Control-Informed Dynamic Mode Decomposition

Dynamic mode decomposition (DMD) is a data-driven system identification and model reduction technique. In some situations, the data used as an input to DMD poorly represents the dynamics of the system, often when the data are used for controller development. This insufficient data set results in a reduced-order model which also poorly captures the desired dynamics. In order to enrich the data set, we apply a control to our system. This control is designed to illicit a more complete and representative response from the data which can then be used to create a more robust DMD model. We use the adjoint method to create a such a control. The control is chosen to minimize a cost functional designed to fit the desired data to the control-informed DMD-reconstruction of the data. The method is demonstrated on the Ginzburg-Landau equation.