Cluster consensus in discrete-time networks of multi-agents with adapted inputs

Details Cluster consensus in discrete-time networks of multi-agents with adapted inputs Cluster consensus in discrete-time networks of multi-agents with adapted inputs

2012-01-13

arxiv.org/abs/1201.2803v1

Mathematics

Optimization and Control

12 pages, 3 figures

Scientific paper

In this paper, cluster consensus of multi-agent systems is studied via adaptive inputs. Here, we consider general graph topologies including time variation. The cluster consensus is defined by two aspects: the intra-cluster synchronization, that the state differences between agents in the same cluster converge to zero, and inter-cluster 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 adapted 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. Numerical examples are provided to illustrate the availability of our results.

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