  The ability to manipulate and control fluid flows is of great importance in
many scientific and engineering applications. Here, a cluster-based control
framework is proposed to determine optimal control laws with respect to a cost
function for unsteady flows. The proposed methodology frames high-dimensional,
nonlinear dynamics into low-dimensional, probabilistic, linear dynamics which
considerably simplifies the optimal control problem while preserving nonlinear
actuation mechanisms. The data-driven approach builds upon a state space
discretization using a clustering algorithm which groups kinematically similar
flow states into a low number of clusters. The temporal evolution of the
probability distribution on this set of clusters is then described by a Markov
model. The Markov model can be used as predictor for the ergodic probability
distribution for a particular control law. This probability distribution
approximates the long-term behavior of the original system on which basis the
optimal control law is determined. The approach is applied to a separating flow
dominated by the Kelvin-Helmholtz shedding.
