  We introduce and analyze a model for decentral- ized control. The model is
broad enough to include problems such as formation control, decentralization of
the power grid and flocking. The objective of this paper is twofold. First, we
show how the issue of decentralization goes beyond having agents know only part
of the state of the system. In fact, we argue that a complete theory of
decentralization should take into account the fact that agents can be made
aware of only part of the global objective of the ensemble. A second
contribution of this paper is the introduction of a rigorous definition of
information flow for a decentralized system: we show how to attach to a general
nonlinear decentralized system a unique information flow graph that is an
invariant of the system. In order to address some finer issues in decentralized
system, such as the existence of so-called "information loops", we further
refine the information flow graph to a simplicial complex-more precisely, a
Whitney complex. We illustrate the main results on a variety of examples.
