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@article{faucris.256888815,
abstract = {We derive a framework to compute optimal controls for problems with states in the space of probability measures. Since many optimal control problems constrained by a system of ordinary differential equations modeling interacting particles converge to optimal control problems constrained by a partial differential equation in the mean-field limit, it is interesting to have a calculus directly on the mesoscopic level of probability measures which allows us to derive the corresponding first-order optimality system. In addition to this new calculus, we provide relations for the resulting system to the first-order optimality system derived on the particle level and the first-order optimality system based on L^{2}-calculus under additional regularity assumptions. We further justify the use of the L^{2}-adjoint in numerical simulations by establishing a link between the adjoint in the space of probability measures and the adjoint corresponding to L^{2}-calculus. Moreover, we prove a convergence rate for the convergence of the optimal controls corresponding to the particle formulation to the optimal controls of the mean-field problem as the number of particles tends to infinity.},
author = {Burger, Martin and Pinnau, RenĂ© and Totzeck, Claudia and Tse, Oliver},
doi = {10.1137/19M1249461},
faupublication = {yes},
journal = {SIAM Journal on Control and Optimization},
keywords = {Interacting particle systems; Mean-field limits; Optimal control with ODE/PDE constraints},
note = {CRIS-Team Scopus Importer:2021-04-30},
pages = {977-1006},
peerreviewed = {Yes},
title = {{Mean}-field optimal control and optimality conditions in the space of probability measures},
volume = {59},
year = {2021}
}