Dynamic Mode Decomposition and Robust Estimation: Case Study of a 2D Turbulent Boussinesq Flow

This paper focuses on an application of dynamic mode decomposition (DMD) identification methods and robust estimation theory to thermo-fluid systems modelled by the Boussinesq equations. First, we use Dynamic Mode Decomposition with control (DMDc) to construct a reduced order linear model for the Boussinesq equations. Due to inherent model uncertainties in real applications, we propose robust estimators that minimize an ${\mathcal{H}_\infty }$ norm from disturbance to estimation error. The disturbances we consider here stem from uncertainty in boundary conditions and unknown inputs acting on walls. Numerical simulations on a challenging turbulent flow, of the 2D Boussinesq equations, is used to demonstrate the potential of our approach.