Consensus and influence power approximation in time‐varying and directed networks subject to perturbations

• Published in: International journal of robust and nonlinear control Vol. 29; no. 11; pp. 3485 - 3501
• Main Authors: Martin, S., Morărescu, I.‐C., Nešić, D.
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 25-07-2019; Wiley
• Subjects: Advertising; Automatic Control Engineering; Computer Science; linear perturbed systems; Parameter uncertainty; robustness; Social networks; time‐varying consensus; Trajectory analysis; uncertain systems; Upper bounds
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.4564

Summary
The paper focuses on the analysis of multi‐agent systems interacting over directed and time‐varying networks in presence of parametric uncertainty on the interaction weights. We assume that agents reach a consensus, and the main goal of this work is to characterize the contribution that each agent has to the consensus value. This information is important for network intervention applications such as targeted advertising over social networks. Indeed, for an advertising campaign to be efficient, it has to take into account the influence power of each agent in the graph (ie, the contribution of each agent to the final consensus value). In our first results, we analytically describe the trajectory of the overall network, and we provide lower and upper bounds on the corresponding consensus value. We show that under appropriate assumptions, the contribution of each agent to the consensus value is smooth both in time and in the variation of the uncertainty parameter. This allows approximating the contribution of each agent when small perturbations affect the influence of each agent on its neighbors. Finally, we provide a numerical example to illustrate how our theoretical results apply in the context of network intervention.