Reduced Order Control using Low-Rank Dynamic Mode Decomposition

In this work we present a non-intrusive data-driven method for reduced order modeling of fluid flows using a low-rank Dynamic Mode Decomposition (lr-DMD). A non-convex matrix optimization problem is formulated and two methods of solving it are discussed along with variants for high-dimensional flows. It is a generalization of Optimal Mode Decomposition (OMD) and Dynamic Mode Decomposition (DMD), and is shown to give lower residual errors in comparison for a given rank of the low-order model. We perform model order reduction on the complex linearized Ginzburg-Landau equation in the globally unstable regime and unsteady flow over flat plate at an high angle of attack. A low-dimensional controller is then constructed using the reduced order model. We compare the performance of controllers constructed using DMD, OMD and lr-DMD.