Publications

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.

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.

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.

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.

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.