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.
| Identifer | oai:union.ndltd.org:unitn.it/oai:iris.unitn.it:11572/350780 |
| Date | 19 July 2022 |
| Creators | Marzufero, Luciano |
| Contributors | Marzufero, Luciano, Bagagiolo, Fabio |
| Publisher | Università degli studi di Trento, place:TRENTO |
| Source Sets | Università di Trento |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/doctoralThesis |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | firstpage:1, lastpage:114, numberofpages:114 |
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