Publikationen am Fachgebiet

Results: 79
Created on: Thu, 11 Aug 2022 23:07:46 +0200 in 0.0811 sec


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.



https://doi.org/10.1109/TAC.2021.3098176
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.



https://doi.org/10.1109/LCSYS.2022.3178478
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.



https://doi.org/10.3390/en15072501
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.



https://doi.org/10.1137/20M1377783
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.



https://doi.org/10.1137/20M1356324
Schmitz, Philipp; Faulwasser, Timm; Worthmann, Karl;
Willems' fundamental lemma for linear descriptor systems and its use for data-driven output-feedback MPC. - In: IEEE control systems letters, ISSN 2475-1456, Bd. 6 (2022), S. 2443-2448

In this letter we investigate data-driven predictive control of discrete-time linear descriptor systems. Specifically, we give a tailored variant of Willems' fundamental lemma, which shows that for descriptor systems the non-parametric modeling via a Hankel matrix requires less data compared to linear time-invariant systems without algebraic constraints. Moreover, we use this description to propose a data-driven framework for optimal control and predictive control of discrete-time linear descriptor systems. For the latter, we provide a sufficient stability condition for receding-horizon control before we illustrate our findings with an example.



https://doi.org/10.1109/LCSYS.2022.3161054
Babovsky, Hans; Bold, Lea;
Balanced states and closure relations: the fluid dynamic limit of kinetic models. - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2022. - 1 Online-Ressource (20 Seiten). - (Preprint ; M22,03)

The paper is concerned with closure relations for moment hierarchies of gaskinetic systems in the uid dynamic limit. We develop the concept of balanced solutions which provides a more detailed description of kinetic solutions that the classical approaches. This allows to compare di_erent models in use like the nonlinear Boltzmann equation, its linearization, and the BGK model and their relation to the classical Navier-Stokes equations.



https://nbn-resolving.org/urn:nbn:de:gbv:ilm1-2022200188
Ilchmann, Achim; Witschel, Jonas; Worthmann, Karl;
Model predictive control for singular differential-algebraic equations. - In: International journal of control, ISSN 1366-5820, Bd. 95 (2022), 8, S. 2141-2150

We study model predictive control for singular differential-algebraic equations with higher index. This is a novelty when compared to the literature where only regular differential-algebraic equations with additional assumptions on the index and/or controllability are considered. By regularisation techniques, we are able to derive an equivalent optimal control problem for an ordinary differential equation to which well-known model predictive control techniques can be applied. This allows the construction of terminal constraints and costs such that the origin is asymptotically stable w.r.t. the resulting closed-loop system.



https://doi.org/10.1080/00207179.2021.1900604
Mordmüller, Mario; Kleyman, Viktoria; Schaller, Manuel; Wilson, Mitsuru; Worthmann, Karl; Müller, Matthias A.; Brinkmann, Ralf;
Towards model-based control techniques for retinal laser treatment using only one laser. - In: Opto-Acoustic Methods and Applications in Biophotonics V, (2021), S. 1192305-1-1192305-3

Repetitively applied laser pulses are used for tissue heating and temperature measurement. The potential of model-based control techniques for temperature regulation by adjusting the energy of the heating pulses is explored.



Sauerteig, Philipp; Baumann, Manuel; Dickert, Jörg; Grundel, Sara; Worthmann, Karl;
Reducing transmission losses via reactive power control. - In: Mathematical modeling, simulation and optimization for power engineering and management, (2021), S. 219-232

Modern smart grids are required to transport electricity along transmission lines from the renewable energy sources to the customers demand in an efficient manner. It is inevitable that power is lost along these lines due to active as well as reactive power flows. However, the losses caused by reactive power flows can be reduced by optimizing the power factor. Therefore, we propose a power flow optimization problem aiming to reduce losses by controlling the power factors within the low-voltage electricity grid online. Furthermore, we show the potential of the proposed scheme in a numerical case study for two scenarios based on real-world data provided by a German distribution system operator.