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The control of nonlinear large-scale dynamical models such as theincompressible Navier-Stokes equations is a challenging task. The computationalchallenges in the controller design come from both the possibly large statespace and the nonlinear dynamics. A general purpose approach certainly willresort to numerical linear algebra techniques which can handle large systemsizes or to model order reduction. In this work we propose a two-folded modelreduction approach tailored to nonlinear controller design for incompressibleNavier-Stokes equations and similar PDE models that come with quadraticnonlinearities. Firstly, we approximate the nonlinear model within in the classof LPV systems with a very low dimension in the parametrization. Secondly, wereduce the system size to a moderate number of states. This way, standardrobust LPV theory for nonlinear controller design becomes feasible. Weillustrate the procedure and its potentials by numerical simulations.

Low-order Linear Parameter Varying Approximations for Nonlinear Controller Design for Flows