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When designing distributed controllers for large-scale systems, theactuation, sensing and communication architectures of the controller can nolonger be taken as given. In particular, controllers implemented using densearchitectures typically outperform controllers implemented using simpler ones-- however, it is also desirable to minimize the cost of building thearchitecture used to implement a controller. The recently introducedRegularization for Design (RFD) framework poses the controllerarchitecture/control law co-design problem as one of jointly optimizing thecompeting metrics of controller architecture cost and closed loop performance,and shows that this task can be accomplished by augmenting the variationalsolution to an optimal control problem with a suitable atomic norm penalty.Although explicit constructions for atomic norms useful for the design ofactuation, sensing and joint actuation/sensing architectures are introduced, nosuch construction is given for atomic norms used to design communicationarchitectures. This paper describes an atomic norm that can be used to designcommunication architectures for which the resulting distributed optimalcontroller is specified by the solution to a convex program. Using this atomicnorm we then show that in the context of $\mathcal{H}_2$ distributed optimalcontrol, the communication architecture/control law co-design task can beperformed through the use of finite dimensional second order cone programming.

Communication Delay Co-Design in $\mathcal{H}_2$ Distributed Control Using Atomic Norm Minimization