Publikationen

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.

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.

We derive sufficient conditions for strict dissipativity for optimal control of linear evolution equations on Hilbert spaces with a cost functional including linear and quadratic terms. We show that strict dissipativity with a particular storage function is equivalent to ellipticity of a Lyapunov-like operator. Further we prove under a spectral decomposition assumption of the underlying generator and an orthogonality condition of the resulting subspaces that this ellipticity property holds under a detectability assumption. We illustrate our result by means of an example involving a heat equation on a one-dimensional domain.

We consider an input-constrained differential-drive robot with actuator dynamics. For this system, we establish asymptotic stability of the origin on arbitrary compact, convex sets using Model Predictive Control (MPC) without stabilizing terminal conditions despite the presence of state constraints and actuator dynamics. We note that the problem without those two additional ingredients was essentially solved beforehand, despite the fact that the linearization is not stabilizable. We propose an approach successfully solving the task at hand by combining the theory of barriers to characterize the viability kernel and an MPC framework based on so-called cost controllability. Moreover, we present a numerical case study to derive quantitative bounds on the required length of the prediction horizon. To this end, we investigate the boundary of the viability kernel and a neighbourhood of the origin, i.e. the most interesting areas.