Controllability of Laplacian Leader Follower Dynamics : Algorithmic Approach

Laplacian leader follower dynamics is a consensus algorithm used for distributed coordination of networked systems, the topology of which is given in the form of a graph. We provide an algorithm to classify graphs into their controllability classes (essentially controllable, conditionally controllable, and completely uncontrollable) which is asymptotically faster than one designed for an arbitrary state space linear system. We use this algorithm to answer questions about resiliency of this dynamic to random changes in topology, and to investigate the probability a topology is essentially controllable.