Flow control by a hybrid use of machine learning and control theory

Flow control has a great potential to contribute to the sustainable society through mitigation of environmental burden. However, high dimensional and nonlinear nature of fluid flows poses challenges in designing efficient control laws. This paper aims to propose a hybrid method (i.e., machine learning and control theory) for feedback control of fluid flows. We propose a partially nonlinear linear-system extraction autoencoder (pn-LEAE), which consists of convolutional neural networks-based autoencoder (CNN-AE) and a custom layer to extract a low-dimensional latent dynamics. This pn-LEAE basically extracts a linear dynamical system so that the modern control theory can easily be applied, but at the same time, it is designed to capture a nonlinear development of the latent dynamics. We demonstrate the effectiveness of the linear system extracted by the pn-LEAE, as well as the designed control law's effectiveness for a flow around a circular cylinder at the Reynolds number of ${\rm Re}_{D}=100$. This is the first attempt utilizing CNN-AE for linearization of fluid flows involving transient development to design a feedback control law.