Multi-agent Fokker-Planck Nash games

Kurzbeschreibung - Abstract

The purpose of this project is the formulation and application of a new mathematical framework for modeling avoidance and/or catching in multi-agents motion in the framework of differential Games with stochastic processes and related Fokker-Planck equations. This project has manifold application as the simulation of motion of multiple agents (individuals, robots, intelligent vehicles, etc.) in a given space (e.g. an exposition hall) and its use to improve design of motion areas to, e.g., facilitate evacuation, manoeuvering, delivering, intercept, etc.. In particular, we refer to the ongoing research and development efforts in the automotive industry to construct autonomous (also driver-less) cars that assist in safe navigation and traffic management. This project would like to contribute to these efforts with the modelling of car-to-car avoidance of collision and catching, where the latter situation may occur in the case of pack delivery or intercept by a polices car. The leading concept of this project is to model decision-making control for collision avoidance or meeting as a Nash game. In this framework, the dynamics of each agent is modelled by a differential equation and to each agent is associated an objective of its motion; for example reach the desired destination with a minimal effort. The second basic concept of our project is to assume a stochastic dynamics of the agents to take into account random variability and uncertainty in the data. Mathematically, the two concepts mentioned above result in the formulation of Nash games governed by multiple Fokker-Planck (FP) partial differential equations where the control mechanism models the agent (as a player) strategy to solve the game. This project is very innovative for its modelling and application aspects, and also from a fundamental mathematical point of view. In fact, the theoretical and numerical investigation of FP Nash games in combination with different agents objectives and different game strategies is novel and would produce important outcomes for many mathematical fields of research. The successful realization of this project relies on preliminary work done by the French and German partners in the field of the FP Nash games for modelling two-pedestrian motion. This project also aims to extend the results of preliminary work to multiple agents and different classes of Nash games.

Projektleiter - Project Manager: Prof. Dr. Alfio Borzì

Beteiligte Wissenschaftlerinnen und Wissenschaftler - Participating scientists: Prof. Dr. Abderrahmane Habbal

Laufzeit: - Projekt period: 01.2018 - 12.2018

Förderinstitution: - Funding institution: Bayerisch-Französisches Hochschulzentrum (BFHZ)

Genehmigungssumme - Funding amount: 1.845,00 €

Genehmigungsdatum - Granting date: 23.01.2018

Förderkennzeichen - Funding number: FK32-17

Extraktion singulärer Merkmale und Artefaktreduktion in der dynamischen Bildgebung - Singular Feature Extraction and Artefact Reduction in Dynamic Imaging

Kurzbeschreibung - Abstract

Gegenstand des Projektes ist die Entwicklung einer Regularisierungstheorie für bildgebende Verfahren mit sich bewegendem Objekt. Das Hinzufügen der Zeitdimension führt im Unterschied zu klassischen statischen Verfahren auf unterbestimmte Probleme, es verändert die Natur des statischen Problems wie den Grad der Schlecht-Gestelltheit, die räumliche Auflösung oder führt zu unvollständigen Daten. Zunächst soll daher das dynamische Problem unter diesen Aspekten bei bekannter Bewegung mathematisch analysiert und geeignete Regularisierungsverfahren entwickelt werden. Die entsprechende Theorie soll darüber hinaus auf unbekannte Bewegungen erweitert werden, indem effiziente Verfahren zur Schätzung der Bewegung direkt aus den gemessenen Daten entwickelt werden.

Projektleiter - Project Manager: Prof. Dr. Bernadette Hahn

Laufzeit: - Projekt period: 06.2017 - 05.2020

Förderinstitution: - Funding institution: DFG

Genehmigungssumme - Funding amount: 154.700,00 €

Genehmigungsdatum - Granting date: 07.12.2016

Förderkennzeichen - Funding number: HA 8176/1-1

Vergangene Projekte - Past Projects