Publikationen am Fachgebiet

Results: 84
Created on: Wed, 30 Nov 2022 23:08:22 +0100 in 0.0758 sec

Faulwasser, Timm; Flaßkamp, Kathrin; Ober-Blöbaum, Sina; Schaller, Manuel; Worthmann, Karl
Manifold turnpikes, trims, and symmetries. - In: Mathematics of control, signals, and systems, ISSN 1435-568X, Bd. 34 (2022), 4, S. 759-788

Classical turnpikes correspond to optimal steady states which are attractors of infinite-horizon optimal control problems. In this paper, motivated by mechanical systems with symmetries, we generalize this concept to manifold turnpikes. Specifically, the necessary optimality conditions projected onto a symmetry-induced manifold coincide with those of a reduced-order problem defined on the manifold under certain conditions. We also propose sufficient conditions for the existence of manifold turnpikes based on a tailored notion of dissipativity with respect to manifolds. Furthermore, we show how the classical Legendre transformation between Euler-Lagrange and Hamilton formalisms can be extended to the adjoint variables. Finally, we draw upon the Kepler problem to illustrate our findings.
Mühlenhoff, Julian; Körbner, Thorben; Miccoli, Giovanni; Keiner, Dörthe; Hoffmann, Matthias K.; Sauerteig, Philipp; Worthmann, Karl; Flaßkamp, Kathrin; Urbschat, Steffi; Oertel, Joachim; Sattel, Thomas
A manually actuated continuum robot research platform for deployable shape-memory curved cannulae in stereotactic neurosurgery. - In: IEEE Xplore digital library, ISSN 2473-2001, (2022), S. 10-13

In this paper, a research platform for concentric tube continuum robots is developed in order to enable advances in deploying curved cannulae for stereotactic neurosurgery. The system consists of a manually operated high-precision actuation apparatus and a photogrammetric system with measurement errors in the range of 100 micrometer. With this platform, previously planned curved paths can be analyzed ex-situ w.r.t., e.g., target precision, follow-the-leader-behavior, and hysteretic phenomena. Regarding research towards an in-vivo application in human brains, first tests with porcine brain cadavers inside an intraoperative CT are conducted in order to pave the way for histological as well as target reachability studies.
Sauerteig, Philipp; Hoffmann, Matthias K.; Mühlenhoff, Julian; Miccoli, Giovanni; Keiner, Dörthe; Urbschat, Steffi; Oertel, Joachim; Sattel, Thomas; Flaßkamp, Kathrin; Worthmann, Karl
Optimal path planning for stereotactic neurosurgery based on an elastostatic cannula model. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 55 (2022), 20, S. 600-605

In this paper, we propose a path-planning problem for stereotactic neurosurgery using concentric tube robots. The main goal is to reach a given region of interest inside the brain, e.g. a tumor, starting from a feasible point on the skull with an ideally short path avoiding certain sensitive brain areas. To describe the shape of the entire cannula from an entry point to the point of interest we use an existing mechanical model for continuum robots. We show numerically that our approach enables the surgeon to reach areas within the brain that would be impossible with a straight cannula as it is currently state of the art.
Schaller, Manuel; Wilson, Mitsuru; Kleyman, Viktoria; Mordmüller, Mario; Brinkmann, Ralf; Müller, Matthias A.; Worthmann, Karl
Parameter estimation and model reduction for model predictive control in retinal laser treatment. - In: Control engineering practice, ISSN 1873-6939, Bd. 128 (2022), 105320

Laser photocoagulation is one of the most frequently used treatment approaches for retinal diseases such as diabetic retinopathy and macular edema. The use of model-based control, such as Model Predictive Control (MPC), enhances a safe and effective treatment by guaranteeing temperature bounds. In general, real-time requirements for model-based control designs are not met since the temperature distribution in the eye fundus is governed by a heat equation with a nonlinear parameter dependency. This issue is circumvented by representing the model by a lower-dimensional system which well-approximates the original model, including the parametric dependency. We combine a global-basis approach with the discrete empirical interpolation method, tailor its hyperparameters to laser photocoagulation, and show its superiority in comparison to a recently proposed method based on Taylor-series approximation. Its effectiveness is measured in computation time for MPC. We further present a case study to estimate the range of absorption parameters in porcine eyes, and by means of a theoretical and numerical sensitivity analysis we show that the sensitivity of the temperature increase is higher with respect to the absorption coefficient of the retinal pigment epithelium (RPE) than of the choroid’s.
Sauerteig, Philipp; Esterhuizen, Willem; Wilson, Mitsuru; Ritschel, Tobias K. S.; Worthmann, Karl; Streif, Stefan
Model predictive control tailored to epidemic models. - In: IEEE Xplore digital library, ISSN 2473-2001, (2022), S. 743-748

