Motivated by the applications in leader-follower multi-agent dynamics, a class of optimal control problems is investigated, where the goal is to influence the behavior of a given population through another controlled one interacting with the first. The evolution of the systems obeys a non-linear Fokker–Planck-type equation as diffusive terms accounting for randomness in the evolution are taken into account. A well-posedness theory under very low regularity of the control vector fields is developed, as well as a rigorous mean-field limit of a stochastic particle approximation.
Optimal control problems in transport dynamics with additive noise
Francesco Solombrino
2023-01-01
Abstract
Motivated by the applications in leader-follower multi-agent dynamics, a class of optimal control problems is investigated, where the goal is to influence the behavior of a given population through another controlled one interacting with the first. The evolution of the systems obeys a non-linear Fokker–Planck-type equation as diffusive terms accounting for randomness in the evolution are taken into account. A well-posedness theory under very low regularity of the control vector fields is developed, as well as a rigorous mean-field limit of a stochastic particle approximation.File in questo prodotto:
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