On-line Mode Decomposition of Fluid Flows Using Moving Horizon Estimation

The on-line analysis and monitoring of a turbulent flow across a channel is really important in a number of applications. Unfortunately, such a problem is difficult to address since the flow is governed by the Navier-Stokes equation. Dynamic mode decomposition is usually adopted to analyze such flows via the on-line identification of local linear approximations of spatio-temporal dynamics of the flow velocities, i.e., the square matrix of a linear system. We propose a new approach to mode decomposition based on moving horizon estimation by providing a rigorous proof of stability for the estimation error. Moreover, we address the problem of computing the distance of a given estimated matrix to stability or instability. Such information is important to measure the "degree" of stability/instability for the purpose of control. Numerical results obtained with an experimental dataset are presented and discussed.