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The control of complex systems is of critical importance in many branches ofscience, engineering, and industry. Controlling an unsteady fluid flow isparticularly important, as flow control is a key enabler for technologies inenergy (e.g., wind, tidal, and combustion), transportation (e.g., planes,trains, and automobiles), security (e.g., tracking airborne contamination), andhealth (e.g., artificial hearts and artificial respiration). However, thehigh-dimensional, nonlinear, and multi-scale dynamics make real-time feedbackcontrol infeasible. Fortunately, these high-dimensional systems exhibitdominant, low-dimensional patterns of activity that can be exploited foreffective control in the sense that knowledge of the entire state of a systemis not required. Advances in machine learning have the potential torevolutionize flow control given its ability to extract principled, low-rankfeature spaces characterizing such complex systems. We present a novel deeplearning model predictive control (DeepMPC) framework that exploits low-rankfeatures of the flow in order to achieve considerable improvements to controlperformance. Instead of predicting the entire fluid state, we use a recurrentneural network (RNN) to accurately predict the control relevant quantities ofthe system. The RNN is then embedded into a MPC framework to construct afeedback loop, and incoming sensor data is used to perform online updates toimprove prediction accuracy. The results are validated using varying fluid flowexamples of increasing complexity.

Deep Model Predictive Control with Online Learning for Complex Physical Systems