Cluster Consensus in Discrete-Time Networks of Multiagents With Inter-Cluster Nonidentical Inputs

Abstract

Abstract-In this paper, cluster consensus of multi-agent systems is studied via inter-cluster nonidentical inputs. Here, we consider general graph topologies, which might be time-varying. The cluster consensus is defined by two aspects: the intracluster synchronization, that the state differences between each pair of agents in the same cluster converge to zero, and intercluster separation, that the states of the agents in different clusters are separated. For intra-cluster synchronization, the concepts and theories of consensus including the spanning trees, scramblingness, infinite stochastic matrix product and Hajnal inequality, are extended. With them, it is proved that if the graph has cluster spanning trees and all vertices self-linked, then static linear system can realize intra-cluster synchronization. For the time-varying coupling cases, it is proved that if there exists T > 0 such that the union graph across any T -length time interval has cluster spanning trees and all graphs has all vertices self-linked, then the time-varying linear system can also realize intra-cluster synchronization. Under the assumption of common inter-cluster influence, a sort of inter-cluster nonidentical inputs are utilized to realize inter-cluster separation, that each agent in the same cluster receives the same inputs and agents in different clusters have different inputs. In addition, the boundedness of the infinite sum of the inputs can guarantee the boundedness of the trajectory. As an application, we employ a modified nonBayesian social learning model to illustrate the effectiveness of our results.

Linear Stochastic Approximation Algorithms and Group Consensus Over Random Signed Networks

“…The group consensus turns to cluster consensus if different groups have different limit values [16].…”

Distributed coordination in multi-agent systems: a graph Laplacian perspective

“…As a result, agents in the network may reach more than one consistent state, while the agents in the same cluster reach consensus. Very recently, increasing attention has been paid to cluster consensus Lu X et al, 2010a;2010b;Yu and Wang, 2010;Liu and Chen, 2011;Xia and Cao, 2011;Han Y et al, 2013;Qin and Yu, 2013), by which it means that for any initial states of the nodes, not only all the nodes within the same cluster reach complete consensus, but also there is no consensus between any two different clusters. Cluster consensus can find examples in engineering control (Passino, 2002), distributed computation (Hwang et al, 2004), etc.…”

Group consensus in generic linear multi-agent systems with inter-group non-identical inputs

“…Second-order group consensus was addressed in Ma, Wang, and Miao (2014) and Feng, Xu, and Zhang (2014). Algebraic criteria for group consensus were reported in Han, Lu, and Chen (2013) and Shang (2013b) for discrete-time single-integrator dynamics. In addition, a group of continuous-time agents with non-linear self-dynamics (Sun, Bai, Jia, Xiong, & Chen, 2011), time delay (Shang, 2013c), linear time-invariant dynamics (Qin & Yu, 2013;Tan, Liu, & Duan, 2011), and choicebased protocols (Liu & Wong, 2013) can also reach group consensus under some conditions.…”

“…Convergence rate and ultimate consensus state can be specified as well. It is worthwhile to mention that similar external inputs mechanisms were dealt with in Han et al (2013) and Shang (2013b) for discrete-time single-integrator agents, where the coupling strengths need to be sufficiently strong. The approaches used are totally different.…”

“…Motivated by Han et al (2013) and Shang (2013b), we introduce the following consensus protocol with inter-group non-identical inputs:…”