Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Variance Optimization and Control Regularity for Mean-Field Dynamics

Benoît Bonnet 1 Francesco Rossi 2
1 CaGE - Control And GEometry
Inria de Paris, LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
Abstract : We study a family of optimal control problems in which one aims at minimizing a cost that mixes a quadratic control penalization and the variance of the system, both for finitely many agents and for the mean-field dynamics as their number goes to infinity. While solutions of the discrete problem always exist in a unique and explicit form, the behavior of their macroscopic counterparts is very sensitive to the magnitude of the time horizon and penalization parameter. When one minimizes the final variance, there always exists a Lipschitz-in-space optimal controls for the infinite dimensional problem, which can be obtained as a suitable extension of the optimal controls for the finite-dimensional problems. The same holds true for variance maximizations whenever the time horizon is sufficiently small. On the contrary, for large final times (or equivalently for small penalizations of the control cost), it can be proven that there does not exist Lipschitz-regular optimal controls for the macroscopic problem.
Complete list of metadata


https://hal.archives-ouvertes.fr/hal-03216326
Contributor : Benoît Bonnet <>
Submitted on : Thursday, July 29, 2021 - 2:01:29 PM
Last modification on : Friday, July 30, 2021 - 4:07:21 AM

Identifiers

  • HAL Id : hal-03216326, version 2

Citation

Benoît Bonnet, Francesco Rossi. Variance Optimization and Control Regularity for Mean-Field Dynamics. 2021. ⟨hal-03216326v2⟩

Share

Metrics

Record views

9

Files downloads

17