Some optimal visiting problems: from a single player to a crowd of agents
Informal Systems Seminar (ISS), Centre for Intelligent Machines (CIM) and Groupe d'Etudes et de Recherche en Analyse des Decisions (GERAD)
Speaker: Luciano Marzufero
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Abstract:
In an optimal visiting problem, we want to control a trajectory that has to pass as close as possible to a collection of target points or regions. We introduce a hybrid-control based approach for the classic problem where the trajectory can switch between a group of discrete states related to the targets of the problem. In particular, we prove existence and uniqueness of a viscosity solution of the corresponding Hamilton-Jacobi equation. The model is subsequently adapted to a mean-field framework to study viability and crowd fluxes to describe a multitude of indistinguishable players.
Bio:
I was born in Camerino (MC), Italy, in 1993. I got the scientific high school diploma in my native city. I took the Bachelor and the M.Sc. in Mathematics at the University of Camerino and the Ph.D. in Mathematics at the University of Trento. Currently, I am a Junior (non-tenure track) Assistant Professor ("RTD-a" in the Italian system) at the Free University of Bozen-Bolzano. I am mainly interested in Optimal Control and Mean-Field Games.
