DFG-Project: Novel models and control for networked problems: from discrete event to continuous dynamics
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
Stephan Gerster (RWTH Aachen)
Kerstin Lux (University of Mannheim)
Funding: German Research Foundation (DFG)
Duration: 2016 – 2019