# Seminario di Equazioni Differenziali e Applicazioni: “Hybrid thermostatic approximations of junctions for some optimal control problems on networks”

## Lunedì 28 Maggio 2018, ore 12:15 - Sala Riunioni VII Piano - Fabio Bagagiolo

ARGOMENTI: Seminari

Lunedì 28 Maggio 2018 alle ore 12:15 in Sala Riunioni VII Piano, Fabio Bagagiolo (Università di Trento) terrà un seminario dal titolo “Hybrid thermostatic approximations of junctions for some optimal control problems on networks”.

Abstract
We study some optimal control problems on networks with junctions. It is well known that, in general, such problems have no uniqueness for the associated Hamilton-Jacobi-Bellman (HJB) equation, and moreover, the right definition of the HJB equation is even not obvious. We consider an approximation of such problems given by the use of a delayed (“thermostatically”) switching rule for the passage from one edge to the others in the network. The goal is to study the limit behavior of the HJB equations when the approximation parameter tends to zero. Under some hypotheses, the value functions of the approximating problems converge to a limit function which turns out to be the maximal subsolution of a suitable HJB limit problem.
Joint work with Rosario Maggistro.