Performance of leader-follower multi-agent systems in directed networks

We consider the leader-follower multiagent systems in which the leader executes the desired trajectory and the followers implement the consensus algorithm subject to stochastic disturbances. The performance of the leader-follower systems is quantified by using the steady-state variance of the deviation of followers from the leader. We study the asymptotic scaling of the variance in directed lattices in 1, 2, and 3 dimensions. We show that in 1D and 2D the variance of the followers’ deviation increases to infinity as one moves away from the leader, while in 3D it remains bounded.