Co-design of reduced-order models and observers from thermo-fluid data

This paper presents a method of co-design of models and observers for buoyancy-driven turbulent flows. Recent work on data-driven techniques for estimating turbulent flows typically involve obtaining a dynamical model using Dynamical Mode Decomposition (DMD) and using the model to design estimators. Unfortunately, such a sequential design could result in state-space models that do not possess control-theoretic properties (such as detectability) that ensure guaranteed performance of the observer. In this paper, we propose semi-definite programs (SDPs) that allow us to simultaneously construct observer gains, along with DMD models which exhibit desired properties. Since DMD models for turbulent flows are typically high-dimensional, we provide a tractable algorithm for solving the high-dimensional SDP. We demonstrate the potential of our proposed approach on an industrial application using real-world data, and illustrate that the co-design significantly outperforms sequential design.