The Value of Communication in Designing Robust Distributed Controllers

We consider computation of optimal distributed controllers with constraints on states and inputs. The problem of distributed control arises in several large-scale systems, such as transportation and power grid systems. Well-established results highlight the non-convexity of the corresponding optimization problem for many cases of interest. In particular, convex computation of structured controllers is not possible for any system whose dynamics propagate according to a strongly connected topology. Such limitation is due to the fact that given enough time, the decisions of each controller spread to all system states and thus affect the future decisions of other controllers. Based on this insight, we propose designing communication links between controllers to propagate relevant output information quickly enough for convexity. We show that a limited number of communication links between controllers can be used to restore convexity for strongly connected systems. The resulting distributed control policy is optimal and satisfies state and input constraints robustly. Additionally, we propose novel graph theoretic interpretations of the result.