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
Conditions for strict dissipativity of infinite-dimensional generalized linear-quadratic problems. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 54 (2021), 19, S. 302-306
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.
https://doi.org/10.1016/j.ifacol.2021.11.094
Towards model-based temperature-control for retinal laser therapies. - In: Zenodo, (2021), insges. 2 S.
Sophisticated control designs for retinal laser therapies, such as model predictive control, allow for safer treatment and a uniform outcome irrespective of spatially varying parameters such as the absorption coefficient. To enable model-based control, the internal states and unknown parameters need to be estimated, which can be done using non-invasive temperature measurements. We present experimental results for joint state and parameter estimation using an extended Kalman filter and a moving horizon estimator. The experiments were conducted on ex vivo porcine eye's explants.
https://doi.org/10.5281/zenodo.4925803
Idempotent relations, semi-projections, and generalized inverses. - In: Contributions to mathematics and statistics, (2021), S. 87-110
PT-symmetric Hamiltonians as couplings of dual pairs. - In: Contributions to mathematics and statistics, (2021), S. 55-68
Twenty years of continuous multiobjective optimization in the twenty-first century. - In: EURO journal on computational optimization, ISSN 2192-4414, Bd. 9 (2021), 100014, insges. 15 S.
The survey highlights some of the research topics which have attracted attention in the last two decades within the area of mathematical optimization of multiple objective functions. We give insights into topics where a huge progress can be seen within the last years. We give short introductions to the specific sub-fields as well as some selected references for further reading. Primarily, the survey covers the progress in the development of algorithms. In particular, we discuss publicly available solvers and approaches for new problem classes such as non-convex and mixed integer problems. Moreover, bilevel optimization problems and the handling of uncertainties by robust approaches and their relation to set optimization are presented. In addition, we discuss why numerical approaches which do not use scalarization techniques are of interest.
https://doi.org/10.1016/j.ejco.2021.100014
Balanced truncation model reduction for symmetric second order systems - a passivity-based approach. - In: SIAM journal on matrix analysis and applications, ISSN 1095-7162, Bd. 42 (2021), 4, S. 1602-1635
We introduce a model reduction approach for linear time-invariant second order systems based on positive real balanced truncation. Our method guarantees to preserve asymptotic stability and passivity of the reduced order model as well as the positive definiteness of the mass and stiffness matrices. Moreover, we receive an a priori gap metric error bound. Finally we show that our method based on positive real balanced truncation preserves the structure of overdamped second order systems.
https://doi.org/10.1137/20M1346109
Hamiltonicity of random subgraphs of the hypercube. - In: Proceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms, (2021), S. 889-898
https://dl.acm.org/doi/10.5555/3458064.3458120
Predictive path following control without terminal constraints. - In: Recent advances in model predictive control, (2021), S. 1-26