Analysis of cluster consensus in continuous - time networks with time delays

Abstract

In recent years, distributed coordination of multi-agent systems has the atten tion of many researchers due to its potential applications in various fields including group robots, distributed sensor networks, bird flocks, the attitude alignment in multi ple spacecraft settings and control in communication systems. All of these applications indicate the importance of design and analysis of consensus protocols with which the agents agree on some particular variable of interest by exchanging information among themselves. Complete consensus where all agents in a system achieve a common ob jective is one of the most popular studies. A network using distributed consensus protocol may be divided into different groups which are called clusters depending on the interaction topology of the network. In this thesis, we investigate the cluster con sensus problem for a multi-agent system with or without delay in continuous-time. Contrary to existing studies on cluster consensus in the literature, we do not assume that the clusters are pre-determined. The main contributions of the dissertation are to determine the number of clusters for a multi-agent system and to state delay con ditions that does not affect the number of clusters and convergence properties of the system. The results are obtained by using primary and secondary layer subgraphs and sub-Laplacian matrices which are explained for the first time in the literature. The upper bound of input delay that does not lead to instability is determined. It is also shown that bounded communication delay does not adversely affect system stability properties, which is also supported by computer simulations.