Abstract
This work is concerned with the existence of optimal controllers for the Bolza optimal control problem governed by the nonlinear Fokker–Planck equation in with control input in the drift term. The solution to the control state system is a weak (mild) solution obtained from a vanishing viscosity approximation scheme. One obtains in particular the existence for the stochastic optimal control problem governed by McKean–Vlasov SDEs. For this problem, one proves the existence of a stochastic Markov optimal controller in feedback form.
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