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Prof. Dr. Achim Ilchmann

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Baidiuk, D.; Derkach, Volodymyr; Hassi, Seppo;
Unitary boundary pairs for isometric operators in Pontryagin spaces and generalized coresolvents. - In: Complex analysis and operator theory. - Cham (ZG) : Springer International Publishing AG, ISSN 1661-8262, Volume 15 (2021), issue 2, article 32, Seite 1-52

https://doi.org/10.1007/s11785-020-01073-4
Berger, Thomas; Snoo, Henk; Trunk, Carsten; Winkler, Henrik;
Linear relations and their singular chains. - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2021. - 1 Online-Ressource (17 Seiten). . - (Preprint. - M21,01)
https://nbn-resolving.org/urn:nbn:de:gbv:ilm1-2021200018
Derkach, Volodymyr; Dym, Harry;
Functional models for entire symmetric operators in rigged de Branges Pontryagin spaces. - In: Journal of functional analysis. - Amsterdam [u.a.] : Elsevier, ISSN 1096-0783, Volume 280 (2021), issue 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
Gernandt, Hannes; Haller, Frederic E.; Reis, Timo; Schaft, Abraham Jan van der;
Port-Hamiltonian formulation of nonlinear electrical circuits. - In: Journal of geometry and physics : JGP.. - Amsterdam [u.a.] : North-Holland, Bd. 159 (2021), 103959, S. 1-15

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
Esterhuizen, Willem; Worthmann, Karl; Streif, Stefan;
Recursive feasibility of continuous-time model predictive control without stabilising constraints. - In: IEEE control systems letters. - New York, NY : IEEE, ISSN 2475-1456, Bd. 5 (2021), 1, S. 265-270

https://doi.org/10.1109/LCSYS.2020.3001514
Kleyman, Viktoria; Abbas, Hossam S.; Brinkmann, Ralf; Worthmann, Karl; Müller, Matthias A.;
Modelling of heat diffusion for temperature-controlled retinal photocoagulation. - In: Proceedings on automation in medical engineering. - Lübeck : Infinite Science GmbH, Vol. 1 (2020), no. 1, paperID: 006, 2 Seiten

https://doi.org/10.18416/AUTOMED.2020
Coron, Jean-Michel; Grüne, Lars; Worthmann, Karl;
Model predictive control, cost controllability, and homogeneity. - In: SIAM journal on control and optimization. - Philadelphia, Pa. : Soc., ISSN 1095-7138, Bd. 58 (2020), 5, S. 2979-2996

We are concerned with the design of Model Predictive Control (MPC) schemes such that asymptotic stability of the resulting closed loop is guaranteed - even if the linearization at the desired set point fails to be stabilizable. Therefore, we propose constructing the stage cost based on the homogeneous approximation and rigorously show that applying MPC yields an asymptotically stable closed-loop behavior if the homogeneous approximation is asymptotically null controllable. To this end, we verify cost controllability - a condition relating the current state, the stage cost, and the growth of the value function with respect to time - for this class of systems in order to provide stability and performance guarantees for the proposed MPC scheme without stabilizing terminal costs or constraints.



https://doi.org/10.1137/19M1265995
Faulwasser, Timm; Göttlich, Simone; Worthmann, Karl;
Mathematical innovations fostering the energy transition - control and optimization. - In: Automatisierungstechnik : AT.. - Berlin : De Gruyter, ISSN 2196-677X, Bd. 68 (2020), 12, S. 982-984
- Editorial

https://doi.org/10.1515/auto-2020-0152
Kleyman, Viktoria; Gernandt, Hannes; Worthmann, Karl; Abbas, Hossam S.; Brinkmann, Ralf; Müller, Matthias A.;
Modeling and parameter identification for real-time temperature controlled retinal laser therapies. - In: Automatisierungstechnik : AT.. - Berlin : De Gruyter, ISSN 2196-677X, Bd. 68 (2020), 11, S. 953-966

Laser photocoagulation is a widely used treatment for a variety of retinal diseases. Temperature-controlled irradiation is a promising approach to enable uniform heating, reduce the risks of over- or undertreatment, and unburden the ophthalmologists from a time consuming manual power titration. In this paper, an approach is proposed for the development of models with different levels of detail, which serve as a basis for improved, more accurate observer and control designs. To this end, we employ a heat diffusion model and propose a suitable discretization and subsequent model reduction procedures. Since the absorption of the laser light can vary strongly at each irradiation site, a method for identifying the absorption coefficient is presented. To identify a parameter in a reduced order model, an optimal interpolatory projection method for parametric systems is used. In order to provide an online identification of the absorption coefficient, we prove and exploit monotonicity of the parameter influence.



https://doi.org/10.1515/auto-2020-0074
Janse van Rensburg, Dawie; Van Straaten, Madelein; Theron, Frieda; Trunk, Carsten;
Square roots of H-nonnegative matrices. - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2020. - 1 Online-Ressource (24 Seiten). . - (Preprint. - M20,01)
https://nbn-resolving.org/urn:nbn:de:gbv:ilm1-2020200426