Robust output-feedback stabilization for incompressible flows using low-dimensional $$\mathcal {H}_{\infty }$$-controllers
Peter Benner, Jan Heiland, Steffen W. R. Werner
Abstract
Abstract Output-based controllers are known to be fragile with respect to model uncertainties. The standard $$\mathcal {H}_{\infty }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>H</mml:mi><mml:mi>∞</mml:mi></mml:msub></mml:math> -control theory provides a general approach to robust controller design based on the solution of the $$\mathcal {H}_{\infty }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>H</mml:mi><mml:mi>∞</mml:mi></mml:msub></mml:math> -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.