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
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
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
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
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
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
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
Convexity and continuity of specific set-valued maps and their extremal value functions. - In: Journal of applied and numerical optimization, ISSN 2562-5535, Bd. 5 (2023), 1, S. 71-92
In this paper, we study several classes of set-valued maps, which can be used in set-valued optimization and its applications, and their respective maximum and minimum value functions. The definitions of these maps are based on scalar-valued, vector-valued, and cone-valued maps. Moreover, we consider those extremal value functions which are obtained when optimizing linear functionals over the image sets of the set-valued maps. Such extremal value functions play an important role for instance for derivative concepts for set-valued maps or for algorithmic approaches in set-valued optimization. We formulate conditions under which the set-valued maps and their extremal value functions inherit properties like (Lipschitz-)continuity and convexity.
https://doi.org/10.23952/jano.5.2023.1.05
Spectral inclusion property for a class of block operator matrices. - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2023. - 1 Online-Ressource (12 Seiten). - (Preprint ; M23,02)
The numerical range and the quadratic numerical range is used to study the spectrum of a class of block operator matrices. We show that the approximate point spectrum is contained in the closure of the quadratic numerical range. In particular, the spectral enclosures yield a spectral gap. It is shown that these spectral bounds are tighter than classical numerical range bounds.
https://nbn-resolving.org/urn:nbn:de:gbv:ilm1-2023200026
Lower bounds for self-adjoint Sturm-Liouville operators. - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2023. - 1 Online-Ressource (11 Seiten). - (Preprint ; M23,01)
https://nbn-resolving.org/urn:nbn:de:gbv:ilm1-2023200011