Consensus of second-order nolinear multi-agent systems with a smart leader via impulsive control

This essay studies the leader-following consensus problem of second-order nolinear multi-agent systems with a smart leader. Taking advantage of impulsive control, a distributed impulsive consensus control protocol is showcased to reduce the communication consumption. In contrast to a conventional leader which is not impacted by other followers, a kind of novel smart leader with an external control input to regulate its own states is deployed by exploiting the information of its neighbors in an impulsive manner. This modified control framework allows the error between the followers and the leader to reduce, thus elevating the tracking control performance of the system. The designed protocol is theoretically analyzed from stability utilizing the Lyapunov function and the impulsive control theory, and several sufficient conditions of achieving leader-following consensus are derived. Finally, several numerical simulation results are provided to corroborate the validity of the theoretical result.