  When designing distributed controllers for large-scale systems, the
actuation, sensing and communication architectures of the controller can no
longer be taken as given. In particular, controllers implemented using dense
architectures typically outperform controllers implemented using simpler ones
-- however, it is also desirable to minimize the cost of building the
architecture used to implement a controller. The recently introduced
Regularization for Design (RFD) framework poses the controller
architecture/control law co-design problem as one of jointly optimizing the
competing metrics of controller architecture cost and closed loop performance,
and shows that this task can be accomplished by augmenting the variational
solution to an optimal control problem with a suitable atomic norm penalty.
Although explicit constructions for atomic norms useful for the design of
actuation, sensing and joint actuation/sensing architectures are introduced, no
such construction is given for atomic norms used to design communication
architectures. This paper describes an atomic norm that can be used to design
communication architectures for which the resulting distributed optimal
controller is specified by the solution to a convex program. Using this atomic
norm we then show that in the context of $\mathcal{H}_2$ distributed optimal
control, the communication architecture/control law co-design task can be
performed through the use of finite dimensional second order cone programming.
