Seminario - From Brownian to pedestrian motion and Fokker-Planck Nash games
il prof. Alfio Borzì, Institute for Mathematics, University of Wuerzburg, alle ore 12:00 presso l'aula 36 terrà una conferenza dal titolo: From Brownian to pedestrian motion and Fokker-Planck Nash games.
Si riporta sotto un abstract.
This talk starts discussing fundamental results of statistical mechanics
focusing on Brownian motion and Fokker-Planck (FP) equations and the
concept of Nash games. Within the resulting framework, a new approach to
avoidance dynamics is presented. This approach leads to the formulation
of a Fokker-Planck Nash game problem that models the dynamics of two
interacting pedestrian with intrinsic variability and the objectives
of reaching a desired destination while
avoiding collision. In this way, a FP Nash differential game is
formulated where the game strategies represent controls
aiming at avoidance by minimizing appropriate collision functionals.
The issue of existence of Nash equilibria solutions is considered in the
realm of optimal control problems.
Results of numerical experiments are presented
that successfully compare the computed Nash equilibria to output of
real experiments (conducted with humans) for 4 test cases.
This talk also aims at outlining the multiple challenges and open
problems posed by the solution
of FP equations, stochastic control problems, and dynamic games.