Robust output-feedback stabilization for incompressible flows using low-dimensional $\mathcal{H}_{\infty}$-controllers

TL;DR

This paper develops low-dimensional robust output-feedback controllers for stabilizing incompressible flows, addressing high-dimensionality and incompressibility constraints, and demonstrates their effectiveness through numerical examples.

Contribution

It introduces a method to synthesize low-dimensional $ ext{H}_ ext{ extonehalf}$-controllers that guarantee robustness margins for incompressible flow stabilization.

Findings

Controllers maintain stability despite model uncertainties

Reduced-order controllers perform well in numerical simulations

Robustness margins are explicitly guaranteed

Abstract

Output-based controllers are known to be fragile with respect to model uncertainties. The standard $\mathcal{H}_{\infty}$-control theory provides a general approach to robust controller design based on the solution of the $\mathcal{H}_{\infty}$-Riccati equations. In view of stabilizing incompressible flows in simulations, two major challenges have to be addressed: the high-dimensional nature of the spatially discretized model and the differential-algebraic structure that comes with the incompressibility constraint. This work demonstrates the synthesis of low-dimensional robust controllers with guaranteed robustness margins for the stabilization of incompressible flow problems. The performance and the robustness of the reduced-order controller with respect to linearization and model reduction errors are investigated and illustrated in numerical examples.