In this paper, the relationship between network synchronizability and the edge-addition of its associated graph is investigated. First, it is shown that adding one edge to a cycle definitely decreases the network synchronizability. Then, since sometimes the synchronizability can be enhanced by changing the network structure, the question of whether the networks with more edges are easier to synchronize is addressed. Based on a subgraph and complementary graph method, it is shown by examples that the answer is negative even if the network structure is arbitrarily optimized. This reveals that generally there are redundant edges in a network, which not only make no contributions to synchronization but actually may reduce the synchronizability. Moreover, a simple example shows that the node betweenness centrality is not always a good indicator for the network synchronizability. Finally, some more examples are presented to illustrate how the network synchronizability varies following the addition of edges, where all the examples show that the network synchronizability globally increases but locally fluctuates as the number of added edges increases.
This paper addresses the distributed attitude synchronization problem of multiple spacecraft with unknown inertia matrices. Two distributed adaptive controllers are proposed for the cases with and without a virtual leader to which a time-varying reference attitude is assigned. The first controller achieves attitude synchronization for a group of spacecraft with a leaderless communication topology having a directed spanning tree. The second controller guarantees that all spacecraft track the reference attitude if the virtual leader has a directed path to all other spacecraft. Simulation examples are presented to illustrate the effectiveness of the results.
Node positioning is a fundamental problem in applications of wireless sensor networks (WSNs). In this paper, a new range-free algorithm, called spring swarm localization algorithm (SSLA), is proposed for positioning WSNs. To determine the locations of sensor nodes, the proposed algorithm uses network topology information and a small fraction of sensor nodes which know their locations. Numerical simulations show that high positioning accuracy can be obtained by using the algorithm. Some examples are given to illustrate the effectiveness of the algorithm.
HE QinBinCHEN FangYueCAI ShuiMingHAO JunJunLIU ZengRong
