We present a data-driven model predictive control (MPC) framework for systems with high state–space dimensionality. 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 captured 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 50 x 50 pixel images, which results in a 2500-dimensional state–space. We show that the dynamics of this high-dimensional space can be accurately captured 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 outperforms a standard MPC controller that uses data collected from a finite set of spatial locations (proxy locations) to manipulate the high-dimensional thermal field. This illustrates the value of information embedded in image data.

我们为具有高状态空间维度的系统提出了数据驱动的模型预测控制 (MPC) 框架。这项工作的动机是需要利用以图像形式出现的传感器数据（例如，由热像仪捕获的 2D 或 3D 空间场）。我们建议使用动态模式分解 (DMD) 直接从图像数据构建低维模型，我们使用这种模型来获得易于处理的 MPC 控制器。我们通过使用 2D 热扩散系统证明了这种方法（我们称之为 DMD-MPC）的可扩展性。在这里，我们假设热场的演变由 50 x 50 像素的图像捕获，从而产生 2500 维的状态空间。我们表明，可以通过使用 40 维 DMD 模型准确捕获该高维空间的动力学，并且表明可以通过使用嵌入低维 DMD 模型的 MPC 控制器来令人满意地操纵该场。我们还表明 DMD-MPC 控制器优于标准 MPC 控制器，该控制器使用从一组有限空间位置（代理位置）收集的数据来操纵高维热场。这说明了嵌入在图像数据中的信息的价值。