489	RWTH Publication No: 755996        2019        IGPM489.pdf
TITLE	Consistent mean field optimality conditions for interacting agent systems
AUTHORS	Michael Herty, Christian Ringhofer
ABSTRACT	We are interested in the derivation of optimality conditions for controlled interacting agent systems. We establish the relation between mean field optimality conditions and the optimality condition of the mean field control problem. This link is important for many recently published articles on control strategies for agent based systems since it establishes the precise relation between multipliers for the individual agents and the probability density distribution of the multipliers in the mean field limit. The relation to different notions of differentiability are also shown.
KEYWORDS	Kinetic Equations, Particle Systems, Optimal Control, Meanfield Limits
DOI	10.4310/CMS.2019.v17.n4.a12
PUBLICATION	Communications in Mathematical Sciences 2019, Volume 17, Number 4, pp 1095 – 1108