New methods to realize the cluster consensus for multi‐agent networks

Abstract

This paper investigates the cluster consensus problem for multi-agent networks via a new method. Firstly, a distributed cluster consensus protocol is proposed by constructing a new Laplacian matrix, which is not required to be row-zero-sum. It is shown that the cluster consensus of directed multi-agent networks can be achieved under the presented protocol, and the final cluster consensus values of the considered system are also given in this paper, which only depend on the initial states of all agents. Next, a pinning cluster consensus law is provided to force the dynamics of the agents to the desired trajectory. Furthermore, it is found that the cluster consensus of directed networks can be reached even in presence of arbitrary finite communication delays. Finally, effectiveness of the obtained results is demonstrated by numerical examples.

Neural network‐based event‐triggered cluster quasi‐consensus for unknown multiagent systems with directed topology

“…In order to facilitate the study of cluster quasi-consensus, we introduce a matrix L whose specific expression is as follows [11]:…”

“…This means the cluster quasi‐consensus problem becomes the complete one. In order to facilitate the study of cluster quasi‐consensus, we introduce a matrix $$$ \hat{L} $$$ whose specific expression is as follows [11]: $$$$ {\hat{l}}_{ij}=\left\{\begin{array}{cc}{\sum}_{j=1}^N{a}_{ij}{p}_{ij}& j=i\\ {}-{a}_{ij}& j\ne i\end{array}\right.,i=1,\cdots, N, $$$$ where $$$ {p}_{ij}={p}_s/{p}_r $$$ for $$$ i\in {V}_s,j\in {V}_r $$$ with $$$ s,r\in \left\{1,\cdots, q\right\} $$$. Before moving forward, some lemmas that are important to obtain the main results are given as follows.…”

“…Obviously, when all the agents in the network belong to a group, the cluster consensus degenerates into the complete one. Most of the previous research works related to cluster consensus focused on first/second-order linear MASs, and fruitful and crucial results have been made [10][11][12]. The work of Yu and Shi [10] investigated the scaled cluster consensus problem for first-and second-order linear MASs, respectively.…”

“…The work of Yu and Shi [10] investigated the scaled cluster consensus problem for first-and second-order linear MASs, respectively. In Guo et al [11], a novel cluster consensus protocol using only local infor-mation was constructed to solve the cluster consensus for first-order linear MASs with directed topology. In An et al [12], the cluster consensus of first-order linear MASs with communication delay was studied.…”