Second-order consensus of multi-agent systems with unknown but bounded disturbance

This paper addresses a consensus problem for second-order agents with unknown but bounded (UBB for short) disturbance which may affect the measure of neighbors' velocities. In this study, the communication topology of the multi-agent system is supposed to be connected. In order to solve this consensus problem, a new velocity estimation called distributed lazy rule is firstly proposed, where each agent can estimate its neighbors' velocities one by one. Then, a group of sufficient conditions for this second-order consensus problem are presented by adopting graph theory and the well-known Barbalat lemma, and the bounded consensus protocol is taken into account due to actuator saturation. Theoretically, the group of agents can reach consensus under the proposed control protocol, which is also validated by some numerical experiments.