Scalable Consensus in Networks of Multiagent Systems Using High-Gain Observers

Consensus algorithms are popular in the field of multiagent systems due to their wide application in formation control, distributed estimation, sensor networks, etc. Generally, for certain classes of undirected graphs, with an increase in the network size, the second smallest eigenvalue of the graph Laplacian decreases toward zero, which leads to a slow convergence rate. We present a scalable consensus algorithm using proportional derivative (PD) control where the eigenvalues of the closed-loop Laplacian matrix are invariant with respect to the size of the network for general directed graphs. The PD controller is realized using a high-gain observer. We show that the trajectories of the closed-loop system when the high-gain observer is used can be brought arbitrarily close to the trajectories under the PD controller. Simulation results are presented to demonstrate the efficacy of the proposed algorithm.