Publikationen

The port-Hamiltonian (pH) modelling framework allows for models that preserve essential physical properties such as energy conservation or dissipative inequalities. If all subsystems are modelled as pH systems and the inputs are related to the output in a linear manner, the overall system can be modelled as a pH system, too, which preserves the properties of the underlying subsystems. If the coupling is given by a skew-symmetric matrix, as usual in many applications, the overall system can be easily derived from the subsystems without the need of introducing dummy variables and therefore artificially increasing the complexity of the system. Hence the framework of pH systems is especially suitable for modelling multiphysical systems.

Current engineering design trends, such as lightweight machines and human-machine interaction, often lead to underactuated systems. Output trajectory tracking of such systems is a challenging control problem. Here, we use a two-design-degree of freedom control approach by combining funnel feedback control with feedforward control based on servo-constraints. We present experimental results to verify the approach and demonstrate that the addition of a feedforward controller mitigates drawbacks of the funnel controller. We also present new experimental results for the real-time implementation of a feedforward controller based on servo-constraints on a minimum phase system.

This paper investigates the concept of self-dual convolutional codes. We derive the basic properties of this interesting class of codes and we show how some of the techniques to construct self-dual linear block codes generalize to self-dual convolutional codes. As for self-dual linear block codes we are able to give a complete classification for some small parameters.

Results on the existence of various types of spanning subgraphs of graphs are milestones in structural graph theory and have been diversified in several directions. In the present paper, we consider “local” versions of such statements. In 1966, for instance, D. W. Barnette proved that a 3-connected planar graph contains a spanning tree of maximum degree at most 3. A local translation of this statement is that if G is a planar graph, X is a subset of specified vertices of G such that X cannot be separated in G by removing two or fewer vertices of G, then G has a tree of maximum degree at most 3 containing all vertices of X. Our results constitute a general machinery for strengthening statements about k-connected graphs (for 1 ≤ k ≤ 4) to locally spanning versions, that is, subgraphs containing a set X ⊆ V (G) of a (not necessarily planar) graph G in which only X has high connectedness. Given a graph G and X ⊆ V (G), we say M is a minor of G rooted at X, if M is a minor of G such that each bag of M contains at most one vertex of X and X is a subset of the union of all bags. We show that G has a highly connected minor rooted at X if X ⊆ V (G) cannot be separated in G by removing a few vertices of G. Combining these investigations and the theory of Tutte paths in the planar case yields locally spanning versions of six well-known results about degree-bounded trees, Hamiltonian paths and cycles, and 2-connected subgraphs of graphs.

Consider the hypergraph bootstrap percolation process in which, given a fixed r-uniform hypergraph H and starting with a given hypergraph G0, at each step we add to G0 all edges that create a new copy of H. We are interested in maximising the number of steps that this process takes before it stabilises. For the case where H = Kr+1(r) with r ≥ 3, we provide a new construction for G0 that shows that the number of steps of this process can be of order Θ (nr). This answers a recent question of Noel and Ranganathan. To demonstrate that different running times can occur, we also prove that, if H is K4(3) minus an edge, then the maximum possible running time is 2n − ⌊log2(n−2)⌋ − 6. However, if H is K5(3) minus an edge, then the process can run for Θ (n3) steps.