On aggregate control of clustered consensus networks

In this paper we address the problem of controlling the slow-time-scale dynamics of clustered consensus networks. Using time-scale separation arising from clustering, we first decompose the actual network model into an approximate model, and define the controller at every node as the sum of two independent state-feedback controls, one for the fast dynamics and another for the slow. We show that the slow controller is identical for every node belonging to the same cluster, indicating that only a single aggregate slow controller needs to be designed per area. This reduces the computational complexity of the design significantly. Applying results from singular perturbation theory, we show that when these individual controllers are implemented on the actual network, the closed-loop response is close to that obtained from the approximate models, provided that the clustering is strong. The design procedure is demonstrated by a simulation example.