ArticleRoyal Society open science2017
Pedestrian motion modelled by Fokker-Planck Nash games.
Article in Royal Society open science, 2017. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 6 papers.
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6 citing papers in PubMed.
- A PINN-driven game-theoretic framework in limited data photoacoustic tomography.Inverse problems · 2025Article
- An evolutionary differential game for regulating the role of monoclonal antibodies in treating signalling pathways in oesophageal cancer.Royal Society open science · 2024Article
- A Fokker-Planck feedback control framework for optimal personalized therapies in colon cancer-induced angiogenesis.Journal of mathematical biology · 2022Article
- A Fokker-Planck Framework for Parameter Estimation and Sensitivity Analysis in Colon Cancer.AIP conference proceedings · 2022Article
- A New Non-Linear Conjugate Gradient Algorithm for Destructive Cure Rate Model and a Simulation Study: Illustration with Negative Binomial Competing Risks.Communications in statistics: Simulation and computation · 2022Article
- On a Variational and Convex Model of the Blake-Zisserman Type for Segmentation of Low-Contrast and Piecewise Smooth Images.Journal of imaging · 2021Article
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3 authors.
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Abstract
A new approach to modelling pedestrians' avoidance dynamics based on a Fokker-Planck (FP) Nash game framework is presented. In this framework, two interacting pedestrians are considered, whose motion variability is modelled through the corresponding probability density functions (PDFs) governed by FP 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) for four test cases.
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