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
Predictive path following control without terminal constraints. - In: Recent advances in model predictive control, (2021), S. 1-26
A dissipativity characterization of velocity turnpikes in optimal control problems for mechanical systems. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 54 (2021), 9, S. 624-629
Turnpikes have recently gained significant research interest in optimal control, since they allow for pivotal insights into the structure of solutions to optimal control problems. So far, mainly steady state solutions which serve as optimal operation points, are studied. This is in contrast to time-varying turnpikes, which are in the focus of this paper. More concretely, we analyze symmetry-induced velocity turnpikes, i.e. controlled relative equilibria, called trim primitives, which are optimal operation points regarding the given cost criterion. We characterize velocity turnpikes by means of dissipativity inequalities. Moreover, we study the equivalence between optimal control problems and steady-state problems via the corresponding necessary optimality conditions. An academic example is given for illustration.
https://doi.org/10.1016/j.ifacol.2021.06.125
On MPC without terminal conditions for dynamic non-holonomic robots. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 54 (2021), 6, S. 133-138
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.
https://doi.org/10.1016/j.ifacol.2021.08.535
Control of port-Hamiltonian systems with minimal energy supply. - In: European journal of control, ISSN 1435-5671, Bd. 62 (2021), S. 33-40
We investigate optimal control of linear port-Hamiltonian systems with control constraints, in which one aims to perform a state transition with minimal energy supply. Decomposing the state space into dissipative and non-dissipative (i.e. conservative) subspaces, we show that the set of reachable states is bounded w.r.t. the dissipative subspace. We prove that the optimal control problem exhibits the turnpike property with respect to the non-dissipative subspace, i.e., for varying initial conditions and time horizons optimal state trajectories evolve close to the conservative subspace most of the time. We analyze the corresponding steady-state optimization problem and prove that all optimal steady states lie in the non-dissipative subspace. We conclude this paper by illustrating these results by a numerical example from mechanics.
https://doi.org/10.1016/j.ejcon.2021.06.017
Neurochirurgische Planung mittels automatisierter Bilderkennung und optimaler Pfadplanung :
Neurosurgery planning based on automated image recognition and optimal path design. - In: Automatisierungstechnik, ISSN 2196-677X, Bd. 69 (2021), 8, S. 708-721
Stereotactic neurosurgery requires a careful planning of cannulae paths to spare eloquent areas of the brain that, if damaged, will result in loss of essential neurological function such as sensory processing, linguistic ability, vision, or motor function. We present an approach based on modelling, simulation, and optimization to set up a computational assistant tool. Thereby, we focus on the modeling of the brain topology, where we construct ellipsoidal approximations of voxel clouds based on processed MRI data. The outcome is integrated in a path-planning problem either via constraints or by penalization terms in the objective function. The surgical planning problem with obstacle avoidance is solved for different types of stereotactic cannulae using numerical simulations. We illustrate our method with a case study using real MRI data.
https://doi.org/10.1515/auto-2021-0044
Distributed optimization using ALADIN for MPC in smart grids. - In: IEEE transactions on control systems technology, ISSN 1558-0865, Bd. 29 (2021), 5, S. 2142-2152
This article presents a distributed optimization algorithm tailored to solve optimization problems arising in smart grids. In detail, we propose a variant of the augmented Lagrangian-based alternating direction inexact Newton (ALADIN) method, which comes along with global convergence guarantees for the considered class of linear-quadratic optimization problems. We establish local quadratic convergence of the proposed scheme and elaborate its advantages compared with the alternating direction method of multipliers (ADMM). In particular, we show that, at the cost of more communication, ALADIN requires fewer iterations to achieve the desired accuracy. Furthermore, it is numerically demonstrated that the number of iterations is independent of the number of subsystems. The effectiveness of the proposed scheme is illustrated by running both an ALADIN and an ADMM-based model predictive controller on a benchmark case study.
https://doi.org/10.1109/TCST.2020.3033010