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.
Funding: Deutsche Forschungsgemeinschaft (DFG)
Duration: 2019 - 2021