Cluster Anticonsensus of Multiagent Systems Based on theQ-Theory

Liping Zhang,Haibo Jiang,Shuguang Guo

doi:10.1155/2014/254749

Liping Zhang, Haibo Jiang + Show 1 more

Open Access

https://doi.org/10.1155/2014/254749

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Abstract

We investigate the problem of cluster anticonsensus of multiagent systems. For multiagent continuous systems, a new control protocol is designed based on theQ-theory. Then by LaSalle's invariance principle we prove that if the graph is connected and bipartite, then the cluster anticonsensus is achieved by the proposed control protocol. On the other hand, a similar control protocol is designed for multiagent discrete-time systems. Then, sufficient conditions are given to guarantee the cluster anticonsensus of multiagent discrete-time systems by using theQ-theory and LaSalle's invariance principle. Numerical simulations show the effectiveness of our theoretical results.

Highlights

Multiagent systems have attracted much attention in various disciplines, such as mathematical, physical, biological, and social sciences [1,2,3,4]
By LaSalle’s invariance principle we prove that if the graph is connected and bipartite, the cluster anticonsensus is achieved by the proposed control protocol
We investigate the problem of cluster anticonsensus of multiagent systems based on the Q-theory

Summary

Introduction

Multiagent systems have attracted much attention in various disciplines, such as mathematical, physical, biological, and social sciences [1,2,3,4]. To the best of our knowledge, there are very few results on cluster anticonsensus of multiagent systems, which motivates this study. The cluster and community structure of bipartite networks has been studied by many researchers [32]. The cluster anticonsensus problem of multiagent systems over the networks whose graphs are connected and bipartite is worth studying. We investigate the problem of cluster anticonsensus of multiagent systems based on the Q-theory. A new control protocol is designed and by LaSalle’s invariance principle we prove that if the graph is connected and bipartite, the cluster anticonsensus is achieved by the proposed control protocol. For real symmetric matrices X and Y, the notation X ≥ Y (X > Y, resp.) means that the matrix X − Y is positive semidefinite (positive definite, resp.); In ∈ Rn×n is an identity matrix

Preliminaries

Cluster Anticonsensus of Multiagent Continuous Systems

Cluster Anticonsensus of Multiagent Discrete-Time Systems

Simulations

Figure 1

Conclusions