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

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.

20 pages, 4 figures, 3 tables

References in corpus (2)

• Example Setups of Navier-Stokes Equations with Control and Observation: Spatial Discretization and Representation via Linear-quadratic Matrix Coefficients
• A low-rank solution method for Riccati equations with indefinite quadratic terms

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• Multi-fidelity robust controller design with gradient sampling
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