Cluster consensus and cluster formation for nonlinear fractional-order multi-agent systems

This paper concerns the cluster consensus and cluster formation for multi-agent systems with fractional-order nonlinear dynamics. The agents can be divided into several clusters to achieve cluster consensus. The cluster consensus means that states/outputs of all agents in the same cluster converge to fixed values or paths which are different between clusters. A sufficient condition is investigated for proving Mittag-Leffler stability of the considered closed loop system. In addition, cluster formation of fractional-order multi-agent systems with nonlinear dynamics is studied in this paper which means each cluster makes the specific pattern. The performance improvement of the considered control law by using fractional-order Lyapunov stability and graph theories is shown. It is shown that if there is a directed spanning tree in the graph and the information exchange between two clusters is balanced, the cluster formation can be obtained. Finally, a number of examples are simulated to show the performance of the obtained results.