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 / Almi, Stefano; Morandotti, Marco; Solombrino, Francesco. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 373:(2023), pp. 1-47. [10.1016/j.jde.2023.07.010]
Optimal control problems in transport dynamics with additive noise
Stefano Almi;Marco Morandotti
;Francesco Solombrino
2023
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 | Dimensione | Formato | |
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