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.

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Abstract-This work presents the design of a decentralized control strategy that allows singularly perturbed multi-agent systems to achieve synchronization with global performance guarantees. The study is mainly motivated by the presence of two features that characterize many physical systems. The first is the complexity in terms of interconnected subsystems and the second is that each subsystem involves processes evolving on different time-scales. The main difficulty that we have to overcome is that we have to avoid the use of centralized information related to the interconnection network structure. This problem is solved by rewriting the synchronization problem in terms of stabilization of a singularly perturbed uncertain linear system. The singularly perturbed dynamics of subsystems generates theoretical challenges related to the stabilizing controller design but also numerical issues related to the computation of the controller gains. We show that these problems can be solved by decoupling the slow and fast dynamics. Our theoretical developments are illustrated by some numerical examples.

The paper provides a computation-oriented necessary and sufficient condition for the global exponential stability of linear impulsive systems, whose impulsions are assumed to occur quasi-periodically. Based on the set-theoretic conditions for robust stability of uncertain linear systems, the existence of polyhedral Lyapunov functions is proved to be necessary and sufficient for global exponential stability of quasi-periodic linear impulsive systems. A constructive method is developed for testing the stability of the system and for computing setinduced polyhedral Lyapunov functions. The method leads to an algorithm whose complexity is similar to the standard algorithm related to discrete-time parametric uncertain systems with the state matrix belonging to a convex polytopic set.

To cite this version:Jihene Ben Rejeb, Irinel-Constantin Morarescu, Jamal Daafouz. Control design with guaranteed cost for synchronization in networks of linear singularly perturbed systems. Automatica, Elsevier, 2018, 91, pp.89-97. 10.1016/j.automatica.2018 Control design with guaranteed cost for synchronization in networks of linear singularly perturbed systems AbstractThis work presents the design of a decentralized control strategy that allows singularly perturbed multi-agent systems to achieve synchronization with global performance guarantees. The study is mainly motivated by the presence of two features that characterize many physical systems. The first is the complexity in terms of interconnected subsystems and the second is that each subsystem involves processes evolving on different time-scales. In the context of interconnected systems, the decentralized control is interesting since it considerably reduces the communication load (and the associated energy) which can be very important when dealing with centralized policies. Therefore, the main difficulty that we have to overcome is that we have to avoid the use of centralized information related to the interconnection network structure. This problem is solved by rewriting the synchronization problem in terms of stabilization of a singularly perturbed uncertain linear system. The singularly perturbed dynamics of subsystems generates theoretical challenges related to the stabilizing controller design but also numerical issues related to the computation of the controller gains. We show that these problems can be solved by decoupling the slow and fast dynamics. Our theoretical developments are illustrated by some numerical examples.