Optimality conditions for set optimization using a directional derivative based on generalized Steiner sets. - In: Optimization, ISSN 1029-4945, Bd. 71 (2022), 8, S. 2273-2314
Set-optimization has attracted increasing interest in the last years, as for instance uncertain multiobjective optimization problems lead to such problems with a set-valued objective function. Thereby, from a practical point of view, most of all the so-called set approach is of interest. However, optimality conditions for these problems, for instance using directional derivatives, are still very limited. The key aspect for a useful directional derivative is the definition of a useful set difference for the evaluation of the numerator in the difference quotient. We present here a new set difference which avoids the use of a convex hull and which applies to arbitrary convex sets, and not to strictly convex sets only. The new set difference is based on the new concept of generalized Steiner sets. We introduce the Banach space of generalized Steiner sets as well as anembedding of convex sets in this space using Steiner points.In this Banach space we can easily define a difference and a directional derivative. We use the latter for new optimality conditions for set optimization. Numerical examples illustrate the new concepts.
https://doi.org/10.1080/02331934.2020.1812605
Make some noise: energy-efficient 38 Gbit/s wide-range fully-configurable linear feedback shift register. - In: SMACD / PRIME 2021, (2021), S. 384-387
https://ieeexplore.ieee.org/document/9547997
On Clarke's subdifferential of marginal functions. - In: Applied set-valued analysis and optimization, ISSN 2562-7783, Bd. 3 (2021), 3, S. 281-292
In this paper, we derive an upper estimate of the Clarke subdifferential of marginal functions in Banach spaces. The structure of the upper estimate is very similar to other results already obtained in the literature. The novelty lies on the fact that we derive our assertions in general Banach spaces, and avoid the use of the Asplund assumption.
https://doi.org/10.23952/asvao.3.2021.3.03
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.
https://doi.org/10.1117/12.2615851
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 customer’s 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.
Optimization and stabilization of hierarchical electrical networks. - In: Mathematical modeling, simulation and optimization for power engineering and management, (2021), S. 171-198
Triggered by the increasing number of renewable energy sources, the German electricity grid is undergoing a fundamental change from mono to bidirectional power flow. This paradigm shift confronts grid operators with new problems but also new opportunities. In this chapter we point out some of these problems arising on different layers of the grid hierarchy and sketch mathematical methods to handle them. While the transmission system operator’s main concern is stability and security of the system in case of contingencies, the distribution system operator aims to exploit inherent flexibilities. We identify possible interconnections among the layers to make the flexibility from the distribution grid available within the whole network. Our presented approaches include: the distributed control of energy storage devices on a residential level; transient stability analysis via a new set-based approach; a new clustering-based model-order reduction technique; and a modeling framework for the power flow problem on the transmission level which incorporates new grid technologies.
Towards temperature controlled retinal laser treatment with a single laser at 10 kHz repetition rate. - In: Advanced Optical Technologies, ISSN 2192-8584, Bd. 10 (2021), 6, S. 423-431
Laser photocoagulation is one of the most frequently used treatment approaches in ophthalmology for a variety of retinal diseases. Depending on indication, treatment intensity varies from application of specific micro injuries down to gentle temperature increases without inducing cell damage. Especially for the latter, proper energy dosing is still a challenging issue, which mostly relies on the physician's experience. Pulsed laser photoacoustic temperature measurement has already proven its ability for automated irradiation control during laser treatment but suffers from a comparatively high instrumental effort due to combination with a conventional continuous wave treatment laser. In this paper, a simplified setup with a single pulsed laser at 10 kHz repetition rate is presented. The setup combines the instrumentation for treatment as well as temperature measurement and control in a single device. In order to compare the solely pulsed heating with continuous wave (cw) tissue heating, pulse energies of 4 [my]J were applied with a repetition rate of 1 kHz to probe the temperature rise, respectively. With the same average laser power of 60 mW an almost identical temporal temperature course was retrieved in both irradiation modes as expected. The ability to reach and maintain a chosen aim temperature of 41 ˚C is demonstrated by means of model predictive control (MPC) and extended Kalman filtering at a the measurement rate of 250 Hz with an accuracy of less than ±0.1 ˚C. A major advantage of optimization-based control techniques like MPC is their capability of rigorously ensuring constraints, e.g., temperature limits, and thus, realizing a more reliable and secure temperature control during retinal laser irradiation.
https://doi.org/10.1515/aot-2021-0041
Minimizing the energy supply of infinite-dimensional linear port-Hamiltonian systems. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 54 (2021), 19, S. 155-160
We consider the problem of minimizing the supplied energy of infinite-dimensional linear port-Hamiltonian systems and prove that optimal trajectories exhibit the turnpike phenomenon towards certain subspaces induced by the dissipation of the dynamics. The theoretical foundations are illustrated by means of numerical examples concerning a Timoshenko beam and the heat equation.
https://doi.org/10.1016/j.ifacol.2021.11.071
State and parameter estimation for model-based retinal laser treatment. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 54 (2021), 6, S. 244-250
We present an approach for state and parameter estimation in retinal laser treatment by a novel setup where both measurement and heating is performed by a single laser. In this medical application, the temperature that is induced by the laser in the patients eye is critical for a successful and safe treatment. To this end, we pursue a model-based approach using a model given by a heat diffusion equation on a cylindrical domain, where the source term is given by the absorbed laser power. The model is parametric in the sense that it involves an absorption coefficient, which depends on the treatment spot and plays a central role in the input-output behavior of the system. After discretization, we apply a particularly suited parametric model order reduction to ensure real-time tractability while retaining parameter dependence. We augment known state estimation techniques, i.e., extended Kalman filtering and moving horizon estimation, with parameter estimation to estimate the absorption coefficient and the current state of the system. Eventually, we show first results for simulated and experimental data from porcine eyes. We find that, regarding convergence speed, the moving horizon estimation slightly outperforms the extended Kalman filter on measurement data in terms of parameter and state estimation, however, on simulated data the results are very similar.
https://doi.org/10.1016/j.ifacol.2021.08.552
Inferring the adjoint turnpike property from the primal turnpike property. - In: 60th IEEE Conference on Decision and Control, (2021), S. 2578-2583
This paper investigates an interval turnpike result for the adjoints/costates of finite- and infinite-dimensional nonlinear optimal control problems under the assumption of an interval turnpike on states and controls. We consider stabilizable dynamics governed by a generator of a semigroup with finite-dimensional unstable part satisfying a spectral decomposition condition and show the desired turnpike property under continuity assumptions on the first-order optimality conditions. We further provide a numerical example with a semilinear heat equation to illustrate the results.
https://doi.org/10.1109/CDC45484.2021.9683079