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CATEGORIES:CCIMI Seminars
SUMMARY:Learning and Sparse Control of Multiagent Systems
- Massimo Fornasier (TUM - Technische Universität
München)
DTSTART;TZID=Europe/London:20170526T140000
DTEND;TZID=Europe/London:20170526T150000
UID:TALK72382AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/72382
DESCRIPTION:In the past decade there has been a large scope of
studies on mathematical models of social dynamics
. Self-organization\, i.e.\, the autonomous format
ion of patterns\, has been so far the main driving
concept. Usually first or second order models are
considered with given predetermined nonlocal inte
raction potentials\, tuned to reproduce\, at least
qualitatively\, certain global patterns (such as
flocks of birds\, milling school of fish or line f
ormations in pedestrian flows\, etc.). However\, o
ften in practice we do not dispose of a precise kn
owledge of the governing dynamics. In the first pa
rt of this talk we present a variational and optim
al transport framework leading to an algorithmic s
olution to the problem of learning the interaction
potentials from the observation of the dynamics o
f a multiagent system. Moreover\, it is common exp
erience that self-organization of a society does n
ot always spontaneously occur. In the second part
of the talk we address the question of whether it
is possible to externally and parsimoniously influ
ence the dynamics\, to promote the formation of ce
rtain desired patterns. In particular\, we address
the issue of finding the sparsest control strateg
y for finite agent models in order to lead the dyn
amics optimally towards a given outcome. We eventu
ally mention the rigorous limit process connecting
finite dimensional sparse optimal control problem
s with ODE constraints to an infinite dimensional
sparse mean-field optimal control problem with a c
onstraint given by a PDE of Vlasov-type\, governin
g the dynamics of the probability distribution of
the agent population.\n\nReference: M. Fornasier\,
Learning and sparse control of multiagent systems
\, Proc. 7thECM\, 2016\nhttps://www-m15.ma.tum.de/
foswiki/pub/M15/Allgemeines/NewPublications/procex
ample.pdf\n
LOCATION:MR4\, Centre for Mathematical Sciences
CONTACT:Rachel Furner
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