## Samenvatting

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.

Originele taal-2 | Engels |
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Pagina's (van-tot) | 977-1006 |

Aantal pagina's | 30 |

Tijdschrift | SIAM Journal on Control and Optimization |

Volume | 59 |

Nummer van het tijdschrift | 2 |

DOI's | |

Status | Gepubliceerd - 9 mrt. 2021 |

### Bibliografische nota

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