DFG Research Grant

DFG-Project: Novel models and control for networked problems: from discrete event to continuous dynamics

Project Description

We are interested in problems arising in physical or technical descriptions of processes like production, traffic flow or fluid dynamics. The basic mechanism not exploited yet so far, is the present and well-understood microscopic description of such processes. Usually, the microscopic scale is considered not worth or possible simulating for realistic description due to its computational complexity. Here, we want to exploit this fine scale locally to derive novel and physically correct conditions and controls. This is contrary to a priori imposed conditions which present the current state-of-the-art. Additionally, we contribute to the rather new field of closed loop control strategies for hyperbolic systems. Here, we consider in particular stabilization questions of flow patterns through a novel combination of microscopic and macroscopic descriptions as well as through game theoretic considerations.

Key words: Differential equations on networks, control theory, asymptotic and numerical analysis

Information

Project Partners:

Prof. Dr. Michael Herty (RWTH Aachen)
Prof. Dr. Simone Göttlich (University of Mannheim)

Further Members:

M. Sc. Stephan Gerster (RWTH Aachen)
M. Sc. Kerstin Lux (University of Mannheim)

Funding: Research Grant by German Research Foundation (DFG); two research assistant positions for three years

Duration: Starting from fall 2016

Relevant Publications

  • L. Forestier-Coste, S. Göttlich, M. Herty - Data-fitted second-order macroscopic production models - SIAM J. on Applied Mathematics (SIAP), Vol. 75(3), pp. 999-1014, 2015.