Project Details
Projekt
Multiscale control concepts for transport-dominated problems
Subject Area
Mathematics
Term
from 2019 to 2024
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 423615040
In recent years, the description of controllable (or active) particle systems using methods of kinetic gas theory has been achieved and allows now to tackle a wide range of applications as for example traffic flow. In this research project, the inherent hierarchy exploited extensively in kinetic theory for theoretical and numerical considerations will be investigated in order to develop novel analytical and numerical methods for control problems posed on multiple scales as well as under aspects of non-smoothness in the control.The work program includes the analysis of consistent optimality conditions within the model hierarchies, numerical analysis for control aspects relevant in particular on the highest level of the model hierarchy, as well as the development of numerical methods for time-dynamic non-smooth optimization problems on all levels. In addition to the sensitivity of non-smooth kinetic equations, the multi-scale nature of the equations raises questions for boundary control problems of nonlocal hyperbolic equations and switching systems.The participating project partners from Germany and South Africa have already cooperated in the past documented in joint work on hyperbolic equations, exchange programmes and jointly organized conferences.
DFG Programme
Priority Programmes
Subproject of
SPP 1962:
Non-smooth and Complementarity-Based Distributed Parameter Systems: Simulation and Hierarchical Optimization
International Connection
South Africa
International Co-Applicant
Professor Mapundi Banda
