Influence Models on Layered Uncertain Networks: A Guaranteed-Cost Design Perspective

Abstract

Control and estimation on large-scale social networks often necessitate the availability of models for the interactions amongst the agents. However characterizing accurate models of social interactions pose new challenges due to inherent complexity and unpredictability. Moreover, model uncertainty becomes more pronounced for large-scale networks. For certain classes of social networks, the layering structure allows a compositional approach. In this paper, we present such an approach to determine performance guarantees on layered networks with inherent model uncertainties. A factorization method is used to determine robust stability and performance and this is accomplished by a layered cost-guaranteed design via a layered Riccati-type solver, mirroring the network structure. We provide an example of the proposed methodology in the context of opinion dynamics on large-scale social networks.