Publications at the Institute of Mathematics

Results: 2072
Created on: Thu, 28 Mar 2024 23:08:23 +0100 in 0.0751 sec


Reis, Timo; Stykel, Tatjana
Passivity, port-Hamiltonian formulation and solution estimates for a coupled magneto-quasistatic system. - In: Evolution equations and control theory, ISSN 2163-2480, Bd. 12 (2023), 4, S. 1208-1232

In this paper, we study a quasilinear coupled magneto-quasistatic model from a systems theoretic perspective. First, by taking the injected voltages as input and the associated currents as output, we prove that the magneto-quasistatic system is passive. Moreover, by defining suitable Dirac and resistive structures, we show that it admits a representation as a port-Hamiltonian system. Thereafter, we consider dependence of the solution on initial and input data. We show that the current and the magnetic vector potential can be estimated by means of the initial magnetic vector potential and the voltage. We also analyse the free dynamics of the system and study the asymptotic behavior of the solutions for $ t\to\infty $.



https://doi.org/10.3934/eect.2023008
Sherratt, Katharine; Gruson, Hugo; Grah, Rok; Johnson, Helen; Niehus, Rene; Prasse, Bastian; Sandmann, Frank; Deuschel, Jannik; Wolffram, Daniel; Abbott, Sam; Ullrich, Alexander; Gibson, Graham; Ray, Evan L.; Reich, Nicholas G.; Sheldon, Daniel; Wang, Yijin; Wattanachit, Nutcha; Wang, Lijing; Trnka, Jan; Obozinski, Guillaume; Sun, Tao; Thanou, Dorina; Pottier, Loic; Krymova, Ekaterina; Meinke, Jan H.; Barbarossa, Maria Vittoria; Leithäuser, Neele; Mohring, Jan; Schneider, Johanna; Wlazło, Jarosław; Fuhrmann, Jan; Lange, Berit; Rodiah, Isti; Baccam, Prasith; Gurung, Heidi; Stage, Steven; Suchoski, Bradley; Budzinski, Jozef; Walraven, Robert; Villanueva, Inmaculada; Tucek, Vit; Smid, Martin; Zajíček, Milan; Pérez Álvarez, Cesar; Reina, Borja; Bosse, Nikos I.; Meakin, Sophie R.; Castro, Lauren; Fairchild, Geoffrey; Michaud, Isaac; Osthus, Dave; Alaimo Di Loro, Pierfrancesco; Maruotti, Antonello; Eclerová, Veronika; Kraus, Andrea; Kraus, David; Pribylova, Lenka; Dimitris, Bertsimas; Li, Michael Lingzhi; Saksham, Soni; Dehning, Jonas; Mohr, Sebastian; Priesemann, Viola; Redlarski, Grzegorz; Bejar Haro, Benjamin; Ardenghi, Giovanni; Parolini, Nicola; Ziarelli, Giovanni; Bock, Wolfgang; Heyder, Stefan; Hotz, Thomas; Singh, David E.; Guzman-Merino, Miguel; Aznarte, Jose L.; Moriña, David; Alonso, Sergio; Álvarez, Enric; López, Daniel; Prats, Clara; Burgard, Jan Pablo; Rodloff, Arne; Zimmermann, Tom; Kuhlmann, Alexander; Zibert, Janez; Pennoni, Fulvia; Divino, Fabio; Català, Marti; Lovison, Gianfranco; Giudici, Paolo; Tarantino, Barbara; Bartolucci, Francesco; Jona Lasinio, Giovanna; Mingione, Marco; Farcomeni, Alessio; Srivastava, Ajitesh; Montero-Manso, Pablo; Adiga, Aniruddha; Hurt, Benjamin; Lewis, Bryan; Marathe, Madhav; Porebski, Przemyslaw; Venkatramanan, Srinivasan; Bartczuk, Rafal P.; Dreger, Filip; Gambin, Anna; Gogolewski, Krzysztof; Gruziel-Słomka, Magdalena; Krupa, Bartosz; Moszyânski, Antoni; Niedzielewski, Karol; Nowosielski, Jedrzej; Radwan, Maciej; Rakowski, Franciszek; Semeniuk, Marcin; Szczurek, Ewa; Zieliânski, Jakub; Kisielewski, Jan; Pabjan, Barbara; Kirsten, Holger; Kheifetz, Yuri; Scholz, Markus; Biecek, Przemysław; Bodych, Marcin; Filinski, Maciej; Idzikowski, Radoslaw; Krueger, Tyll; Ozanski, Tomasz; Bracher, Johannes; Funk, Sebastian
Predictive performance of multi-model ensemble forecasts of COVID-19 across European nations. - In: eLife, ISSN 2050-084X, Bd. 12 (2023), e81916, S. 1-23, insges. 23 S.

https://doi.org/10.7554/eLife.81916
Behrndt, Jussi; Schmitz, Philipp; Teschl, Gerald; Trunk, Carsten
Perturbations of periodic Sturm-Liouville operators. - In: Advances in mathematics, ISSN 1090-2082, Bd. 422 (2023), 109022, S. 1-22

https://doi.org/10.1016/j.aim.2023.109022
Kleyman, Viktoria; Schaller, Manuel; Mordmüller, Mario; Wilson, Mitsuru; Brinkmann, Ralf; Worthmann, Karl; Müller, Matthias A.
State and parameter estimation for retinal laser treatment. - In: IEEE transactions on control systems technology, ISSN 1558-0865, Bd. 31 (2023), 3, S. 1366-1378

