Cluster consensus for inherently nonlinear cooperative networks

Abstract

This paper investigates the cluster consensus problem for inherently nonlinear cooperative networks with first and second-order system dynamics. For a first order multi-agent network evolving over a directed graph, not necessarily containing a spanning tree, a sufficient condition based on Lyapunov theory is derived on the single controller parameter so that the system achieves cluster consensus. These stability results are extended to second-order nonlinear systems that utilize two parameters in the distributed control law. Furthermore, the total number of clusters and members of each cluster are explicitly computed from the primary and secondary layer subgraphs of the underlying directed graph. The results are the first in the literature to address the cluster consensus problem for inherently nonlinear cooperative networks evolving over directed graphs that do not contain a spanning tree.