  We present a data-driven model predictive control (MPC) framework for systems
with high state-space dimensionalities. This work is motivated by the need to
exploit sensor data that appears in the form of images (e.g., 2D or 3D spatial
fields reported by thermal cameras). We propose to use dynamic mode
decomposition (DMD) to directly build a low-dimensional model from image data
and we use such model to obtain a tractable MPC controller. We demonstrate the
scalability of this approach (which we call DMD-MPC) by using a 2D thermal
diffusion system. Here, we assume that the evolution of the thermal field is
captured by 50x50 pixel images, which results in a 2500-dimensional
state-space. We show that the dynamics of this high-dimensional space can be
accurately predicted by using a 40-dimensional DMD model and we show that the
field can be manipulated satisfactorily by using an MPC controller that embeds
the low-dimensional DMD model. We also show that the DMD-MPC controller
significantly outperforms a standard MPC controller that uses data from a
finite set of spatial locations (proxy locations) to manipulate the
high-dimensional thermal field. This comparison illustrates the value of
information embedded in image data.
