Computationally efficient guaranteed cost control design for homogeneous clustered networks

Abstract

We consider a clustered network where connections inside the cluster are dense and between clusters are sparse. This leads us to a classical decoupling into fast (intra-cluster) and slow (inter-cluster) dynamics. Our objective is to provide a computationally efficient method to design control strategies that guarantee a certain bound on the cost for each cluster. Basically, we design a composite synchronizing controller with two terms: one responsible for the intra-cluster synchronization and the other achieving the synchronization between clusters. The first one does not require much computational effort since an analytic expression describes it. The second term is designed through a satisfaction equilibrium approach. In other words, the internal (fast) and external (slow) controllers are independently designed, and they ensure a guaranteed satisfactory cost for each cluster. Moreover, we show that the internal control affects the cluster cost only for a short time period. Finally, numerical simulations illustrate the theoretical results.