Robust output-feedback stabilization for incompressible flows using low-dimensional $$\mathcal {H}_{\infty }$$-controllers
针对不可压缩流模拟中高维模型和微分代数结构带来的挑战，研究如何设计低维鲁棒控制器来镇定流动，并保证鲁棒性边界，数值例子验证了性能。
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.