Consensus Analysis of Multiagent Networks via Aggregated and Pinning Approaches

• Published in: IEEE transaction on neural networks and learning systems 2011-08, Vol.22 (8), p.1231-1240
• Main Authors: Wenjun Xiong, Ho, Daniel W. C., Zidong Wang
• Format: Article
• Language: English
• Subjects: Absolute consensus; Aggregates; Applied sciences; Artificial intelligence; Bias; Computer science; control theory; systems; Computer simulation; Computer systems and distributed systems. User interface; Data Interpretation, Statistical; directed networks; Eigenvalues and eigenfunctions; Exact sciences and technology; graph Laplacian; Information retrieval. Graph; Laplace equations; Lead; Lie algebra; Lie groups; Matrices; Multiagent systems; Networks; Neural networks; Neural Networks (Computer); node-and-node pinning method; Nonlinear Dynamics; Nonlinearity; Optimization; Pinning; pinning consensus; Software; Symmetric matrices; Theoretical computing
• ISSN: 1045-9227; 2162-237X; 1941-0093; 2162-2388
• DOI: 10.1109/TNN.2011.2157938

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.