Robust Reduced-Order Model Stabilization for Partial Differential Equations Based on Lyapunov Theory and Extremum Seeking with Application to the 3D Boussinesq Equations

Abstract

We present some results on stabilization for reduced-order models (ROMs) of partial differential equations. The stabilization is achieved using Lyapunov theory to design a new closure model that is robust to parametric uncertainties. The free parameters in the proposed ROM stabilization method are optimized using a model-free multi-parametric extremum seeking (MES) algorithm. The 3D Boussinesq equations provide a challenging numerical test-problem that is used to demonstrate the advantages of the proposed method.