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

Peter Benner (), Jan Heiland () and Steffen W. R. Werner ()
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Peter Benner: Max Planck Institute for Dynamics of Complex Technical Systems
Jan Heiland: Max Planck Institute for Dynamics of Complex Technical Systems
Steffen W. R. Werner: Max Planck Institute for Dynamics of Complex Technical Systems

Computational Optimization and Applications, 2022, vol. 82, issue 1, No 9, 225-249

Abstract: Abstract Output-based controllers are known to be fragile with respect to model uncertainties. The standard $$\mathcal {H}_{\infty }$$ H ∞ -control theory provides a general approach to robust controller design based on the solution of the $$\mathcal {H}_{\infty }$$ H ∞ -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.

Keywords: Robust control; Incompressible flows; Stabilizing feedback controller (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10589-022-00359-x

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