Neural network controllers applied to flow control

We report the application of a novel control approach based on the backpropagation of neural network models of dynamical systems. By leveraging sampled open-loop data, we train black box models with control inputs capable of learning important features from nonlinear systems. A neural network controller (NNC) is trained as a control law in a recurrent approach through backpropagation in closed loop. The methodology is first applied to four low-dimensional nonlinear plants presenting different features such as chaos and limit cycles around different equilibrium types. We also apply NNC to the high-order Kuramoto-Sivashinsky equation so as to attenuate the propagation of convective instabilities. Finally, we apply the technique to a cylinder flow with the goal of reducing the effects of instabilities. Results suggest that NNC presents implementation advantages over gradient based model predictive control due to its lower evaluation cost.