied dynamical systems, ISSN 1536-0040, Bd. 20 (2021), 2, S. 1135-1157

Most countries have started vaccinating people against COVID-19. However, due to limited production capacities and logistical challenges it will take months/years until herd immunity is achieved. Therefore, vaccination and social distancing have to be coordinated. In this paper, we provide some insight on this topic using optimization-based control on an age-differentiated compartmental model. For real-life decision-making, we investigate the impact of the planning horizon on the optimal vaccination/social distancing strategy. We find that in order to reduce social distancing in the long run, without overburdening the health care system, it is essential to vaccinate the people with the highest contact rates first. That is also the case if the objective is to minimize fatalities provided that the social distancing measures are sufficiently strict. However, for short-term planning it is optimal to focus on the high-risk group.
Grüne, Lars; Schaller, Manuel; Schiela, Anton;
Abstract nonlinear sensitivity and turnpike analysis and an application to semilinear parabolic PDEs. - In: Control, optimisation and calculus of variations, ISSN 1262-3377, Bd. 27 (2021), 56, S. 1-28

We analyze the sensitivity of the extremal equations that arise from the first order necessary optimality conditions of nonlinear optimal control problems with respect to perturbations of the dynamics and of the initial data. To this end, we present an abstract implicit function approach with scaled spaces. We will apply this abstract approach to problems governed by semilinear PDEs. In that context, we prove an exponential turnpike result and show that perturbations of the extremal equation's dynamics, e.g., discretization errors decay exponentially in time. The latter can be used for very efficient discretization schemes in a Model Predictive Controller, where only a part of the solution needs to be computed accurately. We showcase the theoretical results by means of two examples with a nonlinear heat equation on a two-dimensional domain.
Esterhuizen, Willem; Worthmann, Karl; Streif, Stefan;
Recursive feasibility of continuous-time model predictive control without stabilising constraints. - In: IEEE control systems letters, ISSN 2475-1456, Bd. 5 (2021), 1, S. 265-270
Sauerteig, Philipp; Jiang, Yuning; Houska, Boris; Worthmann, Karl;
Distributed control enforcing group sparsity in smart grids. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 53 (2020), 2, S. 13269-13274

In modern smart grids, charging of local energy storage devices is coordinated within the distribution grid to compensate the volatile aggregated power demand on the time interval of interest. However, this results in a perpetual usage of all batteries which in return reduces their lifetime. In this paper, we enforce group sparsity by using an lp,q-regularization on the control to counteract this phenomenon. This leads to a non-smooth convex optimization problem, for which a tailored Alternating Direction Method of Multipliers algorithm is proposed. Furthermore, the algorithm is embedded in a Model Predictive Control framework. Numerical simulations show that the proposed scheme yields sparse control while achieving reasonable overall peak shaving.
Berger, Thomas; Kästner, Carolin; Worthmann, Karl;
Learning-based funnel-MPC for output-constrained nonlinear systems. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 53 (2020), 2, S. 5177-5182

We exploit an adaptive control technique, namely funnel control, to establish both initial and recursive feasibility in Model Predictive Control (MPC) for output-constrained nonlinear systems. Moreover, we show that the resulting feedback controller outperforms the funnel controller both w.r.t. the required sampling rate for a zero-order-hold implementation and required control action. We further propose a combination of funnel control and MPC, exploiting the performance guarantees of the model-free funnel controller during a learning phase and the advantages of the model-based MPC scheme thereafter.