71 research outputs found
On the number of unlabeled vertices in edge-friendly labelings of graphs
Let be a graph with vertex set and edge set , and be a
0-1 labeling of so that the absolute difference in the number of edges
labeled 1 and 0 is no more than one. Call such a labeling
\emph{edge-friendly}. We say an edge-friendly labeling induces a \emph{partial
vertex labeling} if vertices which are incident to more edges labeled 1 than 0,
are labeled 1, and vertices which are incident to more edges labeled 0 than 1,
are labeled 0. Vertices that are incident to an equal number of edges of both
labels we call \emph{unlabeled}. Call a procedure on a labeled graph a
\emph{label switching algorithm} if it consists of pairwise switches of labels.
Given an edge-friendly labeling of , we show a label switching algorithm
producing an edge-friendly relabeling of such that all the vertices are
labeled. We call such a labeling \textit{opinionated}.Comment: 7 pages, accepted to Discrete Mathematics, special issue dedicated to
Combinatorics 201
Similarity Decomposition Approach to Oscillatory Synchronization for Multiple Mechanical Systems With a Virtual Leader
This paper addresses the oscillatory synchronization problem for multiple
uncertain mechanical systems with a virtual leader, and the interaction
topology among them is assumed to contain a directed spanning tree. We propose
an adaptive control scheme to achieve the goal of oscillatory synchronization.
Using the similarity decomposition approach, we show that the position and
velocity synchronization errors between each mechanical system (or follower)
and the virtual leader converge to zero. The performance of the proposed
adaptive scheme is shown by numerical simulation results.Comment: 15 pages, 3 figures, published in 2014 Chinese Control Conferenc
Second-Order Consensus of Networked Mechanical Systems With Communication Delays
In this paper, we consider the second-order consensus problem for networked
mechanical systems subjected to nonuniform communication delays, and the
mechanical systems are assumed to interact on a general directed topology. We
propose an adaptive controller plus a distributed velocity observer to realize
the objective of second-order consensus. It is shown that both the positions
and velocities of the mechanical agents synchronize, and furthermore, the
velocities of the mechanical agents converge to the scaled weighted average
value of their initial ones. We further demonstrate that the proposed
second-order consensus scheme can be used to solve the leader-follower
synchronization problem with a constant-velocity leader and under constant
communication delays. Simulation results are provided to illustrate the
performance of the proposed adaptive controllers.Comment: 16 pages, 5 figures, submitted to IEEE Transactions on Automatic
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