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Vortrag auf dem Doktorandenkolloquium des Kooperativen Promotionskollegs der HTWG, 09.07.2015
We consider classes of (Formula presented.)-by-(Formula presented.) sign regular matrices, i.e. of matrices with the property that all their minors of fixed order (Formula presented.) have one specified sign or are allowed also to vanish, (Formula presented.). If the sign is nonpositive for all (Formula presented.), such a matrix is called totally nonpositive. The application of the Cauchon algorithm to nonsingular totally nonpositive matrices is investigated and a new determinantal test for these matrices is derived. Also matrix intervals with respect to the checkerboard ordering are considered. This order is obtained from the usual entry-wise ordering on the set of the (Formula presented.)-by-(Formula presented.) matrices by reversing the inequality sign for each entry in a checkerboard fashion. For some classes of sign regular matrices, it is shown that if the two bound matrices of such a matrix interval are both in the same class then all matrices lying between these two bound matrices are in the same class, too.
Model Order Reduction
(2015)
This chapter offers an introduction to Model Order Reduction (MOR). It gives an overview on the methods that are mostly used. It also describes the main concepts behind the methods and the properties that are aimed to be preserved. The sections are in a prefered order for reading, but can be read independentlty. Section 4.1, written by Michael Striebel, E. Jan W. ter Maten, Kasra Mohaghegh and Roland Pulch, overviews the basic material for MOR and its use in circuit simulation. Issues like Stability, Passivity, Structure preservation, Realizability are discussed. Projection based MOR methods include Krylov-space methods (like PRIMA and SPRIM) and POD-methods. Truncation based MOR includes Balanced Truncation, Poor Man’s TBR and Modal Truncation.Section 4.2, written by Joost Rommes and Nelson Martins, focuses on Modal Truncation. Here eigenvalues are the starting point. The eigenvalue problems related to large-scale dynamical systems are usually too large to be solved completely. The algorithms described in this section are efficient and effective methods for the computation of a few specific dominant eigenvalues of these large-scale systems. It is shown how these algorithms can be used for computing reduced-order models with modal approximation and Krylov-based methods.Section 4.3, written by Maryam Saadvandi and Joost Rommes, concerns passivity preserving model order reduction using the spectral zero method. It detailedly discusses two algorithms, one by Antoulas and one by Sorenson. These two approaches are based on a projection method by selecting spectral zeros of the original transfer function to produce a reduced transfer function that has the specified roots as its spectral zeros. The reduced model preserves passivity.Section 4.4, written by Roxana Ionutiu, Joost Rommes and Athanasios C. Antoulas, refines the spectral zero MOR method to dominant spectral zeros. The new model reduction method for circuit simulation preserves passivity by interpolating dominant spectral zeros. These are computed as poles of an associated Hamiltonian system, using an iterative solver: the subspace accelerated dominant pole algorithm (SADPA). Based on a dominance criterion, SADPA finds relevant spectral zeros and the associated invariant subspaces, which are used to construct the passivity preserving projection. RLC netlist equivalents for the reduced models are provided.Section 4.5, written by Roxana Ionutiu and Joost Rommes, deals with synthesis of a reduced model: reformulate it as a netlist for a circuit. A framework for model reduction and synthesis is presented, which greatly enlarges the options for the re-use of reduced order models in circuit simulation by simulators of choice. Especially when model reduction exploits structure preservation, we show that using the model as a current-driven element is possible, and allows for synthesis without controlled sources. Two synthesis techniques are considered: (1) by means of realizing the reduced transfer function into a netlist and (2) by unstamping the reduced system matrices into a circuit representation. The presented framework serves as a basis for reduction of large parasitic R/RC/RCL networks.
The improvement of collision avoidance for vessels in close range encounter situations is an important topic for maritime traffic safety. Typical approaches generate evasive trajectories or optimise the trajectories of all involved vessels. Such a collision avoidance system has to produce evasive manoeuvres that do not confuse other navigators. To achieve this behaviour, a probabilistic obstacle handling based on information from a radar sensor with target tracking, that considers measurement and tracking uncertainties is proposed. A grid based path search algorithm, that takes the information from the probabilistic obstacle handling into account, is then used to generate evasive trajectories. The proposed algorithms have been tested and verified in a simulated environment for inland waters.