Data-guided control: Clustering, graph products, and decentralized control

Airlie Chapman, Andrés D. González, Mehran Mesbahi, Leonardo Dueñas-Osorio, Raissa M. D'Souza

Abstract: This paper presents a novel approach to form an interdependent network model from time-varying system data. The research incorporates system meta-data using k-means clustering to form a layered structure within the dynamics. To compactly encode the layering, a Cartesian product model is fit to time-varying data using convex optimization. We show that under special situations a closed form solution of this model can be acquired. The Cartesian form is particularly conducive to reasoning about the role of the interdependent network layers within the dynamics. This is illustrated through the derivation of a distributed LQR controller which requires only knowledge of local layers in the network to apply. To demonstrate the applicability of this work, the proposed methods and analysis is applied to time-series data from a high-fidelity interdependent infrastructure network simulation.