Characterizing the Predictive Accuracy of Dynamic Mode Decomposition for Data-Driven Control

Abstract

Dynamic mode decomposition (DMD) is a versatile approach that enables the construction of low-order models from data. Controller design tasks based on such models require estimates and guarantees on predictive accuracy. In this work, we provide a theoretical analysis of DMD model errors that reveals impacts of model order and data availability. The analysis also establishes conditions under which DMD models can be made asymptotically exact. We numerically validate our theoretical results using a 2D diffusion system.