Xiong Wenjun, Ho Daniel W C, Wang Zidong
Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong.
IEEE Trans Neural Netw. 2011 Aug;22(8):1231-40. doi: 10.1109/TNN.2011.2157938. Epub 2011 Jun 30.
In this paper, the consensus problem of multiagent nonlinear directed networks (MNDNs) is discussed in the case that a MNDN does not have a spanning tree to reach the consensus of all nodes. By using the Lie algebra theory, a linear node-and-node pinning method is proposed to achieve a consensus of a MNDN for all nonlinear functions satisfying a given set of conditions. Based on some optimal algorithms, large-size networks are aggregated to small-size ones. Then, by applying the principle minor theory to the small-size networks, a sufficient condition is given to reduce the number of controlled nodes. Finally, simulation results are given to illustrate the effectiveness of the developed criteria.
