707	RWTH Publication No: 1021433        2025
TITLE	Turnpike property for hierarchical optimal control problems: from particle systems to hydrodynamic equations
AUTHORS	Michael Herty, Yizhou Zhou
ABSTRACT	This work is concerned with a hierarchical framework of optimal control prob- lems connecting interacting particle systems, the mean field limit equations, and associated hydrodynamic models. By assuming the existence of solutions, we establish the exponential turnpike property for each level of the hierarchy, showing that optimal trajectories remain close to the associated steady states over long time horizons. The results demonstrate that the exponential turnpike behavior persists consistently across scales, providing a unified connection between microscopic, kinetic, and macroscopic optimal control frameworks.
KEYWORDS	Exponential turnpike property, particle system, mean-field limit, hydrodynamic limit, optimal control