This talk is devoted to the formulation of ensemble optimal control problems governed by kinetic models. The starting point for this presentation is the Liouville equation, which is the fundamental building block of models that govern the evolution of probability and material density functions like the Fokker-Planck equation and the Boltzmann equation. In this framework, optimal control problems arise in a multitude of application fields ranging from plasma physics to pedestrians’ motion, where it is required to design control mechanisms that are able to drive the underlying stochastic process or microscopic system in order to perform given tasks. It is shown that many of these tasks can be formulated in terms of ensemble (expected value) cost functionals. It is also illustrated how ensemble cost functionals allow to draw a connection between open-loop Fokker-Planck control problems and Hamilton-Jacobi-Bellman problems arising in the computation of closed-loop controls. The talk is concluded with a brief discussion on Fokker-Planck Nash games for modelling the avoidance problem in, e.g., pedestrian motion.
This video was produced by the SITE Research Center at New York University, as part of their talk series.