We propose a model predictive control (MPC) approach for minimising the social distancing and quarantine measures during a pandemic while maintaining a hard infection cap. To this end, we study the admissible and the maximal robust positively invariant set (MRPI) of the standard SEIR compartmental model with control inputs. Exploiting the fact that in the MRPI all restrictions can be lifted without violating the infection cap, we choose a suitable subset of the MRPI to define terminal constraints in our MPC routine and show that the number of infected people decays exponentially within this set. Furthermore, under mild assumptions we prove existence of a uniform bound on the time required to reach this terminal region (without violating the infection cap) starting in the admissible set. The findings are substantiated based on a numerical case study.
Kirchhoff, Jonas;
Linear port-Hamiltonian systems are generically controllable. - In: IEEE transactions on automatic control, ISSN 1558-2523, Bd. 67 (2022), 6, S. 3220-3222

The new concept of relative generic subsets is introduced. It is shown that the set of controllable linear finite-dimensional port-Hamiltonian systems is a relative generic subset of the set of all linear finite-dimensional port-Hamiltonian systems. This implies that a random, continuously distributed port-Hamiltonian system is almost surely controllable.
Berger, Thomas; Dennstädt, Dario
Funnel MPC with feasibility constraints for nonlinear systems with arbitrary relative degree. - In: IEEE control systems letters, ISSN 2475-1456, Bd. 6 (2022), S. 2804-2809

We study tracking control for nonlinear systems with known relative degree and stable internal dynamics by the recently introduced technique of Funnel MPC. The objective is to achieve the evolution of the tracking error within a prescribed performance funnel. We propose a novel stage cost for Funnel MPC, extending earlier designs to the case of arbitrary relative degree, and show that the control objective as well as initial and recursive feasibility are always achieved - without requiring any terminal conditions or a sufficiently long prediction horizon. We only impose an additional feasibility constraint in the optimal control problem.
Öztürk, Emrah; Rheinberger, Klaus; Faulwasser, Timm; Worthmann, Karl; Preißinger, Markus
Aggregation of demand-side flexibilities: a comparative study of approximation algorithms. - In: Energies, ISSN 1996-1073, Bd. 15 (2022), 7, 2501, S. 1-14

Traditional power grids are mainly based on centralized power generation and subsequent distribution. The increasing penetration of distributed renewable energy sources and the growing number of electrical loads is creating difficulties in balancing supply and demand and threatens the secure and efficient operation of power grids. At the same time, households hold an increasing amount of flexibility, which can be exploited by demand-side management to decrease customer cost and support grid operation. Compared to the collection of individual flexibilities, aggregation reduces optimization complexity, protects households' privacy, and lowers the communication effort. In mathematical terms, each flexibility is modeled by a set of power profiles, and the aggregated flexibility is modeled by the Minkowski sum of individual flexibilities. As the exact Minkowski sum calculation is generally computationally prohibitive, various approximations can be found in the literature. The main contribution of this paper is a comparative evaluation of several approximation algorithms in terms of novel quality criteria, computational complexity, and communication effort using realistic data. Furthermore, we investigate the dependence of selected comparison criteria on the time horizon length and on the number of households. Our results indicate that none of the algorithms perform satisfactorily in all categories. Hence, we provide guidelines on the application-dependent algorithm choice. Moreover, we demonstrate a major drawback of some inner approximations, namely that they may lead to situations in which not using the flexibility is impossible, which may be suboptimal in certain situations.
Grundel, Sara; Heyder, Stefan; Hotz, Thomas; Ritschel, Tobias K. S.; Sauerteig, Philipp; Worthmann, Karl
How much testing and social distancing is required to control COVID-19? : some insight based on an age-differentiated compartmental model. - In: SIAM journal on control and optimization, ISSN 1095-7138, Bd. 60 (2022), 2, S. S145-S169

In this paper, we provide insights on how much testing and social distancing is required to control COVID-19. To this end, we develop a compartmental model that accounts for key aspects of the disease: incubation time, age-dependent symptom severity, and testing and hospitalization delays; the model's parameters are chosen based on medical evidence, and, for concreteness, adapted to the German situation. Then, optimal mass-testing and age-dependent social distancing policies are determined by solving optimal control problems both in open loop and within a model predictive control framework. We aim to minimize testing and/or social distancing until herd immunity sets in under a constraint on the number of available intensive care units. We find that an early and short lockdown is inevitable but can be slowly relaxed over the following months.
Grüne, Lars; Schaller, Manuel; Schiela, Anton
Efficient model predictive control for parabolic PDEs with goal oriented error estimation. - In: SIAM journal on scientific computing, ISSN 1095-7197, Bd. 44 (2022), 1, S. A471-A500

We show how a posteriori goal oriented error estimation can be used to efficiently solve the subproblems occurring in a model predictive control (MPC) algorithm. In MPC, only an initial part of a computed solution is implemented as a feedback, which motivates grid refinement particularly tailored to this context. To this end, we present a truncated cost functional as an objective for goal oriented adaptivity and prove under stabilizability assumptions that error indicators decay exponentially outside the support of this quantity. This leads to very efficient time and space discretizations for MPC, which we will illustrate by means of various numerical examples.