Expensive multi-objective optimization of electromagnetic mixing in a liquid metal. - In: Optimization and engineering, ISSN 1573-2924, Bd. 22 (2021), 2, S. 1065-1089
This paper presents a novel trust-region method for the optimization of multiple expensive functions. We apply this method to a biobjective optimization problem in fluid mechanics, the optimal mixing of particles in a flow in a closed container. The three-dimensional time-dependent flows are driven by Lorentz forces that are generated by an oscillating permanent magnet located underneath the rectangular vessel. The rectangular magnet provides a spatially non-uniform magnetic field that is known analytically. The magnet oscillation creates a steady mean flow (steady streaming) similar to those observed from oscillating rigid bodies. In the optimization problem, randomly distributed mass-less particles are advected by the flow to achieve a homogeneous distribution (objective function 1) while keeping the work done to move the permanent magnet minimal (objective function 2). A single evaluation of these two objective functions may take more than two hours. For that reason, to save computational time, the proposed method uses interpolation models on trust-regions for finding descent directions. We show that, even for our significantly simplified model problem, the mixing patterns vary significantly with the control parameters, which justifies the use of improved optimization techniques and their further development.
https://doi.org/10.1007/s11081-020-09561-4
Functional models for entire symmetric operators in rigged de Branges Pontryagin spaces. - In: Journal of functional analysis, ISSN 1096-0783, Bd. 280 (2021), 2, 108776
The theory of operator extensions in rigged Pontryagin spaces is used to develop two functional models for closed symmetric entire operators S with finite deficiency indices (p,p) acting in a separable Pontryagin space K. In the first functional model it is shown that every such operator S is unitarily equivalent to the multiplication operator in a de Branges-Pontryagin space B(E) of p×1 vector valued entire functions. The second functional model is used to parametrize a class of compressed resolvents of extensions ÜÞS of S in terms of the range of a linear fractional transformation that is associated with the model. This approach is independent of the methods used by Krein and Langer to parameterize a related class of extensions.
https://doi.org/10.1016/j.jfa.2020.108776
Port-Hamiltonian formulation of nonlinear electrical circuits. - In: Journal of geometry and physics, Bd. 159 (2021), 103959, insges. 15 S.
We consider nonlinear electrical circuits for which we derive a port-Hamiltonian formulation. After recalling a framework for nonlinear port-Hamiltonian systems, we model each circuit component as an individual port-Hamiltonian system. The overall circuit model is then derived by considering a port-Hamiltonian interconnection of the components. We further compare this modeling approach with standard formulations of nonlinear electrical circuits.
https://doi.org/10.1016/j.geomphys.2020.103959
Coordinate transformation and its uncertainty under consideration of a non-orthogonal coordinate base. - In: Measurement science and technology, ISSN 1361-6501, Bd. 32 (2021), 4, 045001, insges. 6 S.
Nanopositioning and nanomeasuring machines are 3D coordinate measuring systems with nanometer precision at measurement volumes in the cubic centimeter range. The coordinate base is formed by an interferometer system with a common mirror corner. The orthogonality deviations of the mirror corner require a coordinate transformation of the measuring axes. The uncertainty of the coordinate transformation must be taken into account in the overall measurement uncertainty budget. Starting from a complete transformation model, the result of model simplications on the transformation behaviour is analysed and discussed.
https://doi.org/10.1088/1361-6501/aba3f5
Partitions of hypergraphs under variable degeneracy constraints. - In: Journal of graph theory, ISSN 1097-0118, Bd. 96 (2021), 1, S. 7-33
https://doi.org/10.1002/jgt.22575
Recursive feasibility of continuous-time model predictive control without stabilising constraints. - In: IEEE control systems letters, ISSN 2475-1456, Bd. 5 (2021), 1, S. 265-270
https://doi.org/10.1109/LCSYS.2020.3001514
Invariance of the essential spectra of operator pencils. - In: Operator theory, operator algebras and their interactions with geometry and topology, (2020), S. 203-219
Distributed control enforcing group sparsity in smart grids. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 53 (2020), 2, S. 13269-13274
In modern smart grids, charging of local energy storage devices is coordinated within the distribution grid to compensate the volatile aggregated power demand on the time interval of interest. However, this results in a perpetual usage of all batteries which in return reduces their lifetime. In this paper, we enforce group sparsity by using an lp,q-regularization on the control to counteract this phenomenon. This leads to a non-smooth convex optimization problem, for which a tailored Alternating Direction Method of Multipliers algorithm is proposed. Furthermore, the algorithm is embedded in a Model Predictive Control framework. Numerical simulations show that the proposed scheme yields sparse control while achieving reasonable overall peak shaving.
https://doi.org/10.1016/j.ifacol.2020.12.156
Learning-based funnel-MPC for output-constrained nonlinear systems. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 53 (2020), 2, S. 5177-5182
We exploit an adaptive control technique, namely funnel control, to establish both initial and recursive feasibility in Model Predictive Control (MPC) for output-constrained nonlinear systems. Moreover, we show that the resulting feedback controller outperforms the funnel controller both w.r.t. the required sampling rate for a zero-order-hold implementation and required control action. We further propose a combination of funnel control and MPC, exploiting the performance guarantees of the model-free funnel controller during a learning phase and the advantages of the model-based MPC scheme thereafter.
https://doi.org/10.1016/j.ifacol.2020.12.1186
Modelling of heat diffusion for temperature-controlled retinal photocoagulation. - In: Proceedings on automation in medical engineering, Vol. 1 (2020), no. 1, paperID: 006, 2 Seiten
https://doi.org/10.18416/AUTOMED.2020