2,015 research outputs found
Partial containment control over signed graphs
In this paper, we deal with the containment control problem in presence of
antagonistic interactions. In particular, we focus on the cases in which it is
not possible to contain the entire network due to a constrained number of
control signals. In this scenario, we study the problem of selecting the nodes
where control signals have to be injected to maximize the number of contained
nodes. Leveraging graph condensations, we find a suboptimal and computationally
efficient solution to this problem, which can be implemented by solving an
integer linear problem. The effectiveness of the selection strategy is
illustrated through representative simulations.Comment: 6 pages, 3 figures, accepted for presentation at the 2019 European
Control Conference (ECC19), Naples, Ital
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
Dynamics over Signed Networks
A signed network is a network with each link associated with a positive or
negative sign. Models for nodes interacting over such signed networks, where
two different types of interactions take place along the positive and negative
links, respectively, arise from various biological, social, political, and
economic systems. As modifications to the conventional DeGroot dynamics for
positive links, two basic types of negative interactions along negative links,
namely the opposing rule and the repelling rule, have been proposed and studied
in the literature. This paper reviews a few fundamental convergence results for
such dynamics over deterministic or random signed networks under a unified
algebraic-graphical method. We show that a systematic tool of studying node
state evolution over signed networks can be obtained utilizing generalized
Perron-Frobenius theory, graph theory, and elementary algebraic recursions.Comment: In press, SIAM Revie
Dynamic Social Balance and Convergent Appraisals via Homophily and Influence Mechanisms
Social balance theory describes allowable and forbidden configurations of the
topologies of signed directed social appraisal networks. In this paper, we
propose two discrete-time dynamical systems that explain how an appraisal
network \textcolor{blue}{converges to} social balance from an initially
unbalanced configuration. These two models are based on two different
socio-psychological mechanisms respectively: the homophily mechanism and the
influence mechanism. Our main theoretical contribution is a comprehensive
analysis for both models in three steps. First, we establish the well-posedness
and bounded evolution of the interpersonal appraisals. Second, we fully
characterize the set of equilibrium points; for both models, each equilibrium
network is composed by an arbitrary number of complete subgraphs satisfying
structural balance. Third, we establish the equivalence among three distinct
properties: non-vanishing appraisals, convergence to all-to-all appraisal
networks, and finite-time achievement of social balance. In addition to
theoretical analysis, Monte Carlo validations illustrates how the non-vanishing
appraisal condition holds for generic initial conditions in both models.
Moreover, numerical comparison between the two models indicate that the
homophily-based model might be a more universal explanation for the formation
of social balance. Finally, adopting the homophily-based model, we present
numerical results on the mediation and globalization of local conflicts, the
competition for allies, and the asymptotic formation of a single versus two
factions
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