Section: New Results

Control of multi-agent systems and opinion dynamics

Robust average consensus over unreliable networks

Participants : F. Acciani [Univ. Twente] , P. Frasca [Contact person] , G. Heijenk [Univ. Twente] , A. Stoorvogel [Univ. Twente] .

Packet loss is a serious issue in wireless consensus networks, as even few failures might prevent a network to converge to the desired consensus value. In the last four years, we have devised some possible ways to compensate for the errors caused by packet collisions, by modifying the updating weights. Since these modifications may result in a reduced convergence speed, a gain parameter is used to increase the convergence speed, and an analysis of the stability of the network is performed, leading to a criterion to choose such gain to guarantee network stability. For the implementation of the compensation method, we propose a new communication algorithm, which uses both synchronous and asynchronous mechanisms to achieve average consensus and to deal with uncertainty in packet delivery. The paper [11] provides a complete account of our results.

Message-passing computation of harmonic influence in social networks

Participants : W. S. Rossi [Univ. Groningen] , P. Frasca [Contact person] .

In the study of networks, identifying the most important nodes is of capital importance. The concept of Harmonic Influence has been recently proposed as a metric for the importance of nodes in a social network. This metric evaluates the ability for one node to sway the opinions of the other nodes in the network, under the assumption of a linear diffusion of opinions in the network. A distributed message passing algorithm for its computation has been proposed by Vassio et al., 2014, but its convergence guarantees were limited to trees and regular graphs. In [29], we prove that the algorithm converges on general graphs.

Hybrid models of opinion dynamics

Participants : P. Frasca [Contact person] , S. Tarbouriech [LAAS CNRS] , L. Zaccarian [LAAS CNRS] .

Hybrid dynamical systems are a promising framework to model social interactions. In this research line, we are beginning to use tools from the theory of hybrid systems to study opinion dynamics on networks with opinion-dependent connectivity. According to the hybrid framework, our dynamics are represented by the combination of continuous flow dynamics and discrete jump dynamics. The flow embodies the attractive forces between the agents and is defined by an ordinary differential equation whose right-hand side is a Laplacian, whereas the jumps describe the activation or deactivation of the pairwise interactions between agents. We first reformulate the classical Hegselmann–Krause model in this framework and then define a novel interaction model, which has the property of being scale-invariant. We study the stability and convergence properties of both models by a Lyapunov analysis, showing convergence and clusterization of opinions [18].

Stability of Metabolic Networks

Participants : F. Garin [Contact person] , B. Piccoli [Rutgers Univ. Camden] , N. Merrill [Rutgers Univ. Camden] , Z. An [Rutgers Univ. Camden] , S. Mc Quade [Rutgers Univ. Camden] .

Quantitative Systems Pharmacology (QSP) aims to gain more information about a potential drug treatment on a human patient before the more expensive stages of development begin. QSP models allow us to perform insilico experiments on a simulated metabolic system that predicts the response ofperturbing a flux. The methodology named LIFE (Linear-in-Flux Expressions) was developed with the purpose of simulating and analyzing large metabolic systems. These systems can be associated to directed graphs: the edges represent the reaction rates (fluxes), and the vertices represent quantities of chemical compounds (metabolites). In [23], we study LIFE systems, addressing two main problems: 1. for fixed metabolite levels, find all fluxes for which the metabolite levels are an equilibrium, and 2. for fixed fluxes, find all metabolite levels which are equilibria for the system. We show how stability analysis from the fields of network flows, compartmental systems, control theory and Markov chains apply to LIFE systems.