We study a class of discrete-time multi-agent systems modelling opinion dynamics with decaying confidence. We consider a network of agents where each agent has an opinion. At each time step, the agents exchange their opinion with their neighbors and update it by taking into account only the opinions that differ from their own less than some confidence bound. This confidence bound is decaying: an agent gives repetitively confidence only to its neighbors that approach sufficiently fast its opinion. Essentially, the agents try to reach an agreement with the constraint that it has to be approached no slower than a prescribed convergence rate. Under that constraint, global consensus may not be achieved and only local agreements may be reached. The agents reaching a local agreement form communities inside the network. In this paper, we analyze this opinion dynamics model: we show that communities correspond to asymptotically connected component of the network and give an algebraic characterization of communities in terms of eigenvalues of the matrix defining the collective dynamics. Finally, we apply our opinion dynamics model to address the problem of community detection in graphs. We propose a new formulation of the community detection problem based on eigenvalues of normalized Laplacian matrix of graphs and show that this problem can be solved using our opinion dynamics model. We consider three examples of networks, and compare the communities we detect with those obtained by existing algorithms based on modularity optimization. We show that our opinion dynamics model not only provides an appealing approach to community detection but that it is also effective.

Abstract. This paper focuses on consensus problems for a class of linear systems with distributed delay that are encountered in modeling traffic flow dynamics. In the application problems the distributed delay, whose kernel is a gamma-distribution with a gap, represents the human drivers' behavior in the average. The aim of the paper is to give a characterization of the regions in the corresponding delay parameter space, where a consensus is reached for all initial conditions. The structure and properties of the system are fully exploited, which leads to explicit and computationally tractable expressions. As a by-product a stability theory for distributed delay systems with a gamma-distribution kernel is developed. Also explicit expressions for the consensus function(al) of time-delay systems with constant and distributed delays that solve a consensus problem are provided. Several illustrative examples complete the presentation.

International audienceIn this study, one considers the tracking control problem of a class of nonsmooth fully actuated Lagrangian systems subject to frictionless unilateral constraints. The task under consideration contains both free-motion and constraint-motion phases. A switching controller that guarantees an approximate tracking is designed. Particular attention is paid to transition (impacting and detachment) between different phases of motion. The exogenous signals that assure the stabilization on (take-off from) some constaints are explicitly defined. This paper extends previous works on the topic as it considers more than one constraint for n -degree-of-freedom systems. Numerical examples illustrate the main results

This paper proposes and analyzes a novel multi-agent opinion dynamics model in which agents have access to actions which are quantized version of the opinions of their neighbors. The model produces different behaviors observed in social networks such as disensus, clustering, oscillations, opinion propagation, even when the communication network is connected. The main results of the paper provides the characterization of preservation and diffusion of actions under general communication topologies. A complete analysis allowing the opinion forecasting is given in the particular cases of complete and ring communication graphs. Numerical examples illustrate the main features of this model.