Control of Interacting Particle Systems, and Their Mean-Field, and Fluid-Dynamic Limits

• Applicants: Professor Dr. Martin Gugat; Professor Dr. Michael Herty
• Subject Area: Mathematics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 560288187

The aim of the proposed project is the development and analysis of the fine structure of the optimal controls across hierarchies of interacting particle systems ranging from microscopic, and mean-field descriptions towards fluid-dynamic models. We plan to develop well-posedness results on the optimal control problems, investigate the links between the microscopic problems and their counterparts with dynamics described by partial differential equations such as mean-field and hydro-dynamics. This will be followed by an analysis of a possible turnpike structure and extension towards noisy data. All theoretical results will be accompanied by a numerical analysis of their respective discretizations. The relation between microscopic interacting particle systems, their meanfield, and their fluid dynamic description will be analysed and subsequently exploited in the analysis of the problem itself as well as the design of novel numerical algorithms for their solution. In particular, we aim to analyse, how results on the fine structure of the control can be preserved across the microsopic, meanfield, and fluid dynamic equations. Moreover, we will study the effect of noisy data in the optimal control problems.

• DFG Programme: Research Grants