Dipartimento di Matematica Guido Castelnuovo Università Sapienza Roma
Abstract: We analyze the problem of controlling a multiagent system with additive white noise through parsimonious interventions on a selected subset of the agents (leaders). For such a controlled system with an SDE constraint, we introduce a rigorous limit process toward an infinite dimensional optimal control problem constrained by the coupling of a system of ODEs for the leaders with a McKean--Vlasov type of SDE, governing the dynamics of the prototypical follower. The latter is, under some assumptions on the distribution of the initial data, equivalent with a (nonlinear parabolic) PDE-ODE system. The derivation of the limit mean-field optimal control problem is achieved by linking the mean-field limit of the governing equations together with the Gamma-limit of the cost functionals for the finite-dimensional problems. This is a joint research project with Francesca Anceschi (Ancona), Giacomo Ascione (SSM Napoli) and Francesco Solombrino (Napoli Federico II). This seminar is part of the activities of the Excellence Department Project CUP B83C23001390001 and it is funded by the European Union – Next Generation EU.
Nadia Ansini ansini@mat.uniroma1.it ,
Azahara DelaTorre Pedraza azahara.delatorrepedraza@uniroma1.it ,
Luca Martinazzi luca.martinazzi@uniroma1.it ,
Adriano Pisante pisante@mat.uniroma1.it