Opinion Dynamics in Social Networks with Hostile Camps: Consensus vs. Polarization

Most of the distributed protocols for multi-agent consensus assume that the agents are mutually cooperative and "trustful," and so the couplings among the agents bring the values of their states closer. Opinion dynamics in social groups, however, require beyond these conventional models due to ubiquitous competition and distrust between some pairs of agents, which are usually characterized by repulsive couplings and may lead to clustering of the opinions. A simple yet insightful model of opinion dynamics with both attractive and repulsive couplings was proposed recently by C. Altafini, who examined first-order consensus algorithms over static signed graphs. This protocol establishes modulus consensus, where the opinions become the same in modulus but may differ in signs. In this paper, we extend the modulus consensus model to the case where the network topology is an arbitrary time-varying signed graph and prove reaching modulus consensus under mild sufficient conditions of uniform connectivity of the graph. For cut-balanced graphs, not only sufficient, but also necessary conditions for modulus consensus are given.Comment: scheduled for publication in IEEE Transactions on Automatic Control, 2016, vol. 61, no. 7 (accepted in August 2015

Emergent Behaviors over Signed Random Networks in Dynamical Environments

We study asymptotic dynamical patterns that emerge among a set of nodes that interact in a dynamically evolving signed random network. Node interactions take place at random on a sequence of deterministic signed graphs. Each node receives positive or negative recommendations from its neighbors depending on the sign of the interaction arcs, and updates its state accordingly. Positive recommendations follow the standard consensus update while two types of negative recommendations, each modeling a different type of antagonistic or malicious interaction, are considered. Nodes may weigh positive and negative recommendations differently, and random processes are introduced to model the time-varying attention that nodes pay to the positive and negative recommendations. Various conditions for almost sure convergence, divergence, and clustering of the node states are established. Some fundamental similarities and differences are established for the two notions of negative recommendations

Resilience and Controllability of Dynamic Collective Behaviors

The network paradigm is used to gain insight into the structural root causes of the resilience of consensus in dynamic collective behaviors, and to analyze the controllability of the swarm dynamics. Here we devise the dynamic signaling network which is the information transfer channel underpinning the swarm dynamics of the directed interagent connectivity based on a topological neighborhood of interactions. The study of the connectedness of the swarm signaling network reveals the profound relationship between group size and number of interacting neighbors, which is found to be in good agreement with field observations on flock of starlings [Ballerini et al. (2008) Proc. Natl. Acad. Sci. USA, 105: 1232]. Using a dynamical model, we generate dynamic collective behaviors enabling us to uncover that the swarm signaling network is a homogeneous clustered small-world network, thus facilitating emergent outcomes if connectedness is maintained. Resilience of the emergent consensus is tested by introducing exogenous environmental noise, which ultimately stresses how deeply intertwined are the swarm dynamics in the physical and network spaces. The availability of the signaling network allows us to analytically establish for the first time the number of driver agents necessary to fully control the swarm dynamics

A Review of Consensus-based Multi-agent UAV Applications

In this paper, a review of distributed control for multi-agent systems is proposed, focusing on consensus-based applications. Both rotary-wing and fixed-wing Unmanned Aerial Vehicles (UAVs) are considered. On one side, methodologies and implementations based on collision and obstacle avoidance through consensus are analyzed for multirotor UAVs. On the other hand, a target tracking through consensus is considered for fixed-wing UAVs. This novel approach to classify the literature could help researchers to assess the outcomes achieved in these two directions in view of potential practical implementations of consensus-based methodologies

Agent-Based Modeling of Consensus Group Formation with Complex Webs of Beliefs

Formation of consensus groups with shared opinions or views is a common feature of human social life and also a well-known phenomenon in cases when views are complex, as in the case of the formation of scholarly disciplines. In such cases, shared views are not simple sets of opinions but rather complex webs of beliefs (WoBs). Here, we approach such consensus group formation through the agent-based model (ABM). Agents’ views are described as complex, extensive web-like structures resembling semantic networks, i.e., webs of beliefs. In the ABM introduced here, the agents’ interactions and participation in sharing their views are dependent on the similarity of the agents’ webs of beliefs; the greater the similarity, the more likely the interaction and sharing of elements of WoBs. In interactions, the WoBs are altered when agents seek consensus and consensus groups are formed. The consensus group formation depends on the agents’ sensitivity to the similarity of their WoBs. If their sensitivity is low, only one large and diffuse group is formed, while with high sensitivity, many separated and segregated consensus groups emerge. To conclude, we discuss how such results resemble the formation of disciplinary, scholarly consensus groups

Analysis and Control of Socio-Cultural Opinion Evolution in Complex Social Systems

The overarching goal of this thesis is to further our understanding about opinion evolution in networked societies. Such insights can be used in a variety of fields such as economy, marketing, transportation, egress, etc. Three main subjects build up this interdisciplinary research: Sociology, Statistical Mechanics, and Network Sciences. In this thesis, for macrolevel (or society-level) analyses, techniques from statistical mechanics have been borrowed to mathematically model the opinion dynamic on different network topologies based on different interaction models. Also, for micro-level (individual-level) analyses, Individual Decision Making Algorithms (IDMA) have been designed. To account for both macro-level and micro-level dynamics, these two regimes are combined resulting in a more accurate model for opinion propagation. Assessing the controllability of such dynamics through experiments in presence of actual humans is the part of this thesis

Swarm Robotics

Collectively working robot teams can solve a problem more efficiently than a single robot, while also providing robustness and flexibility to the group. Swarm robotics model is a key component of a cooperative algorithm that controls the behaviors and interactions of all individuals. The robots in the swarm should have some basic functions, such as sensing, communicating, and monitoring, and satisfy the following properties