Consensus Problems on Networks With Antagonistic Interactions

Altafini, Claudio

doi:10.1109/tac.2012.2224251

Cited by 1,647 publications

(1,284 citation statements)

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“…Differently, Assumptions 4 and 5 have simultaneously the features to require the existence of a spanning tree for a graph defined by means of a time average of interaction strength performed over all state values (frozen in time) or just around the equilibrium, and to be applied to nonlinear time varying monotone systems to assess exponential consensus. In [Altafini, 2013] the notion of bipartite consensus is introduced for signed graph networks in which the edges can assume also negative weights. Remarkably, the relation between strong monotonicity property and bipartite consensus achievement is pointed out.…”

Section: Discussionmentioning

confidence: 99%

“…Firstly, most of the network models considered in the literature of agreement problems are linear timevarying (or embedded in such models through the use of state-dependent weights) or nonlinear time invariant (i.e. [Hendrickx & Tsitsiklis, 2013], [Altafini, 2013], [Lin et al, 2007]). Only few other approaches (i.e.…”

Section: Paper Contributionmentioning

confidence: 99%

“…This only entails integrals performed in time on frozen state variables. Therefore, it enlarges the class of networks for which consensuability may be a priori and easier assessed with respect to related conditions in the literature that have to hold instantaneously ([Slotine & Wang, 2004], [Hendrickx & Tsitsiklis, 2013], [Martin & Girard, 2013]) or require stronger graph connectivity ( [Altafini, 2013]) or are restricted to specific class of nonlinear time invariant systems (i.e. [Cao & Ren, 2011]).…”

Section: Paper Contributionmentioning

confidence: 99%

“…In this direction agreement conditions for a class of both nonlinear time invariant and swithing/time varying networks are outlined in [Lin et al, 2007], [Hendrickx & Tsitsiklis, 2013], [Slotine & Wang, 2004], [Cao & Ren, 2011], [Chopra & Spong, 2007]. Recently in [Altafini, 2013] it is shown that bipartite consensus (i.e., the agents agree to a common absolute value) is achieved if and only if the signed graph of the network is structurally balanced.…”

Section: Introductionmentioning

confidence: 99%

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Frozen state conditions for exponential consensus of time-varying cooperative nonlinear networks

Manfredi

Angeli

2016

Automatica

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In this paper we present new results on exponential consensus for continuous-time nonlinear time varying cooperative networks. We endow the well known assumption of integral connectivity proposed by Moreau with a remarkable additional feature of being frozen in state variables, making its direct verification more straightforward. Moreover, we give an estimate of the exponential rate of convergence towards the agreement space. Finally, the proposed results are validated for representative examples.

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Section: Discussionmentioning

confidence: 99%

Section: Paper Contributionmentioning

confidence: 99%

Section: Paper Contributionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Frozen state conditions for exponential consensus of time-varying cooperative nonlinear networks

Manfredi

Angeli

2016

Automatica

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“…Similar to continuous-time clustering protocols with "informed" leaders (Xia and Cao, 2011), the heterogeneity of the prejudices and its linkage to individuals' susceptibilities to interpersonal influence may lead to persistent disagreement of opinions and outcomes such as polarization and clustering. With the FJ model, the clustering of opinions does not require the existence of repulsive couplings, or "negative ties" among individuals (Fläche and Macy, 2011;Altafini, 2013;Proskurnikov et al, 2016a;Xia et al, 2016) whose ubiquity in interpersonal interactions is still waiting for supporting experimental evidence (Takács et al, 2016). Unlike models with discrete opinions (Castellano et al, 2009) and bounded confidence models (Hegselmann and Krause, 2002;Weisbuch et al, 2005;Blondel et al, 2009), the FJ model describes the opinion evolution by linear discrete-time equations, and is thus much simpler for mathematical analysis.…”

Section: Introductionmentioning

confidence: 99%

Opinion evolution in time-varying social influence networks with prejudiced agents

et al. 2017

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Investigation of social influence dynamics requires mathematical models that are "simple" enough to admit rigorous analysis, and yet sufficiently "rich" to capture salient features of social groups. Thus, the mechanism of iterative opinion pooling from (DeGroot, 1974), which can explain the generation of consensus, was elaborated in (Friedkin and Johnsen, 1999) to take into account individuals' ongoing attachments to their initial opinions, or prejudices. The "anchorage" of individuals to their prejudices may disable reaching consensus and cause disagreement in a social influence network. Further elaboration of this model may be achieved by relaxing its restrictive assumption of a time-invariant influence network. During opinion dynamics on an issue, arcs of interpersonal influence may be added or subtracted from the network, and the influence weights assigned by an individual to his/her neighbors may alter. In this paper, we establish new important properties of the (Friedkin and Johnsen, 1999) opinion formation model, and also examine its extension to time-varying social influence networks.

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Consensus in Multi‐Agent Systems

Proskurnikov

Cao

2016

Wiley Encyclopedia of Electrical and Electronics Engineering

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Many cooperative behaviors of multi‐agent teams emerge from local interactions among the agents, where an agent interacts with a few “adjacent” teammates, but has no information about the remaining agents. For instance, the self‐organization of many biological populations –including swarms of insects, flocks of birds, and schools of fish –are based on such local interaction rules: the motion and decisions of an individual agent are determined by the behavior of its nearest neighbors in the population. A special case of multi‐agent coordination is consensus , that is, the agreement of agents on some quantity of interest or, more generally, the full or partial synchronization of their state trajectories. Establishing consensus is a “benchmark” problem in multi‐agent systems study, which allows to reveal the main principles of multi‐agent coordination and, in particular, the role of the system's interaction graph (or topology). Consensus lies in the heart of many natural phenomena (e.g., synchronous oscillation of neural cells, which maintains a stable heart rhythm) and engineering designs (e.g., attitude synchronization of satellites). In this article, we give a brief review of distributed consensus algorithms, focusing on the basic ideas and relevant mathematical theory, in particular, graph‐theoretic methods.

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Consensus Problems on Networks With Antagonistic Interactions

Cited by 1,647 publications

References 41 publications

Frozen state conditions for exponential consensus of time-varying cooperative nonlinear networks

Frozen state conditions for exponential consensus of time-varying cooperative nonlinear networks

Opinion evolution in time-varying social influence networks with prejudiced agents

Consensus in Multi‐Agent Systems

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