The design of flow control systems remains a challenge due to the nonlinear nature of the equations that govern fluid flow. However, recent advances in computational fluid dynamics (CFD) have enabled the simulation of complex fluid flows with high accuracy, opening the possibility of using learning-based approaches to facilitate controller design. We present a method for learning the forced and unforced dynamics of airflow over a cylinder directly from CFD data. The proposed approach, grounded in Koopman theory, is shown to produce stable dynamical models that can predict the time evolution of the cylinder system over extended time horizons. Finally, by performing model predictive control with the learned dynamical models, we are able to find a straightforward, interpretable control law for suppressing vortex shedding in the wake of the cylinder.

The dynamics describing such flows are nonlinear, making modeling and control challenging. The approach adopted in this paper is based on spectral analysis of the Koopman operator (a popular approach that has received considerable attention in the literature), which (roughly speaking) models the finite-dimensional nonlinear dynamics with infinite-dimensional linear dynamics. For tractable analysis it is desirable to find a finite-dimensional approximation of these infinite-dimensional dynamics (i.e., a Koopman invariant subspace). The strategy presented in this paper is dynamic mode decomposition (DMD), another popular approach that has received much attention in the literature. The key challenge in DMD is coming up with a basis for the Koopman invariant subspace (i.e., a collection of nonlinear functions referred to as'observables'). Here lies the main contribution of the paper: a data-driven way to learn appropriate observables, where each observable function is modeled by a deep neural network (encoder). The resulting finite-dimensional linear model is then used for control design (standard MPC for linear systems). It is observed that the MPC strategy coincides with proportional feedback (i.e.

The design of flow control systems remains a challenge due to the nonlinear nature of the equations that govern fluid flow. However, recent advances in computational fluid dynamics (CFD) have enabled the simulation of complex fluid flows with high accuracy, opening the possibility of using learning-based approaches to facilitate controller design. We present a method for learning the forced and unforced dynamics of airflow over a cylinder directly from CFD data. The proposed approach, grounded in Koopman theory, is shown to produce stable dynamical models that can predict the time evolution of the cylinder system over extended time horizons. Finally, by performing model predictive control with the learned dynamical models, we are able to find a straightforward, interpretable control law for suppressing vortex shedding in the wake of the cylinder.