  The control of complex systems is of critical importance in many branches of
science, engineering, and industry. Controlling an unsteady fluid flow is
particularly important, as flow control is a key enabler for technologies in
energy (e.g., wind, tidal, and combustion), transportation (e.g., planes,
trains, and automobiles), security (e.g., tracking airborne contamination), and
health (e.g., artificial hearts and artificial respiration). However, the
high-dimensional, nonlinear, and multi-scale dynamics make real-time feedback
control infeasible. Fortunately, these high-dimensional systems exhibit
dominant, low-dimensional patterns of activity that can be exploited for
effective control in the sense that knowledge of the entire state of a system
is not required. Advances in machine learning have the potential to
revolutionize flow control given its ability to extract principled, low-rank
feature spaces characterizing such complex systems. We present a novel deep
learning model predictive control (DeepMPC) framework that exploits low-rank
features of the flow in order to achieve considerable improvements to control
performance. Instead of predicting the entire fluid state, we use a recurrent
neural network (RNN) to accurately predict the control relevant quantities of
the system. The RNN is then embedded into a MPC framework to construct a
feedback loop, and incoming sensor data is used to perform online updates to
improve prediction accuracy. The results are validated using varying fluid flow
examples of increasing complexity.
