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Convergence of coprime factor perturbations for robust stabilization of Oseen systems
Jan Heiland ,
Max Planck Institute for Dynamics of, Complex Technical Systems and OVGU Magdeburg, 39106 Magdeburg, Germany
* Corresponding author: Jan Heiland
Received September 2019 Revised February 2021 Early access September 2021
Fund Project: This article was recruited by Andrii Mironchenko
Figure(1)
Linearization based controllers for incompressible flows have been proven to work in theory and in simulations. To realize such a controller numerically, the infinite dimensional system has to be linearized and discretized. The unavoidable consistency errors add a small but critical uncertainty to the controller model which will likely make it fail, especially when an observer is involved. Standard robust controller designs can compensate small uncertainties if they can be qualified as a coprime factor perturbation of the plant. We show that for the linearized Navier-Stokes equations, a linearization error can be expressed as a coprime factor perturbation and that this perturbation smoothly depends on the size of the linearization error. In particular, improving the linearization makes the perturbation smaller so that, eventually, standard robust controller will stabilize the system.
Keywords: Robust control, descriptor systems, parameter-varying systems, output feedback control, infinite-dimensional systems.
Mathematics Subject Classification: Primary: 93B52, 35Q30; Secondary: 93C73.
Citation: Jan Heiland. Convergence of coprime factor perturbations for robust stabilization of Oseen systems. Mathematical Control & Related Fields, doi: 10.3934/mcrf.2021043
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Figure 1. Computational domain of the cylinder wake
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Jan Heiland