836,936 research outputs found
Distributed Synthesis in Continuous Time
We introduce a formalism modelling communication of distributed agents
strictly in continuous-time. Within this framework, we study the problem of
synthesising local strategies for individual agents such that a specified set
of goal states is reached, or reached with at least a given probability. The
flow of time is modelled explicitly based on continuous-time randomness, with
two natural implications: First, the non-determinism stemming from interleaving
disappears. Second, when we restrict to a subclass of non-urgent models, the
quantitative value problem for two players can be solved in EXPTIME. Indeed,
the explicit continuous time enables players to communicate their states by
delaying synchronisation (which is unrestricted for non-urgent models). In
general, the problems are undecidable already for two players in the
quantitative case and three players in the qualitative case. The qualitative
undecidability is shown by a reduction to decentralized POMDPs for which we
provide the strongest (and rather surprising) undecidability result so far
Optimal output consensus for linear systems: A topology free approach
In this paper, for any homogeneous system of agents with linear continuous
time dynamics, we formulate an optimal control problem. In this problem a
convex cost functional of the control signals of the agents shall be minimized,
while the outputs of the agents shall coincide at some given finite time. This
is an instance of the rendezvous or finite time consensus problem. We solve
this problem without any constraints on the communication topology and provide
a solution as an explicit feedback control law for the case when the dynamics
of the agents is output controllable. It turns out that the communication graph
topology induced by the solution is complete. Based on this solution for the
finite time consensus problem, we provide a solution to the case of infinite
time horizon. Furthermore, we investigate under what circumstances it is
possible to express the controller as a feedback control law of the output
instead of the states.Comment: 8 page
Opinion fluctuations and disagreement in social networks
We study a tractable opinion dynamics model that generates long-run
disagreements and persistent opinion fluctuations. Our model involves an
inhomogeneous stochastic gossip process of continuous opinion dynamics in a
society consisting of two types of agents: regular agents, who update their
beliefs according to information that they receive from their social neighbors;
and stubborn agents, who never update their opinions. When the society contains
stubborn agents with different opinions, the belief dynamics never lead to a
consensus (among the regular agents). Instead, beliefs in the society fail to
converge almost surely, the belief profile keeps on fluctuating in an ergodic
fashion, and it converges in law to a non-degenerate random vector. The
structure of the network and the location of the stubborn agents within it
shape the opinion dynamics. The expected belief vector evolves according to an
ordinary differential equation coinciding with the Kolmogorov backward equation
of a continuous-time Markov chain with absorbing states corresponding to the
stubborn agents and converges to a harmonic vector, with every regular agent's
value being the weighted average of its neighbors' values, and boundary
conditions corresponding to the stubborn agents'. Expected cross-products of
the agents' beliefs allow for a similar characterization in terms of coupled
Markov chains on the network. We prove that, in large-scale societies which are
highly fluid, meaning that the product of the mixing time of the Markov chain
on the graph describing the social network and the relative size of the
linkages to stubborn agents vanishes as the population size grows large, a
condition of \emph{homogeneous influence} emerges, whereby the stationary
beliefs' marginal distributions of most of the regular agents have
approximately equal first and second moments.Comment: 33 pages, accepted for publication in Mathematics of Operation
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