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Mehrez, Mohamed W.; Sprodowski, Tobias; Worthmann, Karl; Mann, George K. I.; Gosine, Raymond G.; Sagawa, Juliana K.; Pannek, Jürgen;
Occupancy grid based distributed MPC for mobile robots. - In: IROS Vancouver 2017 : IEEE/RSJ International Conference on Intelligent Robots and Systems, Vancouver, BC, Canada September 24-28, 2017 : conference digest.. - [Piscataway, NJ] : IEEE, (2017), S. 4842-4847

https://doi.org/10.1109/IROS.2017.8206360
Mehrez, Mohamed W.; Worthmann, Karl; Mann, George K.I.; Gosine, Raymond G.; Pannek, Jürgen;
Experimental speedup and stability validation for multi-step MPC. - In: IFAC-PapersOnLine. - Frankfurt : Elsevier, ISSN 2405-8963, Bd. 50 (2017), 1, S. 8698-8703

https://doi.org/10.1016/j.ifacol.2017.08.1551
Mehrez, Mohamed W.; Worthmann, Karl; Mann, George K.I.; Gosine, Raymond G.; Faulwasser, Timm;
Predictive path following of mobile robots without terminal stabilizing constraints. - In: IFAC-PapersOnLine. - Frankfurt : Elsevier, ISSN 2405-8963, Bd. 50 (2017), 1, S. 9852-9857

https://doi.org/10.1016/j.ifacol.2017.08.907
Ioan, Daniel-Mihail; Stoican, Florin; Worthmann, Karl;
Active fault detection and isolation in a zonotopic framework. - In: 2017 21st International Conference on System Theory, Control and Computing (ICSTCC) : October 19-21, 2017, Sinaia, Romania : proceedings.. - [Piscataway, NJ] : IEEE, ISBN 978-1-5386-3842-2, (2017), S. 595-600

https://doi.org/10.1109/ICSTCC.2017.8107100
Hasse, Seppo; Sandovici, Adrian; Snoo, Henk S. V.; Winkler, Henrik;
Extremal maximal sectorial extensions of sectorial relations. - In: Indagationes mathematicae. - Amsterdam : Elsevier, Bd. 28 (2017), 5, S. 1019-1055

https://doi.org/10.1016/j.indag.2017.07.003
Behrndt, Jussii; Schmitz, Philipp; Trunk, Carsten;
Spectral bounds for singular indefinite Sturm-Liouville operators with L1-potentials. - Ilmenau : Technische Universität, Institut für Mathematik, 2017. - 1 Online-Ressource (7 Seiten). . - (Preprint. - M17,12) - Im Titel ist "1" hochgestellt

The spectrum of the singular indefinite Sturm-Liouville operator A=sgn(.) (-d^2/dx^2)+q with a real potential q in L^1(R)$ covers the whole real line and, in addition, non-real eigenvalues may appear if the potential q assumes negative values. A quantitative analysis of the non-real eigenvalues is a challenging problem, and so far only partial results in this direction were obtained. In this paper the bound l lambda | <= |q|_{L^1}^2 on the absolute values of the non-real eigenvalues lambda of A is obtained. Furthermore, separate bounds on the imaginary parts and absolute values of these eigenvalues are proved in terms of the L^1-norm of q and its negative part q_-.



http://nbn-resolving.de/urn:nbn:de:gbv:ilm1-2017200509
Behrndt, Jussii; Gsell, Bernhard; Schmitz, Philipp; Trunk, Carsten;
An estimate on the non-real spectrum of a singular indefinite Sturm-Liouville operator. - Ilmenau : Technische Universität, Institut für Mathematik, 2017. - 1 Online-Ressource (5 Seiten). . - (Preprint. - M17,10)

It will be shown with the help of the Birman-Schwinger principle that the non-real spectrum of the singular indefinite Sturm-Liouville operator $\operatorname{sgn}(\cdot)(-\mathrm d^2/\mathrm d x^2 +q)$ with a real potential $q\in L^1\cap L^2$ is contained in a circle around the origin with radius $\|q\|_{L^1}^2$.



https://www.db-thueringen.de/receive/dbt_mods_00032787
Berger, Thomas; Gernandt, Hannes; Trunk, Carsten; Wojtylak, Micha&lstrok;;
New lower bound for the distance to singularity of regular matrix pencils. - Ilmenau : Technische Universität, Institut für Mathematik, 2017. - 1 Online-Ressource (5 Seiten). . - (Preprint. - M17,10)

For regular matrix pencils $\Ac(s)=sE-A$ the distance to the nearest singular pencil in the Frobenius norm of the coefficients is called the distance to singularity. We derive a new lower bound for this distance by using the spectral theory of tridiagonal Toeplitz matrices.



https://www.db-thueringen.de/receive/dbt_mods_00032786
Bergmann, Jean Pierre; Bielenin, Martin; Herzog, Roland A.; Hildebrand, Jörg; Riedel, Ilka; Schricker, Klaus; Trunk, Carsten; Worthmann, Karl;
Prevention of solidification cracking during pulsed laser beam welding. - Ilmenau : Technische Universität, Institut für Mathematik, 2017. - 1 Online-Ressource (7 Seiten). . - (Preprint. - M17,09)

We present a mathematical model to describe laser beam welding based on the heat equation. Since the material coeff cients depend on the temperature, this leads to a quasi-linear parabolic partial differential equation. It is our goal to prevent solidif cation cracking. We address this problem by means of optimal control. It is the intensity prof le of the laser beam which acts as the control function. The main challenge is the formulation of a suitable objective function. In particular, high velocities of the solidif cation interface need to be properly penalized in order to deal with and avoid cracking phenomena.



https://www.db-thueringen.de/receive/dbt_mods_00032771
Gernandt, Hannes; Krauße, Dominik; Sommer, Ralf; Trunk, Carsten;
A new method for network redesign via rank one updates. - Ilmenau : Technische Universität, Institut für Mathematik, 2017. - 1 Online-Ressource (5 Seiten). . - (Preprint. - M17,08)

We present a method to place the eigenvalues of an electrical network towards a prescribed set of complex numbers by inserting an additional capacitance into the network. We use recent results on rank one perturbations of regular matrix pencils and provide an upper bound on the approximation error of the eigenvalues in the chordal distance.



https://www.db-thueringen.de/receive/dbt_mods_00032770