Second-order consensus in multi-agent systems with nonlinear dynamics and intermittent control

In this paper, the second-order leader-following consensus of coupled nonlinear agents with intermittent control is investigated. A subset of followers is pinned while it is assumed that the underlying digraph contains a directed spanning tree with the leader node as the root. By using multiple Lyapunov functions method and algebraic graph theory, it is proved that second-order consensus is guaranteed by choosing the control and rest durations appropriately in each time interval. This result provides high flexibility in control gain design, allowing multiple switching with different gains in arbitrarily-chosen time intervals. As a result, it not only encompasses many existing intermittent control schemes but can also manage practical situations, such as recovery from occasional control failures. Numerical simulations are also given to demonstrate our theoretical results.