Leader-following consensus of multi-agent systems with dynamic leader and measurement noises

This paper studies a leader-following consensus problem of multi-agent systems with a dynamic leader. It is assumed that the leader moves along a polynomial trajectory with respect to time, while followers have first-order integral dynamics. Every follower is equipped with the positioning system and ranger finder sensor to measure its own position and the relative positions with its neighbors. The measured information is corrupted by measurement noise. We first study a specials case of leader-following consensus problem (tracking problem), then we extend the results to the general case. It is assumed that leader's velocity is unknown to all followers. To deal with this challenge, the least square is used to estimate leader's velocity. Base on the estimated velocity and measured information, a consensus protocol is proposed. It is proved that the proposed protocol can solve the mean square leader-following consensus problem under some mild conditions. Some simulation examples are also presented to demonstrate the effectiveness of the proposed protocol.