Seminar Details
2010-10-19 (15.00) : A new result on unconditional convergence in continuous-time consensus
At Euler building
Organized by Mathematical Engineering
Speaker :
Hendrickx, Julien
Abstract :
We consider systems of n agents holding each a real value. This value is
continuously attracted by the values of some other agents according to
pre-determined or dynamical rules. These simple continuous-time
consensus-seeking systems are the basis on which is built several
decentralized control laws.
We give a new weak condition under which the convergence of the system
is guaranteed, and characterize the limiting points of the systems.
Unlike previous results on such systems, our condition is instantaneous:
It concerns the nature of the interactions at every time as opposed to
their evolution. This aspect is particularly important when treating
systems with state-dependent interactions, whose evolution is a priori
unknown. Moreover, our condition is weaker than all previously proposed
conditions for convergence.
We explore different possibilities of extension of our results to
similar consensus seeking systems and survey some particular cases. We
also show how our result helps analyzing systems to which no previous
generic result could be applied, with a particular focus on opinion
dynamics.