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 modelling pedestrian’s 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.
|
