Finite-time consensus for multi-agent systems with nonlinear dynamics under Euler digraph via pinning control

This paper addresses the finite-time consensus problem for multi-agent systems with nonlinear dynamics under Euler digraph. By pinning control technique, a nonlinear distributed protocol is proposed, which ensures that all the agents can be controlled to the pinner's trajectory in finite time. Furthermore, we solve the challenging and fundamental question that how many nodes should be pinned to reach finite-time consensus. A sufficient condition is proposed to achieve finite-time consensus for multi-agent systems with nonlinear dynamics under Euler digraph. It is found that adding communication connections or increasing feedback gains is an effective way to reduce the settling time. Finally, numerical simulations are presented to verify the effectiveness of the obtained theoretical results.