Pulling the Strings on Agreement: Anchoring, Controllability, and Graph Automorphisms

This work examines the controlled Laplacian (or agreement) over a network of interconnected dynamic units. This dynamics has recently been the focus of a large number of research work in the systems community. Most of the existing work in this area- however- consider the unforced agreement protocol. In the present paper, we consider the controlled version of this dynamics and introduce graph theoretic conditions for its system theoretic properties. In particular, we show how the symmetry structure of the network, characterized in terms of its automorphism group, relates to the network controllability. Some of the ramifications of such a characterization are then explored.