Analysis On Cluster Consensus Of First-order Discrete-time Multi-agent Systems

In recent years,the consensus problem of multi-agent systems(MASs)has been widely investigated by scholars from different fields such as mathematics,biology,automation,control science and so on.In this paper,we study the bipartite consensus and cluster consensus problems of first-order discrete-time MASs.The research focus of this paper is summarized as follows:1.In Chapter 3,based on undirected topology and directed topology,respectively,we mainly study the bipartite consensus problem of first-order discrete-time MASs.As far as we know,most of the existing literature deal with the problem of obtaining bipartite consensus solutions for the continuous-time systems.In this chapter,we first establish the mathematical model of first-order discrete-time MASs.Then,under the premise of structural balance,the bipartite consensus problem of MASs with cooperation and competition mechanism is transformed into the consensus problem of MASs with cooperation by the method of gauge transformation.Finally,the bipartite consensus criteria for first-order discrete system are established by designing the consensus control protocol.2.In Chapter 4,we mainly study the cluster consensus problem of first-order discrete-time MASs.The topological graphs are assumed to be strongly connected.For MASs with n agents,we introduce interaction weights.By classifying the ring products of induced graphs,the graphs are divided into interactively balanced graphs and interactively unbalanced graphs.Our results show that we can establish the cluster consensus theory of MASs whether the graph is interactively or not.For interactively balanced graph,MASs can achieve cluster consensus.For interactively unbalanced graph,MASs can still achieve cluster consensus by introducing the pinning control and adding special control input.