69 research outputs found
The Total s-Energy of a Multiagent System
We introduce the "total s-energy" of a multiagent system with time-dependent
links. This provides a new analytical lens on bidirectional agreement dynamics,
which we use to bound the convergence rates of dynamical systems for
synchronization, flocking, opinion dynamics, and social epistemology
Eminence Grise Coalitions: On the Shaping of Public Opinion
We consider a network of evolving opinions. It includes multiple individuals
with first-order opinion dynamics defined in continuous time and evolving based
on a general exogenously defined time-varying underlying graph. In such a
network, for an arbitrary fixed initial time, a subset of individuals forms an
eminence grise coalition, abbreviated as EGC, if the individuals in that subset
are capable of leading the entire network to agreeing on any desired opinion,
through a cooperative choice of their own initial opinions. In this endeavor,
the coalition members are assumed to have access to full profile of the
underlying graph of the network as well as the initial opinions of all other
individuals. While the complete coalition of individuals always qualifies as an
EGC, we establish the existence of a minimum size EGC for an arbitrary
time-varying network; also, we develop a non-trivial set of upper and lower
bounds on that size. As a result, we show that, even when the underlying graph
does not guarantee convergence to a global or multiple consensus, a generally
restricted coalition of agents can steer public opinion towards a desired
global consensus without affecting any of the predefined graph interactions,
provided they can cooperatively adjust their own initial opinions. Geometric
insights into the structure of EGC's are given. The results are also extended
to the discrete time case where the relation with Decomposition-Separation
Theorem is also made explicit.Comment: 35 page
Asymptotic Consensus Without Self-Confidence
This paper studies asymptotic consensus in systems in which agents do not
necessarily have self-confidence, i.e., may disregard their own value during
execution of the update rule. We show that the prevalent hypothesis of
self-confidence in many convergence results can be replaced by the existence of
aperiodic cores. These are stable aperiodic subgraphs, which allow to virtually
store information about an agent's value distributedly in the network. Our
results are applicable to systems with message delays and memory loss.Comment: 13 page
Optimal strategies in the average consensus problem
We prove that for a set of communicating agents to compute the average of
their initial positions (average consensus problem), the optimal topology of
communication is given by a de Bruijn's graph. Consensus is then reached in a
finitely many steps. A more general family of strategies, constructed by block
Kronecker products, is investigated and compared to Cayley strategies.Comment: 9 pages; extended preprint with proofs of a CDC 2007 (Conference on
decision and Control) pape
Continuous-Time Consensus under Non-Instantaneous Reciprocity
We consider continuous-time consensus systems whose interactions satisfy a
form or reciprocity that is not instantaneous, but happens over time. We show
that these systems have certain desirable properties: They always converge
independently of the specific interactions taking place and there exist simple
conditions on the interactions for two agents to converge to the same value.
This was until now only known for systems with instantaneous reciprocity. These
result are of particular relevance when analyzing systems where interactions
are a priori unknown, being for example endogenously determined or random. We
apply our results to an instance of such systems.Comment: 12 pages, 4 figure
Consensus Formation in First-Order Graphon Models with Time-Varying Topologies
In this article, we investigate the asymptotic formation of consensus for
several classes of time-dependent cooperative graphon dynamics. After
motivating the use of this type of macroscopic models to describe multi-agent
systems, we adapt the classical notion of scrambling coefficient to this
setting, leverage it to establish sufficient conditions ensuring the
exponential convergence to consensus with respect to the -norm
topology. We then shift our attention to consensus formation expressed in terms
of the -norm, and prove three different consensus result for symmetric,
balanced and strongly connected topologies, which involve a suitable
generalisation of the notion of algebraic connectivity to this
infinite-dimensional framework. We then show that, just as in the
finite-dimensional setting, the notion of algebraic connectivity that we
propose encodes information about the connectivity properties of the underlying
interaction topology. We finally use the corresponding results to shed some
light on the relation between - and -consensus formation, and
illustrate our contributions by a series of numerical simulations.Comment: 48 pages, 16 figure
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