Irinel-Constantin Morarescu

Opinion Dynamics With Decaying Confidence: Application to Community Detection in Graphs

We study a class of discrete-time multi-agent systems modeling 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 components 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.

Trajectory Tracking Control of Multiconstraint Complementarity Lagrangian Systems

In 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 constraints 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.

Highway traffic model-based density estimation

The travel time spent in traffic networks is one of the main concerns of the societies in developed countries. A major requirement for providing traffic control and services is the continuous prediction, for several minutes into the future. This paper focuses on an important ingredient necessary for the traffic forecasting which is the real-time traffic state estimation using only a limited amount of data. Simulation results illustrate the performances of the proposed state-estimation technique.

Coordination in networks of linear impulsive agents

The paper focuses on consensus in heterogeneous networks containing both linear and linear impulsive dynamics. This model applies for networks that are formed by several clusters. Most agents can only update their state in a continuous way using inner-cluster agent states. On top of this, few agents also have the peculiarity to update their states in a discrete way by reseting it using states from agents outside their clusters. The motivation of this behavior is that communication constraints hamper continuous inter-clusters interactions. Under appropriate assumptions we prove that all subsystems asymptotically agree and we provide an upper-bound of the convergence speed. We illustrate the behavior with an academic example containing five agents grouped in two clusters.

Stability crossing boundaries and fragility characterization of PID controllers for SISO systems with I/O delays

This paper focuses on the closed-loop stability analysis of single-input-single-output (SISO) systems subject to input (or output) delays in the presence of PID-controllers. More precisely, using a geometric approach, we present a simple and user-friendly method for the closed-loop stability analysis as well as for the fragility of such PID controllers. The proposed approach is illustrated on several examples encountered in the control literature.

Set theory conditions for stability of linear impulsive systems

In this paper we give tractable necessary and sufficient condition for the global exponential stability of a linear impulsive system. The reset rule considered in the paper is quasi-periodic and the stability analysis is based on a standard tool in set theory that is Minkowski functional. Firstly, we reformulate the problem in term of discrete-time parametric uncertain system with the state matrix belonging to a compact but non-convex set. Secondly, we provide a tractable algorithm for testing the stability and computing the associated polyhedral Lyapunov function when the system is stable. The main result is an algorithm whose computational effort is analogous to that of classical algorithms for contractive polytopes computation for discrete-time parametric uncertain systems with the state matrix belonging to a polytopic set.

Consensus for black-box nonlinear agents using optimistic optimization☆

An important problem in multiagent systems is consensus, which requires the agents to agree on certain controlled variables of interest. We focus on the challenge of dealing in a generic way with nonlinear agent dynamics, represented as a black box with unknown mathematical form. Our approach designs a reference behavior with a classical consensus method. The main novelty is using optimistic optimization (OO) to find controls that closely follow the reference behavior. The first advantage of OO is that it only needs to sample the black-box model of the agent, and so achieves our goal of handling unknown nonlinearities. Secondly, a tight relationship is guaranteed between computation invested and closeness to the reference behavior. Our main results exploit these properties to prove practical consensus. An analysis of representative examples builds additional insight and shows that in some nontrivial problems the optimization is easy to solve by OO. Simulations on these examples accompany the analysis.

Continuous opinions and discrete actions in social networks: A multi-agent system approach

This paper proposes and analyzes a novel multiagent 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.

Constructive Necessary and Sufficient Condition for the Stability of Quasi-Periodic Linear Impulsive Systems

The technical note 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 set-induced 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.

Set theory based condition in LMI form for network topology preservation for decentralized control

Connectivity preservation of the interconnection network is an essential ingredient in decentralized control. This paper focuses on the preservation of a given network topology which ensures the connectivity. We consider a networked system with a discrete dynamics in which two subsystems are able to communicate if an algebraic relation between their states is satisfied. The connected subsystems are called neighbours. The subsystems updates their state in a decentralized manner by taking into account their neighbours state. Each connection is preserved as far as the algebraic relation is verified. The objective of the proposed set theory based control law is to keep the state of each subsystem in a specific domain that ensures the algebraic constraint satisfaction. The resulting control design reduces to the solution of convex problems involving Linear Matrix Inequalities (LMI), then easily solvable. Beside the network preservation, the global coordination may be imposed by adding supplementary constraints in the control design.