Adequate therapeutic retinal laser irradiation needs to be adapted to local absorption. This leads to time-consuming treatments as the laser power needs to be successively adjusted to avoid undertreatment and overtreatment caused by too low or too high temperatures. Closed-loop control can overcome this burden by means of temperature measurements. To allow for model predictive control schemes, the current state and the spot-dependent absorption need to be estimated. In this article, we thoroughly compare moving horizon estimator (MHE) and extended Kalman filter (EKF) designs for joint state and parameter estimation. We consider two different scenarios, the estimation of one or two unknown absorption coefficients. For one unknown parameter, both estimators perform very similarly. For two unknown parameters, we found that the MHE benefits from active parameter constraints at the beginning of the estimation, whereas after a settling time, both estimators perform again very similarly as long as the parameters are inside the considered parameter bounds.



https://doi.org/10.1109/TCST.2022.3228442
Caragea, Andrei; Lee, Dae Gwan; Philipp, Friedrich; Voigtlaender, Felix
A Balian-Low type theorem for Gabor Riesz sequences of arbitrary density. - In: Mathematische Zeitschrift, ISSN 1432-1823, Bd. 303 (2023), 2, 48, S. 1-22

https://doi.org/10.1007/s00209-022-03182-6
Eichfelder, Gabriele; Warnow, Leo
Advancements in the computation of enclosures for multi-objective optimization problems. - In: European journal of operational research, ISSN 0377-2217, Bd. 310 (2023), 1, S. 315-327

A central goal for multi-objective optimization problems is to compute their nondominated sets. In most cases these sets consist of infinitely many points and it is not a practical approach to compute them exactly. One solution to overcome this problem is to compute an enclosure, a special kind of coverage, of the nondominated set. For that computation one often makes use of so-called local upper bounds. In this paper we present a generalization of this concept. For the first time, this allows to apply a warm start strategy to the computation of an enclosure. We also show how this generalized concept allows to remove empty areas of an enclosure by deleting certain parts of the lower and upper bound sets which has not been possible in the past. We demonstrate how to apply our ideas to the box approximation algorithm, a general framework to compute an enclosure, as recently used in the solver called BAMOP. We show how that framework can be simplified and improved significantly, especially concerning its practical numerical use. In fact, we show for selected numerical instances that our new approach is up to eight times faster than the original one. Hence, our new framework is not only of theoretical but also of practical use, for instance for continuous convex or mixed-integer quadratic optimization problems.



https://doi.org/10.1016/j.ejor.2023.02.032
âCurgus, Branko; Derkach, Volodymyr; Trunk, Carsten
Indefinite Sturm-Liouville operators in polar form. - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2023. - 1 Online-Ressource (49 Seiten). - (Preprint ; M23,05)
https://nbn-resolving.org/urn:nbn:de:gbv:ilm1-2023200114
Aschenbruck, Tim; Dickert, Jörg; Esterhuizen, Willem; Filipecki, Bartosz; Grundel, Sara; Helmberg, Christoph; Ritschel, Tobias K. S.; Sauerteig, Philipp; Streif, Stefan; Wasserrab, Andreas; Worthmann, Karl
Hierarchical power systems: optimal operation using grid flexibilities. - Cham : Springer International Publishing, 2023. - 1 Online-Ressource (viii, 55 Seiten). - (SpringerBriefs in Energy) ISBN 978-3-031-25699-8

Introduction -- Preliminary theory -- Providing flexibility via residential batteries -- Flexibility in the distribution grid -- Security and stability on the transmission grid -- Implementation in the distribution grid and the microgrids -- Numerical example -- Conclusion.



https://doi.org/10.1007/978-3-031-25699-8
Chill, Ralph; Reis, Timo; Stykel, Tatjana
Analysis of a quasilinear coupled magneto-quasistatic model: solvability and regularity of solutions. - In: Journal of mathematical analysis and applications, ISSN 1096-0813, Bd. 523 (2023), 2, 127033

We consider a quasilinear model arising from dynamical magnetization. This model is described by a magneto-quasistatic (MQS) approximation of Maxwell's equations. Assuming that the medium consists of a conducting and a non-conducting part, the derivative with respect to time is not fully entering, whence the system can be described by an abstract differential-algebraic equation. Furthermore, via magnetic induction, the system is coupled with an equation which contains the induced electrical currents along the associated voltages, which form the input of the system. The aim of this paper is to study well-posedness of the coupled MQS system and regularity of its solutions. Thereby, we rely on the classical theory of gradient systems on Hilbert spaces combined with the concept of E-subgradients using in particular the magnetic energy. The coupled MQS system precisely fits into this general framework.



https://doi.org/10.1016/j.jmaa.2023.127033
Derkach, Volodymyr; Trunk, Carsten
PT-symmetric couplings of dual pairs. - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2023. - 1 Online-Ressource (24 Seiten). - (Preprint ; M23,03)
https://nbn-resolving.org/urn:nbn:de:gbv:ilm1-2023200049