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Mean-Field Optimal Control

Massimo FornasierFrancesco Solombrino — 2014

ESAIM: Control, Optimisation and Calculus of Variations

We introduce the concept of which is the rigorous limit process connecting finite dimensional optimal control problems with ODE constraints modeling multi-agent interactions to an infinite dimensional optimal control problem with a constraint given by a PDE of Vlasov-type, governing the dynamics of the probability distribution of interacting agents. While in the classical mean-field theory one studies the behavior of a large number of small individuals with each other, by simplifying the effect...

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