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A Fokker-Planck Nash Differential Game to Model Crowd Motion with Avoidance
A seminar to be conducted by by by Souvik Roy, Faculty of Mathematics, Kolkata Univ, India
Abstract: In this talk, we present a new approach to modeling pedestrian's avoidance dynamics based on a Fokker-Planck Nash game framework. In this framework, we consider two interacting pedestrians, whose motion variability is modeled through the corresponding probability density functions (PDFs) governed by Fokker-Planck equations. Based on these equations, a Nash differential game is formulated where the game strategies represent controls aiming at avoidance by minimizing appropriate collision cost functionals. The existence of Nash equilibria solutions is proved and characterized as a solution to an optimal control problem that is solved numerically. Results of numerical experiments are presented that successfully compare the computed Nash equilibria to the output of real experiments (conducted with humans).
Speaker: Professor Souvik Roy is a professor of mathematics at Kolkata Univ, India. His area of research is in ODE and numerical methods.