Some optimal visiting problems: from a single player to a mean-field type model

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. The model is subsequently adapted to a mean-field game framework, that is when a huge population of agents plays the optimal visiting problem with a controlled dynamics and with costs also depending on the distribution of the population. In particular, we investigate a single continuity equation with possible sinks and sources and the field possibly depending on the mass of the agents. The same problem is also studied on a network framework. More precisely, we study a mean-field game model by proving the existence of a suitable definition of an approximated mean-field equilibrium and then we address the passage to the limit.

Grantor dc:publisher

Università degli studi di Trento

Year dc:date

2022

Author dc:creator

• Marzufero, Luciano

Contributors dc:contributor

• Bagagiolo, Fabio

• Optimal control
• optimal stopping
• optimal switching
• mean-field game
• continuity equation
• transport equation
• networks
• Settore MAT/05 - Analisi Matematica

Statement dc:rights

• info:eu-repo/semantics/openAccess
• license:Creative commons
• license uri:http://creativecommons.org/licenses/by-nd/4.0/

Language dc:language

eng

Identifier

http://dx.doi.org/10.15168/11572_350780
10.15168/11572_350780

OAI identifier oai:identifier

oai:iris.unitn.it:11572/350780