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SUMMARY:Learning and Sparse Control of Multiagent Systems - Massimo Fornas
 ier (TUM - Technische Universität München)
DTSTART:20170526T130000Z
DTEND:20170526T140000Z
UID:TALK72382@talks.cam.ac.uk
CONTACT:Rachel Furner
DESCRIPTION:In the past decade there has been a large scope of studies on 
 mathematical models of social dynamics. Self-organization\, i.e.\, the aut
 onomous formation of patterns\, has been so far the main driving concept. 
 Usually first or second order models are considered with given predetermin
 ed nonlocal interaction potentials\, tuned to reproduce\, at least qualita
 tively\, certain global patterns (such as flocks of birds\, milling school
  of fish or line formations in pedestrian flows\, etc.). However\, often i
 n practice we do not dispose of a precise knowledge of the governing dynam
 ics. In the first part of this talk we present a variational and optimal t
 ransport framework leading to an algorithmic solution to the problem of le
 arning the interaction potentials from the observation of the dynamics of 
 a multiagent system. Moreover\, it is common experience that self-organiza
 tion of a society does not always spontaneously occur. In the second part 
 of the talk we address the question of whether it is possible to externall
 y and parsimoniously influence the dynamics\, to promote the formation of 
 certain desired patterns. In particular\, we address the issue of finding 
 the sparsest control strategy for finite agent models in order to lead the
  dynamics optimally towards a given outcome. We eventually mention the rig
 orous limit process connecting finite dimensional sparse optimal control p
 roblems with ODE constraints to an infinite dimensional sparse mean-field 
 optimal control problem with a constraint given by a PDE of Vlasov-type\, 
 governing the dynamics of the probability distribution of the agent popula
 tion.\n\nReference: M. Fornasier\, Learning and sparse control of multiage
 nt systems\, Proc. 7thECM\, 2016\nhttps://www-m15.ma.tum.de/foswiki/pub/M1
 5/Allgemeines/NewPublications/procexample.pdf\n
LOCATION:MR4\, Centre for Mathematical Sciences
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