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Flow control has a great potential to contribute to a sustainable society through mitigation of environmental burden. However, the high dimensional and nonlinear nature of fluid flows poses challenges in designing efficient control laws using the control theory. This paper aims to propose a hybrid method (i.e. machine learning and control theory) for feedback control of fluid flows, by which the flow is mapped to the latent space in such a way that the linear control theory can be applied therein.

The authors 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 low-dimensional latent dynamics from fluid velocity field data. This pn-LEAE is designed to extract a linear dynamical system so that the modern control theory can easily be applied, while a nonlinear compression is done with the autoencoder (AE) part so that the latent dynamics conform to that linear system. The key technique is to train this pn-LEAE with the ground truths at two consecutive time instants, whereby the AE part retains its capability as the AE, and the weights in the linear dynamical system are trained simultaneously.

The authors 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 Re_D = 100. When the control law derived in the latent space was applied to the direct numerical simulation, the lift fluctuations were suppressed over 50%.

To the best of the authors’ knowledge, this is the first attempt using CNN-AE for linearization of fluid flows involving transient development to design a feedback control law.