Cluster consensus for second-order mobile multi-agent systems via distributed adaptive pinning control under directed topology

This paper investigates adaptive pinning control for cluster consensus of second-order mobile multi-agent systems with inherent nonlinear dynamics under fixed directed topologies. Using tools from matrix, graph and Lyapunov stability theories, sufficient conditions for cluster consensus are obtained by virtue of a distributed adaptive pinning control scheme. Moreover, an adaptive strategy on the strengths is designed to guarantee that the cluster consensus condition does not require any global information except a connection assumption. The obtained results are also extended to complete consensus for second-order mobile multi-agent systems. Finally, numerical simulations are presented to illustrate the theoretical results.